initial commit, 4.5 stable

thirdparty/embree/kernels/subdiv/bezier_curve.h

@@ -0,0 +1,729 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "../common/default.h"
+//#include "../common/scene_curves.h"
+#include "../common/context.h"
+
+namespace embree
+{
+  class BezierBasis
+  {
+  public:
+
+    template<typename T>
+      static __forceinline Vec4<T> eval(const T& u) 
+    {
+      const T t1 = u;
+      const T t0 = 1.0f-t1;
+      const T B0 = t0 * t0 * t0;
+      const T B1 = 3.0f * t1 * (t0 * t0);
+      const T B2 = 3.0f * (t1 * t1) * t0;
+      const T B3 = t1 * t1 * t1;
+      return Vec4<T>(B0,B1,B2,B3);
+    }
+    
+    template<typename T>
+      static __forceinline Vec4<T>  derivative(const T& u)
+    {
+      const T t1 = u;
+      const T t0 = 1.0f-t1;
+      const T B0 = -(t0*t0);
+      const T B1 = madd(-2.0f,t0*t1,t0*t0);
+      const T B2 = msub(+2.0f,t0*t1,t1*t1);
+      const T B3 = +(t1*t1);
+      return T(3.0f)*Vec4<T>(B0,B1,B2,B3);
+    }
+
+    template<typename T>
+      static __forceinline Vec4<T>  derivative2(const T& u)
+    {
+      const T t1 = u;
+      const T t0 = 1.0f-t1;
+      const T B0 = t0;
+      const T B1 = madd(-2.0f,t0,t1);
+      const T B2 = madd(-2.0f,t1,t0);
+      const T B3 = t1;
+      return T(6.0f)*Vec4<T>(B0,B1,B2,B3);
+    }
+  };
+  
+  struct PrecomputedBezierBasis
+  {
+    enum { N = 16 };
+  public:
+    PrecomputedBezierBasis() {}
+    PrecomputedBezierBasis(int shift);
+
+    /* basis for bezier evaluation */
+  public:
+    float c0[N+1][N+1];
+    float c1[N+1][N+1];
+    float c2[N+1][N+1];
+    float c3[N+1][N+1];
+    
+    /* basis for bezier derivative evaluation */
+  public:
+    float d0[N+1][N+1];
+    float d1[N+1][N+1];
+    float d2[N+1][N+1];
+    float d3[N+1][N+1];
+  };
+  extern PrecomputedBezierBasis bezier_basis0;
+  extern PrecomputedBezierBasis bezier_basis1;
+
+  
+  template<typename V>
+    struct LinearBezierCurve
+    {
+      V v0,v1;
+      
+      __forceinline LinearBezierCurve () {}
+      
+      __forceinline LinearBezierCurve (const LinearBezierCurve& other)
+        : v0(other.v0), v1(other.v1) {}
+      
+      __forceinline LinearBezierCurve& operator= (const LinearBezierCurve& other) {
+        v0 = other.v0; v1 = other.v1; return *this;
+      }
+        
+        __forceinline LinearBezierCurve (const V& v0, const V& v1)
+          : v0(v0), v1(v1) {}
+      
+      __forceinline V begin() const { return v0; }
+      __forceinline V end  () const { return v1; }
+      
+      bool hasRoot() const;
+      
+      friend embree_ostream operator<<(embree_ostream cout, const LinearBezierCurve& a) {
+        return cout << "LinearBezierCurve (" << a.v0 << ", " << a.v1 << ")";
+      }
+    };
+  
+  template<> __forceinline bool LinearBezierCurve<Interval1f>::hasRoot() const {
+    return numRoots(v0,v1);
+  }
+  
+  template<typename V>
+    struct QuadraticBezierCurve
+    {
+      V v0,v1,v2;
+      
+      __forceinline QuadraticBezierCurve () {}
+      
+      __forceinline QuadraticBezierCurve (const QuadraticBezierCurve& other)
+        : v0(other.v0), v1(other.v1), v2(other.v2) {}
+      
+      __forceinline QuadraticBezierCurve& operator= (const QuadraticBezierCurve& other) {
+        v0 = other.v0; v1 = other.v1; v2 = other.v2; return *this;
+      }
+        
+        __forceinline QuadraticBezierCurve (const V& v0, const V& v1, const V& v2)
+          : v0(v0), v1(v1), v2(v2) {}
+      
+      __forceinline V begin() const { return v0; }
+      __forceinline V end  () const { return v2; }
+      
+      __forceinline V interval() const {
+        return merge(v0,v1,v2);
+      }
+      
+      __forceinline BBox<V> bounds() const {
+        return merge(BBox<V>(v0),BBox<V>(v1),BBox<V>(v2));
+      }
+      
+      friend embree_ostream operator<<(embree_ostream cout, const QuadraticBezierCurve& a) {
+        return cout << "QuadraticBezierCurve (" << a.v0 << ", " << a.v1 << ", " << a.v2 << ")";
+      }
+    };
+  
+  
+  typedef QuadraticBezierCurve<float> QuadraticBezierCurve1f;
+  typedef QuadraticBezierCurve<Vec2fa> QuadraticBezierCurve2fa;
+  typedef QuadraticBezierCurve<Vec3fa> QuadraticBezierCurve3fa;
+
+  template<typename Vertex>
+    struct CubicBezierCurve
+    {
+      Vertex v0,v1,v2,v3;
+      
+      __forceinline CubicBezierCurve() {}
+
+      template<typename T1>
+      __forceinline CubicBezierCurve (const CubicBezierCurve<T1>& other)
+      : v0(other.v0), v1(other.v1), v2(other.v2), v3(other.v3) {}
+      
+      __forceinline CubicBezierCurve& operator= (const CubicBezierCurve& other) {
+        v0 = other.v0; v1 = other.v1; v2 = other.v2; v3 = other.v3; return *this;
+      }
+      
+      __forceinline CubicBezierCurve(const Vertex& v0, const Vertex& v1, const Vertex& v2, const Vertex& v3)
+        : v0(v0), v1(v1), v2(v2), v3(v3) {}
+
+      __forceinline Vertex begin() const {
+        return v0;
+      }
+
+      __forceinline Vertex end() const {
+        return v3;
+      }
+
+      __forceinline Vertex center() const {
+        return 0.25f*(v0+v1+v2+v3);
+      }
+
+      __forceinline Vertex begin_direction() const {
+        return v1-v0;
+      }
+
+      __forceinline Vertex end_direction() const {
+        return v3-v2;
+      }
+
+      __forceinline CubicBezierCurve<float> xfm(const Vertex& dx) const {
+        return CubicBezierCurve<float>(dot(v0,dx),dot(v1,dx),dot(v2,dx),dot(v3,dx));
+      }
+
+      template<int W>
+      __forceinline CubicBezierCurve<vfloat<W>> vxfm(const Vertex& dx) const {
+        return CubicBezierCurve<vfloat<W>>(dot(v0,dx),dot(v1,dx),dot(v2,dx),dot(v3,dx));
+      }
+      
+      __forceinline CubicBezierCurve<float> xfm(const Vertex& dx, const Vertex& p) const {
+        return CubicBezierCurve<float>(dot(v0-p,dx),dot(v1-p,dx),dot(v2-p,dx),dot(v3-p,dx));
+      }
+
+       __forceinline CubicBezierCurve<Vec3fa> xfm(const LinearSpace3fa& space) const
+      {
+        const Vec3fa q0 = xfmVector(space,v0);
+        const Vec3fa q1 = xfmVector(space,v1);
+        const Vec3fa q2 = xfmVector(space,v2);
+        const Vec3fa q3 = xfmVector(space,v3);
+        return CubicBezierCurve<Vec3fa>(q0,q1,q2,q3);
+      }
+      
+      __forceinline CubicBezierCurve<Vec3fa> xfm(const LinearSpace3fa& space, const Vec3fa& p) const
+      {
+        const Vec3fa q0 = xfmVector(space,v0-p);
+        const Vec3fa q1 = xfmVector(space,v1-p);
+        const Vec3fa q2 = xfmVector(space,v2-p);
+        const Vec3fa q3 = xfmVector(space,v3-p);
+        return CubicBezierCurve<Vec3fa>(q0,q1,q2,q3);
+      }
+
+      __forceinline CubicBezierCurve<Vec3ff> xfm_pr(const LinearSpace3fa& space, const Vec3fa& p) const
+      {
+        const Vec3ff q0(xfmVector(space,(Vec3fa)v0-p), v0.w);
+        const Vec3ff q1(xfmVector(space,(Vec3fa)v1-p), v1.w);
+        const Vec3ff q2(xfmVector(space,(Vec3fa)v2-p), v2.w);
+        const Vec3ff q3(xfmVector(space,(Vec3fa)v3-p), v3.w);
+        return CubicBezierCurve<Vec3ff>(q0,q1,q2,q3);
+      }
+
+      __forceinline CubicBezierCurve<Vec3fa> xfm(const LinearSpace3fa& space, const Vec3fa& p, const float s) const
+      {
+        const Vec3fa q0 = xfmVector(space,s*(v0-p));
+        const Vec3fa q1 = xfmVector(space,s*(v1-p));
+        const Vec3fa q2 = xfmVector(space,s*(v2-p));
+        const Vec3fa q3 = xfmVector(space,s*(v3-p));
+        return CubicBezierCurve<Vec3fa>(q0,q1,q2,q3);
+      }
+      
+      __forceinline int maxRoots() const;
+      
+      __forceinline BBox<Vertex> bounds() const {
+        return merge(BBox<Vertex>(v0),BBox<Vertex>(v1),BBox<Vertex>(v2),BBox<Vertex>(v3));
+      }
+      
+      __forceinline friend CubicBezierCurve operator +( const CubicBezierCurve& a, const CubicBezierCurve& b ) {
+        return CubicBezierCurve(a.v0+b.v0,a.v1+b.v1,a.v2+b.v2,a.v3+b.v3);
+      }
+      
+      __forceinline friend CubicBezierCurve operator -( const CubicBezierCurve& a, const CubicBezierCurve& b ) {
+        return CubicBezierCurve(a.v0-b.v0,a.v1-b.v1,a.v2-b.v2,a.v3-b.v3);
+      }
+      
+      __forceinline friend CubicBezierCurve operator -( const CubicBezierCurve& a, const Vertex& b ) {
+        return CubicBezierCurve(a.v0-b,a.v1-b,a.v2-b,a.v3-b);
+      }
+      
+      __forceinline friend CubicBezierCurve operator *( const Vertex& a, const CubicBezierCurve& b ) {
+        return CubicBezierCurve(a*b.v0,a*b.v1,a*b.v2,a*b.v3);
+      }
+
+      __forceinline friend CubicBezierCurve cmadd( const Vertex& a, const CubicBezierCurve& b,  const CubicBezierCurve& c) {
+        return CubicBezierCurve(madd(a,b.v0,c.v0),madd(a,b.v1,c.v1),madd(a,b.v2,c.v2),madd(a,b.v3,c.v3));
+      }
+      
+      __forceinline friend CubicBezierCurve clerp ( const CubicBezierCurve& a, const CubicBezierCurve& b, const Vertex& t ) {
+        return cmadd((Vertex(1.0f)-t),a,t*b);
+      }
+      
+      __forceinline friend CubicBezierCurve merge ( const CubicBezierCurve& a, const CubicBezierCurve& b ) {
+        return CubicBezierCurve(merge(a.v0,b.v0),merge(a.v1,b.v1),merge(a.v2,b.v2),merge(a.v3,b.v3));
+      }
+      
+      __forceinline void split(CubicBezierCurve& left, CubicBezierCurve& right, const float t = 0.5f) const
+      {
+        const Vertex p00 = v0;
+        const Vertex p01 = v1;
+        const Vertex p02 = v2;
+        const Vertex p03 = v3;
+        
+        const Vertex p10 = lerp(p00,p01,t);
+        const Vertex p11 = lerp(p01,p02,t);
+        const Vertex p12 = lerp(p02,p03,t);
+        const Vertex p20 = lerp(p10,p11,t);
+        const Vertex p21 = lerp(p11,p12,t);
+        const Vertex p30 = lerp(p20,p21,t);
+        
+        new (&left ) CubicBezierCurve(p00,p10,p20,p30);
+        new (&right) CubicBezierCurve(p30,p21,p12,p03);
+      }
+      
+      __forceinline CubicBezierCurve<Vec2vfx> split() const
+      {
+        const float u0 = 0.0f, u1 = 1.0f;
+        const float dscale = (u1-u0)*(1.0f/(3.0f*(VSIZEX-1)));
+        const vfloatx vu0 = lerp(u0,u1,vfloatx(StepTy())*(1.0f/(VSIZEX-1)));
+        Vec2vfx P0, dP0du; evalN(vu0,P0,dP0du); dP0du = dP0du * Vec2vfx(dscale);
+        const Vec2vfx P3 = shift_right_1(P0);
+        const Vec2vfx dP3du = shift_right_1(dP0du); 
+        const Vec2vfx P1 = P0 + dP0du; 
+        const Vec2vfx P2 = P3 - dP3du;
+        return CubicBezierCurve<Vec2vfx>(P0,P1,P2,P3);
+      }
+      
+      __forceinline CubicBezierCurve<Vec2vfx> split(const BBox1f& u) const
+      {
+        const float u0 = u.lower, u1 = u.upper;
+        const float dscale = (u1-u0)*(1.0f/(3.0f*(VSIZEX-1)));
+        const vfloatx vu0 = lerp(u0,u1,vfloatx(StepTy())*(1.0f/(VSIZEX-1)));
+        Vec2vfx P0, dP0du; evalN(vu0,P0,dP0du); dP0du = dP0du * Vec2vfx(dscale);
+        const Vec2vfx P3 = shift_right_1(P0);
+        const Vec2vfx dP3du = shift_right_1(dP0du); 
+        const Vec2vfx P1 = P0 + dP0du; 
+        const Vec2vfx P2 = P3 - dP3du;
+        return CubicBezierCurve<Vec2vfx>(P0,P1,P2,P3);
+      }
+
+      template<int W>
+      __forceinline CubicBezierCurve<Vec2vf<W>> split(const BBox1f& u, int i, int N) const
+      {
+        const float u0 = u.lower, u1 = u.upper;
+        const float dscale = (u1-u0)*(1.0f/(3.0f*N));
+        const vfloat<W> vu0 = lerp(u0,u1,(vfloat<W>(i)+vfloat<W>(StepTy()))*(1.0f/N));
+        Vec2vf<W> P0, dP0du; evalN(vu0,P0,dP0du); dP0du = dP0du * Vec2vf<W>(dscale);
+        const Vec2vf<W> P3 = shift_right_1(P0);
+        const Vec2vf<W> dP3du = shift_right_1(dP0du); 
+        const Vec2vf<W> P1 = P0 + dP0du; 
+        const Vec2vf<W> P2 = P3 - dP3du;
+        return CubicBezierCurve<Vec2vf<W>>(P0,P1,P2,P3);
+      }
+
+       __forceinline CubicBezierCurve<Vec2f> split1(const BBox1f& u, int i, int N) const
+      {
+        const float u0 = u.lower, u1 = u.upper;
+        const float dscale = (u1-u0)*(1.0f/(3.0f*N));
+        const float vu0 = lerp(u0,u1,(float(i)+0)*(1.0f/N));
+        const float vu1 = lerp(u0,u1,(float(i)+1)*(1.0f/N));
+        Vec2fa P0, dP0du; eval(vu0,P0,dP0du); dP0du = dP0du * Vec2fa(dscale);
+        Vec2fa P3, dP3du; eval(vu1,P3,dP3du); dP3du = dP3du * Vec2fa(dscale);
+        const Vec2fa P1 = P0 + dP0du; 
+        const Vec2fa P2 = P3 - dP3du;
+        return CubicBezierCurve<Vec2f>(P0,P1,P2,P3);
+      }
+      
+      __forceinline void eval(float t, Vertex& p, Vertex& dp) const
+      {
+        const Vertex p00 = v0;
+        const Vertex p01 = v1;
+        const Vertex p02 = v2;
+        const Vertex p03 = v3;
+        
+        const Vertex p10 = lerp(p00,p01,t);
+        const Vertex p11 = lerp(p01,p02,t);
+        const Vertex p12 = lerp(p02,p03,t);
+        const Vertex p20 = lerp(p10,p11,t);
+        const Vertex p21 = lerp(p11,p12,t);
+        const Vertex p30 = lerp(p20,p21,t);
+        
+        p = p30;
+        dp = Vertex(3.0f)*(p21-p20);
+      }
+
+#if 0
+      __forceinline Vertex eval(float t) const
+      {
+        const Vertex p00 = v0;
+        const Vertex p01 = v1;
+        const Vertex p02 = v2;
+        const Vertex p03 = v3;
+        
+        const Vertex p10 = lerp(p00,p01,t);
+        const Vertex p11 = lerp(p01,p02,t);
+        const Vertex p12 = lerp(p02,p03,t);
+        const Vertex p20 = lerp(p10,p11,t);
+        const Vertex p21 = lerp(p11,p12,t);
+        const Vertex p30 = lerp(p20,p21,t);
+        
+        return p30;
+      }
+#else
+      __forceinline Vertex eval(const float t) const 
+      {
+        const Vec4<float> b = BezierBasis::eval(t);
+        return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
+      }
+#endif
+      
+      __forceinline Vertex eval_dt(float t) const
+      {
+        const Vertex p00 = v1-v0;
+        const Vertex p01 = v2-v1;
+        const Vertex p02 = v3-v2;
+        const Vertex p10 = lerp(p00,p01,t);
+        const Vertex p11 = lerp(p01,p02,t);
+        const Vertex p20 = lerp(p10,p11,t);
+        return Vertex(3.0f)*p20;
+      }
+
+      __forceinline Vertex eval_du(const float t) const
+      {
+        const Vec4<float> b = BezierBasis::derivative(t);
+        return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
+      }
+
+      __forceinline Vertex eval_dudu(const float t) const 
+      {
+        const Vec4<float> b = BezierBasis::derivative2(t);
+        return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
+      }
+      
+      __forceinline void evalN(const vfloatx& t, Vec2vfx& p, Vec2vfx& dp) const
+      {
+        const Vec2vfx p00 = v0;
+        const Vec2vfx p01 = v1;
+        const Vec2vfx p02 = v2;
+        const Vec2vfx p03 = v3;
+        
+        const Vec2vfx p10 = lerp(p00,p01,t);
+        const Vec2vfx p11 = lerp(p01,p02,t);
+        const Vec2vfx p12 = lerp(p02,p03,t);
+        
+        const Vec2vfx p20 = lerp(p10,p11,t);
+        const Vec2vfx p21 = lerp(p11,p12,t);
+        
+        const Vec2vfx p30 = lerp(p20,p21,t);
+        
+        p = p30;
+        dp = vfloatx(3.0f)*(p21-p20);
+      }
+
+      __forceinline void eval(const float t, Vertex& p, Vertex& dp, Vertex& ddp) const
+      {
+        const Vertex p00 = v0;
+        const Vertex p01 = v1;
+        const Vertex p02 = v2;
+        const Vertex p03 = v3;
+        const Vertex p10 = lerp(p00,p01,t);
+        const Vertex p11 = lerp(p01,p02,t);
+        const Vertex p12 = lerp(p02,p03,t);
+        const Vertex p20 = lerp(p10,p11,t);
+        const Vertex p21 = lerp(p11,p12,t);
+        const Vertex p30 = lerp(p20,p21,t);
+        p = p30;
+        dp = 3.0f*(p21-p20);
+        ddp = eval_dudu(t);
+      }
+      
+      __forceinline CubicBezierCurve clip(const Interval1f& u1) const
+      {
+        Vertex f0,df0; eval(u1.lower,f0,df0);
+        Vertex f1,df1; eval(u1.upper,f1,df1);
+        float s = u1.upper-u1.lower;
+        return CubicBezierCurve(f0,f0+s*(1.0f/3.0f)*df0,f1-s*(1.0f/3.0f)*df1,f1);
+      }
+      
+      __forceinline QuadraticBezierCurve<Vertex> derivative() const
+      {
+        const Vertex q0 = 3.0f*(v1-v0);
+        const Vertex q1 = 3.0f*(v2-v1);
+        const Vertex q2 = 3.0f*(v3-v2);
+        return QuadraticBezierCurve<Vertex>(q0,q1,q2);
+      }
+      
+      __forceinline BBox<Vertex> derivative_bounds(const Interval1f& u1) const
+      {
+        Vertex f0,df0; eval(u1.lower,f0,df0);
+        Vertex f3,df3; eval(u1.upper,f3,df3);
+        const float s = u1.upper-u1.lower;
+        const Vertex f1 = f0+s*(1.0f/3.0f)*df0;
+        const Vertex f2 = f3-s*(1.0f/3.0f)*df3;
+        const Vertex q0 = s*df0;
+        const Vertex q1 = 3.0f*(f2-f1);
+        const Vertex q2 = s*df3;
+        return merge(BBox<Vertex>(q0),BBox<Vertex>(q1),BBox<Vertex>(q2));
+      }
+      
+      template<int M>
+      __forceinline Vec4vf<M> veval(const vfloat<M>& t) const 
+      {
+        const Vec4vf<M> b = BezierBasis::eval(t);
+        return madd(b.x, Vec4vf<M>(v0), madd(b.y, Vec4vf<M>(v1), madd(b.z, Vec4vf<M>(v2), b.w * Vec4vf<M>(v3))));
+      }
+
+      template<int M>
+      __forceinline Vec4vf<M> veval_du(const vfloat<M>& t) const 
+      {
+        const Vec4vf<M> b = BezierBasis::derivative(t);
+        return madd(b.x, Vec4vf<M>(v0), madd(b.y, Vec4vf<M>(v1), madd(b.z, Vec4vf<M>(v2), b.w * Vec4vf<M>(v3))));
+      }
+
+      template<int M>
+      __forceinline Vec4vf<M> veval_dudu(const vfloat<M>& t) const 
+      {
+        const Vec4vf<M> b = BezierBasis::derivative2(t);
+        return madd(b.x, Vec4vf<M>(v0), madd(b.y, Vec4vf<M>(v1), madd(b.z, Vec4vf<M>(v2), b.w * Vec4vf<M>(v3))));
+      }
+      
+      template<int M, typename Vec>
+      __forceinline void veval(const vfloat<M>& t, Vec& p, Vec& dp) const
+      {
+        const Vec p00 = v0;
+        const Vec p01 = v1;
+        const Vec p02 = v2;
+        const Vec p03 = v3;
+        
+        const Vec p10 = lerp(p00,p01,t);
+        const Vec p11 = lerp(p01,p02,t);
+        const Vec p12 = lerp(p02,p03,t);
+        const Vec p20 = lerp(p10,p11,t);
+        const Vec p21 = lerp(p11,p12,t);
+        const Vec p30 = lerp(p20,p21,t);
+        
+        p = p30;
+        dp = vfloat<M>(3.0f)*(p21-p20);
+      }
+      
+      template<int M, typename Vec = Vec4vf<M>>
+      __forceinline Vec eval0(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedBezierBasis::N);
+        assert(ofs <= size);
+#if defined(EMBREE_SYCL_SUPPORT) && defined(__SYCL_DEVICE_ONLY__)
+        assert(size > 0);
+        const vfloat<M> t = (vfloat<M>(step) + vfloat<M>(ofs+0))*rcp(float(size));
+        Vec p,dp; veval<M>(t,p,dp);
+        return p;
+#else
+        return madd(vfloat<M>::loadu(&bezier_basis0.c0[size][ofs]), Vec(v0),
+                    madd(vfloat<M>::loadu(&bezier_basis0.c1[size][ofs]), Vec(v1),
+                         madd(vfloat<M>::loadu(&bezier_basis0.c2[size][ofs]), Vec(v2),
+                              vfloat<M>::loadu(&bezier_basis0.c3[size][ofs]) * Vec(v3))));
+#endif
+      }
+      
+      template<int M, typename Vec = Vec4vf<M>>
+      __forceinline Vec eval1(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedBezierBasis::N);
+        assert(ofs <= size);
+#if defined(EMBREE_SYCL_SUPPORT) && defined(__SYCL_DEVICE_ONLY__)
+        assert(size > 0);
+        const vfloat<M> t = (vfloat<M>(step) + vfloat<M>(ofs+1))*rcp(float(size));
+        Vec p,dp; veval<M>(t,p,dp);
+        return p;
+#else
+        return madd(vfloat<M>::loadu(&bezier_basis1.c0[size][ofs]), Vec(v0), 
+                    madd(vfloat<M>::loadu(&bezier_basis1.c1[size][ofs]), Vec(v1),
+                         madd(vfloat<M>::loadu(&bezier_basis1.c2[size][ofs]), Vec(v2),
+                              vfloat<M>::loadu(&bezier_basis1.c3[size][ofs]) * Vec(v3))));
+#endif
+      }
+      
+      template<int M, typename Vec = Vec4vf<M>>
+      __forceinline Vec derivative0(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedBezierBasis::N);
+        assert(ofs <= size);
+#if defined(EMBREE_SYCL_SUPPORT) && defined(__SYCL_DEVICE_ONLY__)
+        assert(size > 0);
+        const vfloat<M> t = (vfloat<M>(step) + vfloat<M>(ofs+0))*rcp(float(size));
+        Vec p,dp; veval<M>(t,p,dp);
+        return dp;
+#else
+        return madd(vfloat<M>::loadu(&bezier_basis0.d0[size][ofs]), Vec(v0),
+                    madd(vfloat<M>::loadu(&bezier_basis0.d1[size][ofs]), Vec(v1),
+                         madd(vfloat<M>::loadu(&bezier_basis0.d2[size][ofs]), Vec(v2),
+                              vfloat<M>::loadu(&bezier_basis0.d3[size][ofs]) * Vec(v3))));
+#endif
+      }
+      
+      template<int M, typename Vec = Vec4vf<M>>
+      __forceinline Vec derivative1(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedBezierBasis::N);
+        assert(ofs <= size);
+#if defined(EMBREE_SYCL_SUPPORT) && defined(__SYCL_DEVICE_ONLY__)
+        assert(size > 0);
+        const vfloat<M> t = (vfloat<M>(step) + vfloat<M>(ofs+1))*rcp(float(size));
+        Vec p,dp; veval<M>(t,p,dp);
+        return dp;
+#else
+        return madd(vfloat<M>::loadu(&bezier_basis1.d0[size][ofs]), Vec(v0),
+                    madd(vfloat<M>::loadu(&bezier_basis1.d1[size][ofs]), Vec(v1),
+                         madd(vfloat<M>::loadu(&bezier_basis1.d2[size][ofs]), Vec(v2),
+                              vfloat<M>::loadu(&bezier_basis1.d3[size][ofs]) * Vec(v3))));
+#endif
+      }
+
+      /* calculates bounds of bezier curve geometry */
+      __forceinline BBox3fa accurateBounds() const
+      {
+        const int N = 7;
+        const float scale = 1.0f/(3.0f*(N-1));
+        Vec3vfx pl(pos_inf), pu(neg_inf);
+        for (int i=0; i<=N; i+=VSIZEX)
+        {
+          vintx vi = vintx(i)+vintx(StepTy());
+          vboolx valid = vi <= vintx(N);
+          const Vec3vfx p  = eval0<VSIZEX,Vec3vf<VSIZEX>>(i,N);
+          const Vec3vfx dp = derivative0<VSIZEX,Vec3vf<VSIZEX>>(i,N);
+          const Vec3vfx pm = p-Vec3vfx(scale)*select(vi!=vintx(0),dp,Vec3vfx(zero));
+          const Vec3vfx pp = p+Vec3vfx(scale)*select(vi!=vintx(N),dp,Vec3vfx(zero));
+          pl = select(valid,min(pl,p,pm,pp),pl); // FIXME: use masked min
+          pu = select(valid,max(pu,p,pm,pp),pu); // FIXME: use masked min
+        }
+        const Vec3fa lower(reduce_min(pl.x),reduce_min(pl.y),reduce_min(pl.z));
+        const Vec3fa upper(reduce_max(pu.x),reduce_max(pu.y),reduce_max(pu.z));
+        return BBox3fa(lower,upper);
+      }
+      
+      /* calculates bounds of bezier curve geometry */
+      __forceinline BBox3fa accurateRoundBounds() const
+      {
+        const int N = 7;
+        const float scale = 1.0f/(3.0f*(N-1));
+        Vec4vfx pl(pos_inf), pu(neg_inf);
+        for (int i=0; i<=N; i+=VSIZEX)
+        {
+          vintx vi = vintx(i)+vintx(StepTy());
+          vboolx valid = vi <= vintx(N);
+          const Vec4vfx p  = eval0<VSIZEX>(i,N);
+          const Vec4vfx dp = derivative0<VSIZEX>(i,N);
+          const Vec4vfx pm = p-Vec4vfx(scale)*select(vi!=vintx(0),dp,Vec4vfx(zero));
+          const Vec4vfx pp = p+Vec4vfx(scale)*select(vi!=vintx(N),dp,Vec4vfx(zero));
+          pl = select(valid,min(pl,p,pm,pp),pl); // FIXME: use masked min
+          pu = select(valid,max(pu,p,pm,pp),pu); // FIXME: use masked min
+        }
+        const Vec3fa lower(reduce_min(pl.x),reduce_min(pl.y),reduce_min(pl.z));
+        const Vec3fa upper(reduce_max(pu.x),reduce_max(pu.y),reduce_max(pu.z));
+        const float r_min = reduce_min(pl.w);
+        const float r_max = reduce_max(pu.w);
+        const Vec3fa upper_r = Vec3fa(max(abs(r_min),abs(r_max)));
+        return enlarge(BBox3fa(lower,upper),upper_r);
+      }
+      
+      /* calculates bounds when tessellated into N line segments */
+      __forceinline BBox3fa accurateFlatBounds(int N) const
+      {
+        if (likely(N == 4))
+        {
+          const Vec4vf4 pi = eval0<4>(0,4);
+          const Vec3fa lower(reduce_min(pi.x),reduce_min(pi.y),reduce_min(pi.z));
+          const Vec3fa upper(reduce_max(pi.x),reduce_max(pi.y),reduce_max(pi.z));
+          const Vec3fa upper_r = Vec3fa(reduce_max(abs(pi.w)));
+          return enlarge(BBox3fa(min(lower,v3),max(upper,v3)),max(upper_r,Vec3fa(abs(v3.w))));
+        } 
+        else
+        {
+          Vec3vfx pl(pos_inf), pu(neg_inf); vfloatx ru(0.0f);
+          for (int i=0; i<N; i+=VSIZEX)
+          {
+            vboolx valid = vintx(i)+vintx(StepTy()) < vintx(N);
+            const Vec4vfx pi = eval0<VSIZEX>(i,N);
+            
+            pl.x = select(valid,min(pl.x,pi.x),pl.x); // FIXME: use masked min
+            pl.y = select(valid,min(pl.y,pi.y),pl.y); 
+            pl.z = select(valid,min(pl.z,pi.z),pl.z); 
+            
+            pu.x = select(valid,max(pu.x,pi.x),pu.x); // FIXME: use masked min
+            pu.y = select(valid,max(pu.y,pi.y),pu.y); 
+            pu.z = select(valid,max(pu.z,pi.z),pu.z); 
+            
+            ru   = select(valid,max(ru,abs(pi.w)),ru);
+          }
+          const Vec3fa lower(reduce_min(pl.x),reduce_min(pl.y),reduce_min(pl.z));
+          const Vec3fa upper(reduce_max(pu.x),reduce_max(pu.y),reduce_max(pu.z));
+          const Vec3fa upper_r(reduce_max(ru));
+          return enlarge(BBox3fa(min(lower,v3),max(upper,v3)),max(upper_r,Vec3fa(abs(v3.w))));
+        }
+      }
+      
+      friend __forceinline embree_ostream operator<<(embree_ostream cout, const CubicBezierCurve& curve) {
+        return cout << "CubicBezierCurve { v0 = " << curve.v0 << ", v1 = " << curve.v1 << ", v2 = " << curve.v2 << ", v3 = " << curve.v3 << " }";
+      }
+    };
+
+#if defined(__AVX__)
+  template<>
+    __forceinline CubicBezierCurve<vfloat4> CubicBezierCurve<vfloat4>::clip(const Interval1f& u1) const
+  {
+    const vfloat8 p00 = vfloat8(v0);
+    const vfloat8 p01 = vfloat8(v1);
+    const vfloat8 p02 = vfloat8(v2);
+    const vfloat8 p03 = vfloat8(v3);
+
+    const vfloat8 t(vfloat4(u1.lower),vfloat4(u1.upper));
+    const vfloat8 p10 = lerp(p00,p01,t);
+    const vfloat8 p11 = lerp(p01,p02,t);
+    const vfloat8 p12 = lerp(p02,p03,t);
+    const vfloat8 p20 = lerp(p10,p11,t);
+    const vfloat8 p21 = lerp(p11,p12,t);
+    const vfloat8 p30 = lerp(p20,p21,t);
+    
+    const vfloat8 f01  = p30;
+    const vfloat8 df01 = vfloat8(3.0f)*(p21-p20);
+        
+    const vfloat4 f0  = extract4<0>(f01),  f1  = extract4<1>(f01);
+    const vfloat4 df0 = extract4<0>(df01), df1 = extract4<1>(df01);
+    const float s = u1.upper-u1.lower;
+    return CubicBezierCurve(f0,f0+s*(1.0f/3.0f)*df0,f1-s*(1.0f/3.0f)*df1,f1);
+  }
+#endif
+  
+  template<typename Vertex> using BezierCurveT = CubicBezierCurve<Vertex>;
+  
+  typedef CubicBezierCurve<float> CubicBezierCurve1f;
+  typedef CubicBezierCurve<Vec2fa> CubicBezierCurve2fa;
+  typedef CubicBezierCurve<Vec3fa> CubicBezierCurve3fa;
+  typedef CubicBezierCurve<Vec3fa> BezierCurve3fa;
+  typedef CubicBezierCurve<Vec3ff> BezierCurve3ff;
+  
+  template<> __forceinline int CubicBezierCurve<float>::maxRoots() const
+  {
+    float eps = 1E-4f;
+    bool neg0 = v0 <= 0.0f; bool zero0 = fabs(v0) < eps;
+    bool neg1 = v1 <= 0.0f; bool zero1 = fabs(v1) < eps;
+    bool neg2 = v2 <= 0.0f; bool zero2 = fabs(v2) < eps;
+    bool neg3 = v3 <= 0.0f; bool zero3 = fabs(v3) < eps;
+    return (neg0 != neg1 || zero0) + (neg1 != neg2 || zero1) + (neg2 != neg3 || zero2 || zero3);
+  }
+  
+  template<> __forceinline int CubicBezierCurve<Interval1f>::maxRoots() const {
+    return numRoots(v0,v1) + numRoots(v1,v2) + numRoots(v2,v3);
+  }
+
+  struct CurveGeometry; // FIXME: this code should move !
+  template<typename CurveGeometry>
+  __forceinline CubicBezierCurve<Vec3ff> enlargeRadiusToMinWidth(const RayQueryContext* context, const CurveGeometry* geom, const Vec3fa& ray_org, const CubicBezierCurve<Vec3ff>& curve)
+  {
+    return CubicBezierCurve<Vec3ff>(enlargeRadiusToMinWidth(context,geom,ray_org,curve.v0),
+                                    enlargeRadiusToMinWidth(context,geom,ray_org,curve.v1),
+                                    enlargeRadiusToMinWidth(context,geom,ray_org,curve.v2),
+                                    enlargeRadiusToMinWidth(context,geom,ray_org,curve.v3));
+  }
+}

thirdparty/embree/kernels/subdiv/bezier_patch.h

@@ -0,0 +1,372 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "catmullclark_patch.h"
+#include "bezier_curve.h"
+
+namespace embree
+{  
+  template<class T, class S>
+    static __forceinline T deCasteljau(const S& uu, const T& v0, const T& v1, const T& v2, const T& v3)
+  {
+    const T v0_1 = lerp(v0,v1,uu);
+    const T v1_1 = lerp(v1,v2,uu);
+    const T v2_1 = lerp(v2,v3,uu);
+    const T v0_2 = lerp(v0_1,v1_1,uu);
+    const T v1_2 = lerp(v1_1,v2_1,uu);
+    const T v0_3 = lerp(v0_2,v1_2,uu);
+    return v0_3;
+  }
+  
+  template<class T, class S>
+    static __forceinline T deCasteljau_tangent(const S& uu, const T& v0, const T& v1, const T& v2, const T& v3)
+  {
+    const T v0_1 = lerp(v0,v1,uu);
+    const T v1_1 = lerp(v1,v2,uu);
+    const T v2_1 = lerp(v2,v3,uu);
+    const T v0_2 = lerp(v0_1,v1_1,uu);
+    const T v1_2 = lerp(v1_1,v2_1,uu);
+    return S(3.0f)*(v1_2-v0_2);
+  }
+
+  template<typename Vertex>
+    __forceinline Vertex computeInnerBezierControlPoint(const Vertex v[4][4], const size_t y, const size_t x) {
+    return 1.0f / 36.0f * (16.0f * v[y][x] + 4.0f * (v[y-1][x] +  v[y+1][x] + v[y][x-1] + v[y][x+1]) + (v[y-1][x-1] + v[y+1][x+1] + v[y-1][x+1] + v[y+1][x-1]));
+  }
+  
+  template<typename Vertex>
+    __forceinline Vertex computeTopEdgeBezierControlPoint(const Vertex v[4][4], const size_t y, const size_t x) {
+    return 1.0f / 18.0f * (8.0f * v[y][x] + 4.0f * v[y-1][x] + 2.0f * (v[y][x-1] + v[y][x+1]) + (v[y-1][x-1] + v[y-1][x+1]));
+  }
+
+  template<typename Vertex>
+    __forceinline Vertex computeBottomEdgeBezierControlPoint(const Vertex v[4][4], const size_t y, const size_t x) {
+    return 1.0f / 18.0f * (8.0f * v[y][x] + 4.0f * v[y+1][x] + 2.0f * (v[y][x-1] + v[y][x+1]) + v[y+1][x-1] + v[y+1][x+1]);
+  }
+  
+  template<typename Vertex>
+    __forceinline Vertex computeLeftEdgeBezierControlPoint(const Vertex v[4][4], const size_t y, const size_t x) {
+    return 1.0f / 18.0f * (8.0f * v[y][x] + 4.0f * v[y][x-1] + 2.0f * (v[y-1][x] + v[y+1][x]) + v[y-1][x-1] + v[y+1][x-1]);
+  }
+  
+  template<typename Vertex>
+    __forceinline Vertex computeRightEdgeBezierControlPoint(const Vertex v[4][4], const size_t y, const size_t x) {
+    return 1.0f / 18.0f * (8.0f * v[y][x] + 4.0f * v[y][x+1] + 2.0f * (v[y-1][x] + v[y+1][x]) + v[y-1][x+1] + v[y+1][x+1]);
+  }
+  
+  template<typename Vertex>
+    __forceinline Vertex computeCornerBezierControlPoint(const Vertex v[4][4], const size_t y, const size_t x, const ssize_t delta_y, const ssize_t delta_x)
+  {
+    return 1.0f / 9.0f * (4.0f * v[y][x] + 2.0f * (v[y+delta_y][x] + v[y][x+delta_x]) + v[y+delta_y][x+delta_x]);
+  }
+
+  template<typename Vertex, typename Vertex_t>
+    class __aligned(64) BezierPatchT
+  {
+   public:
+      Vertex matrix[4][4];
+    
+  public:
+
+    __forceinline BezierPatchT() {}
+
+    __forceinline BezierPatchT (const HalfEdge* edge, const char* vertices, size_t stride);
+
+    __forceinline BezierPatchT(const CatmullClarkPatchT<Vertex,Vertex_t>& patch);
+
+    __forceinline BezierPatchT(const CatmullClarkPatchT<Vertex,Vertex_t>& patch,
+                               const BezierCurveT<Vertex>* border0,
+                               const BezierCurveT<Vertex>* border1,
+                               const BezierCurveT<Vertex>* border2,
+                               const BezierCurveT<Vertex>* border3);
+                               
+    __forceinline BezierPatchT(const BSplinePatchT<Vertex,Vertex_t>& source)
+    {
+      /* compute inner bezier control points */
+      matrix[0][0] = computeInnerBezierControlPoint(source.v,1,1);
+      matrix[0][3] = computeInnerBezierControlPoint(source.v,1,2);
+      matrix[3][3] = computeInnerBezierControlPoint(source.v,2,2);
+      matrix[3][0] = computeInnerBezierControlPoint(source.v,2,1);
+      
+      /* compute top edge control points */
+      matrix[0][1] = computeRightEdgeBezierControlPoint(source.v,1,1);
+      matrix[0][2] = computeLeftEdgeBezierControlPoint(source.v,1,2); 
+      
+      /* compute bottom edge control points */
+      matrix[3][1] = computeRightEdgeBezierControlPoint(source.v,2,1);
+      matrix[3][2] = computeLeftEdgeBezierControlPoint(source.v,2,2);
+      
+      /* compute left edge control points */
+      matrix[1][0] = computeBottomEdgeBezierControlPoint(source.v,1,1);
+      matrix[2][0] = computeTopEdgeBezierControlPoint(source.v,2,1);
+      
+      /* compute right edge control points */
+      matrix[1][3] = computeBottomEdgeBezierControlPoint(source.v,1,2);
+      matrix[2][3] = computeTopEdgeBezierControlPoint(source.v,2,2);
+      
+      /* compute corner control points */
+      matrix[1][1] = computeCornerBezierControlPoint(source.v,1,1, 1, 1);
+      matrix[1][2] = computeCornerBezierControlPoint(source.v,1,2, 1,-1);
+      matrix[2][2] = computeCornerBezierControlPoint(source.v,2,2,-1,-1);
+      matrix[2][1] = computeCornerBezierControlPoint(source.v,2,1,-1, 1);      
+    }
+
+    static __forceinline Vertex_t bilinear(const Vec4f Bu, const Vertex matrix[4][4], const Vec4f Bv)
+    {
+      const Vertex_t M0 = madd(Bu.x,matrix[0][0],madd(Bu.y,matrix[0][1],madd(Bu.z,matrix[0][2],Bu.w * matrix[0][3]))); 
+      const Vertex_t M1 = madd(Bu.x,matrix[1][0],madd(Bu.y,matrix[1][1],madd(Bu.z,matrix[1][2],Bu.w * matrix[1][3])));
+      const Vertex_t M2 = madd(Bu.x,matrix[2][0],madd(Bu.y,matrix[2][1],madd(Bu.z,matrix[2][2],Bu.w * matrix[2][3])));
+      const Vertex_t M3 = madd(Bu.x,matrix[3][0],madd(Bu.y,matrix[3][1],madd(Bu.z,matrix[3][2],Bu.w * matrix[3][3])));
+      return madd(Bv.x,M0,madd(Bv.y,M1,madd(Bv.z,M2,Bv.w*M3)));
+    }
+
+    static __forceinline Vertex_t eval(const Vertex matrix[4][4], const float uu, const float vv) 
+    {      
+      const Vec4f Bu = BezierBasis::eval(uu);
+      const Vec4f Bv = BezierBasis::eval(vv);
+      return bilinear(Bu,matrix,Bv);
+    }
+
+    static __forceinline Vertex_t eval_du(const Vertex matrix[4][4], const float uu, const float vv) 
+    {
+      const Vec4f Bu = BezierBasis::derivative(uu);
+      const Vec4f Bv = BezierBasis::eval(vv);
+      return bilinear(Bu,matrix,Bv);
+    }
+
+    static __forceinline Vertex_t eval_dv(const Vertex matrix[4][4], const float uu, const float vv) 
+    {
+      const Vec4f Bu = BezierBasis::eval(uu);
+      const Vec4f Bv = BezierBasis::derivative(vv);
+      return bilinear(Bu,matrix,Bv);
+    }
+
+    static __forceinline Vertex_t eval_dudu(const Vertex matrix[4][4], const float uu, const float vv) 
+    {
+      const Vec4f Bu = BezierBasis::derivative2(uu);
+      const Vec4f Bv = BezierBasis::eval(vv);
+      return bilinear(Bu,matrix,Bv);
+    }
+
+    static __forceinline Vertex_t eval_dvdv(const Vertex matrix[4][4], const float uu, const float vv) 
+    {
+      const Vec4f Bu = BezierBasis::eval(uu);
+      const Vec4f Bv = BezierBasis::derivative2(vv);
+      return bilinear(Bu,matrix,Bv);
+    }
+
+    static __forceinline Vertex_t eval_dudv(const Vertex matrix[4][4], const float uu, const float vv) 
+    {
+      const Vec4f Bu = BezierBasis::derivative(uu);
+      const Vec4f Bv = BezierBasis::derivative(vv);
+      return bilinear(Bu,matrix,Bv);
+    }
+
+    static __forceinline Vertex_t normal(const Vertex matrix[4][4], const float uu, const float vv) 
+    {
+      const Vertex_t dPdu = eval_du(matrix,uu,vv);
+      const Vertex_t dPdv = eval_dv(matrix,uu,vv);
+      return cross(dPdu,dPdv);
+    }
+
+    __forceinline Vertex_t normal(const float uu, const float vv) 
+    {
+      const Vertex_t dPdu = eval_du(matrix,uu,vv);
+      const Vertex_t dPdv = eval_dv(matrix,uu,vv);
+      return cross(dPdu,dPdv);
+    }
+
+    __forceinline Vertex_t eval(const float uu, const float vv) const {
+      return eval(matrix,uu,vv);
+    }
+
+    __forceinline Vertex_t eval_du(const float uu, const float vv) const { 
+      return eval_du(matrix,uu,vv);
+    }
+
+    __forceinline Vertex_t eval_dv(const float uu, const float vv) const {
+      return eval_dv(matrix,uu,vv);
+    }
+
+    __forceinline Vertex_t eval_dudu(const float uu, const float vv) const { 
+      return eval_dudu(matrix,uu,vv);
+    }
+    
+    __forceinline Vertex_t eval_dvdv(const float uu, const float vv) const { 
+      return eval_dvdv(matrix,uu,vv);
+    }
+
+    __forceinline Vertex_t eval_dudv(const float uu, const float vv) const { 
+      return eval_dudv(matrix,uu,vv);
+    }
+
+    __forceinline void eval(const float u, const float v, Vertex* P, Vertex* dPdu, Vertex* dPdv, Vertex* ddPdudu, Vertex* ddPdvdv, Vertex* ddPdudv, const float dscale = 1.0f) const
+    {
+      if (P) {
+        *P = eval(u,v); 
+      }
+      if (dPdu) {
+        assert(dPdu); *dPdu = eval_du(u,v)*dscale; 
+        assert(dPdv); *dPdv = eval_dv(u,v)*dscale; 
+      }
+      if (ddPdudu) {
+        assert(ddPdudu); *ddPdudu = eval_dudu(u,v)*sqr(dscale); 
+        assert(ddPdvdv); *ddPdvdv = eval_dvdv(u,v)*sqr(dscale); 
+        assert(ddPdudv); *ddPdudv = eval_dudv(u,v)*sqr(dscale); 
+      }
+    }
+
+    template<class vfloat>
+      __forceinline vfloat eval(const size_t i, const vfloat& uu, const vfloat& vv, const Vec4<vfloat>& u_n, const Vec4<vfloat>& v_n) const
+      {
+        const vfloat curve0_x = v_n[0] * vfloat(matrix[0][0][i]) + v_n[1] * vfloat(matrix[1][0][i]) + v_n[2] * vfloat(matrix[2][0][i]) + v_n[3] * vfloat(matrix[3][0][i]);
+        const vfloat curve1_x = v_n[0] * vfloat(matrix[0][1][i]) + v_n[1] * vfloat(matrix[1][1][i]) + v_n[2] * vfloat(matrix[2][1][i]) + v_n[3] * vfloat(matrix[3][1][i]);
+        const vfloat curve2_x = v_n[0] * vfloat(matrix[0][2][i]) + v_n[1] * vfloat(matrix[1][2][i]) + v_n[2] * vfloat(matrix[2][2][i]) + v_n[3] * vfloat(matrix[3][2][i]);
+        const vfloat curve3_x = v_n[0] * vfloat(matrix[0][3][i]) + v_n[1] * vfloat(matrix[1][3][i]) + v_n[2] * vfloat(matrix[2][3][i]) + v_n[3] * vfloat(matrix[3][3][i]);
+        return u_n[0] * curve0_x + u_n[1] * curve1_x + u_n[2] * curve2_x + u_n[3] * curve3_x;
+      }
+
+    template<typename vbool, typename vfloat>
+      __forceinline void eval(const vbool& valid, const vfloat& uu, const vfloat& vv, 
+                              float* P, float* dPdu, float* dPdv, float* ddPdudu, float* ddPdvdv, float* ddPdudv,
+                              const float dscale, const size_t dstride, const size_t N) const
+      {
+        if (P) {
+          const Vec4<vfloat> u_n = BezierBasis::eval(uu); 
+          const Vec4<vfloat> v_n = BezierBasis::eval(vv); 
+          for (size_t i=0; i<N; i++) vfloat::store(valid,P+i*dstride,eval(i,uu,vv,u_n,v_n));
+        }
+        if (dPdu) 
+        {
+          {
+            assert(dPdu);
+            const Vec4<vfloat> u_n = BezierBasis::derivative(uu);
+            const Vec4<vfloat> v_n = BezierBasis::eval(vv); 
+            for (size_t i=0; i<N; i++) vfloat::store(valid,dPdu+i*dstride,eval(i,uu,vv,u_n,v_n)*dscale);
+          }
+          {
+            assert(dPdv);
+            const Vec4<vfloat> u_n = BezierBasis::eval(uu);
+            const Vec4<vfloat> v_n = BezierBasis::derivative(vv); 
+            for (size_t i=0; i<N; i++) vfloat::store(valid,dPdv+i*dstride,eval(i,uu,vv,u_n,v_n)*dscale);
+          }
+        }
+        if (ddPdudu) 
+        {
+          {
+            assert(ddPdudu);
+            const Vec4<vfloat> u_n = BezierBasis::derivative2(uu);
+            const Vec4<vfloat> v_n = BezierBasis::eval(vv); 
+            for (size_t i=0; i<N; i++) vfloat::store(valid,ddPdudu+i*dstride,eval(i,uu,vv,u_n,v_n)*sqr(dscale));
+          }
+          {
+            assert(ddPdvdv);
+            const Vec4<vfloat> u_n = BezierBasis::eval(uu);
+            const Vec4<vfloat> v_n = BezierBasis::derivative2(vv); 
+            for (size_t i=0; i<N; i++) vfloat::store(valid,ddPdvdv+i*dstride,eval(i,uu,vv,u_n,v_n)*sqr(dscale));
+          }
+          {
+            assert(ddPdudv);
+            const Vec4<vfloat> u_n = BezierBasis::derivative(uu);
+            const Vec4<vfloat> v_n = BezierBasis::derivative(vv); 
+            for (size_t i=0; i<N; i++) vfloat::store(valid,ddPdudv+i*dstride,eval(i,uu,vv,u_n,v_n)*sqr(dscale));
+          }
+        }
+      }
+
+    template<typename T>
+      static __forceinline Vec3<T> eval(const Vertex matrix[4][4], const T& uu, const T& vv) 
+    {      
+      const T one_minus_uu = 1.0f - uu;
+      const T one_minus_vv = 1.0f - vv;      
+
+      const T B0_u = one_minus_uu * one_minus_uu * one_minus_uu;
+      const T B0_v = one_minus_vv * one_minus_vv * one_minus_vv;
+      const T B1_u = 3.0f * (one_minus_uu * uu * one_minus_uu);
+      const T B1_v = 3.0f * (one_minus_vv * vv * one_minus_vv);
+      const T B2_u = 3.0f * (uu * one_minus_uu * uu);
+      const T B2_v = 3.0f * (vv * one_minus_vv * vv);
+      const T B3_u = uu * uu * uu;
+      const T B3_v = vv * vv * vv;
+      
+      const T x = 
+        madd(B0_v,madd(B0_u,matrix[0][0].x,madd(B1_u,matrix[0][1].x,madd(B2_u,matrix[0][2].x,B3_u*matrix[0][3].x))), 
+        madd(B1_v,madd(B0_u,matrix[1][0].x,madd(B1_u,matrix[1][1].x,madd(B2_u,matrix[1][2].x,B3_u*matrix[1][3].x))),
+        madd(B2_v,madd(B0_u,matrix[2][0].x,madd(B1_u,matrix[2][1].x,madd(B2_u,matrix[2][2].x,B3_u*matrix[2][3].x))),
+             B3_v*madd(B0_u,matrix[3][0].x,madd(B1_u,matrix[3][1].x,madd(B2_u,matrix[3][2].x,B3_u*matrix[3][3].x)))))); 
+
+      const T y = 
+        madd(B0_v,madd(B0_u,matrix[0][0].y,madd(B1_u,matrix[0][1].y,madd(B2_u,matrix[0][2].y,B3_u*matrix[0][3].y))), 
+        madd(B1_v,madd(B0_u,matrix[1][0].y,madd(B1_u,matrix[1][1].y,madd(B2_u,matrix[1][2].y,B3_u*matrix[1][3].y))),
+        madd(B2_v,madd(B0_u,matrix[2][0].y,madd(B1_u,matrix[2][1].y,madd(B2_u,matrix[2][2].y,B3_u*matrix[2][3].y))),
+             B3_v*madd(B0_u,matrix[3][0].y,madd(B1_u,matrix[3][1].y,madd(B2_u,matrix[3][2].y,B3_u*matrix[3][3].y)))))); 
+      
+      const T z = 
+        madd(B0_v,madd(B0_u,matrix[0][0].z,madd(B1_u,matrix[0][1].z,madd(B2_u,matrix[0][2].z,B3_u*matrix[0][3].z))), 
+        madd(B1_v,madd(B0_u,matrix[1][0].z,madd(B1_u,matrix[1][1].z,madd(B2_u,matrix[1][2].z,B3_u*matrix[1][3].z))),
+        madd(B2_v,madd(B0_u,matrix[2][0].z,madd(B1_u,matrix[2][1].z,madd(B2_u,matrix[2][2].z,B3_u*matrix[2][3].z))),
+             B3_v*madd(B0_u,matrix[3][0].z,madd(B1_u,matrix[3][1].z,madd(B2_u,matrix[3][2].z,B3_u*matrix[3][3].z)))))); 
+      
+      return Vec3<T>(x,y,z);
+    }
+
+    template<typename vfloat>
+      __forceinline Vec3<vfloat> eval(const vfloat& uu, const vfloat& vv) const {     
+      return eval(matrix,uu,vv);
+    }
+
+    template<class T>
+      static __forceinline Vec3<T> normal(const Vertex matrix[4][4], const T& uu, const T& vv) 
+    {
+      
+      const Vec3<T> matrix_00 = Vec3<T>(matrix[0][0].x,matrix[0][0].y,matrix[0][0].z);
+      const Vec3<T> matrix_01 = Vec3<T>(matrix[0][1].x,matrix[0][1].y,matrix[0][1].z);
+      const Vec3<T> matrix_02 = Vec3<T>(matrix[0][2].x,matrix[0][2].y,matrix[0][2].z);
+      const Vec3<T> matrix_03 = Vec3<T>(matrix[0][3].x,matrix[0][3].y,matrix[0][3].z);
+
+      const Vec3<T> matrix_10 = Vec3<T>(matrix[1][0].x,matrix[1][0].y,matrix[1][0].z);
+      const Vec3<T> matrix_11 = Vec3<T>(matrix[1][1].x,matrix[1][1].y,matrix[1][1].z);
+      const Vec3<T> matrix_12 = Vec3<T>(matrix[1][2].x,matrix[1][2].y,matrix[1][2].z);
+      const Vec3<T> matrix_13 = Vec3<T>(matrix[1][3].x,matrix[1][3].y,matrix[1][3].z);
+
+      const Vec3<T> matrix_20 = Vec3<T>(matrix[2][0].x,matrix[2][0].y,matrix[2][0].z);
+      const Vec3<T> matrix_21 = Vec3<T>(matrix[2][1].x,matrix[2][1].y,matrix[2][1].z);
+      const Vec3<T> matrix_22 = Vec3<T>(matrix[2][2].x,matrix[2][2].y,matrix[2][2].z);
+      const Vec3<T> matrix_23 = Vec3<T>(matrix[2][3].x,matrix[2][3].y,matrix[2][3].z);
+
+      const Vec3<T> matrix_30 = Vec3<T>(matrix[3][0].x,matrix[3][0].y,matrix[3][0].z);
+      const Vec3<T> matrix_31 = Vec3<T>(matrix[3][1].x,matrix[3][1].y,matrix[3][1].z);
+      const Vec3<T> matrix_32 = Vec3<T>(matrix[3][2].x,matrix[3][2].y,matrix[3][2].z);
+      const Vec3<T> matrix_33 = Vec3<T>(matrix[3][3].x,matrix[3][3].y,matrix[3][3].z);
+            
+      /* tangentU */
+      const Vec3<T> col0 = deCasteljau(vv, matrix_00, matrix_10, matrix_20, matrix_30);
+      const Vec3<T> col1 = deCasteljau(vv, matrix_01, matrix_11, matrix_21, matrix_31);
+      const Vec3<T> col2 = deCasteljau(vv, matrix_02, matrix_12, matrix_22, matrix_32);
+      const Vec3<T> col3 = deCasteljau(vv, matrix_03, matrix_13, matrix_23, matrix_33);
+      
+      const Vec3<T> tangentU = deCasteljau_tangent(uu, col0, col1, col2, col3);
+      
+      /* tangentV */
+      const Vec3<T> row0 = deCasteljau(uu, matrix_00, matrix_01, matrix_02, matrix_03);
+      const Vec3<T> row1 = deCasteljau(uu, matrix_10, matrix_11, matrix_12, matrix_13);
+      const Vec3<T> row2 = deCasteljau(uu, matrix_20, matrix_21, matrix_22, matrix_23);
+      const Vec3<T> row3 = deCasteljau(uu, matrix_30, matrix_31, matrix_32, matrix_33);
+      
+      const Vec3<T> tangentV = deCasteljau_tangent(vv, row0, row1, row2, row3);
+      
+      /* normal = tangentU x tangentV */
+      const Vec3<T> n = cross(tangentU,tangentV);
+      return n;
+    }
+
+    template<typename vfloat>
+      __forceinline Vec3<vfloat> normal(const vfloat& uu, const vfloat& vv) const {     
+      return normal(matrix,uu,vv);
+    }
+  };
+
+  typedef BezierPatchT<Vec3fa,Vec3fa_t> BezierPatch3fa;
+}

thirdparty/embree/kernels/subdiv/bilinear_patch.h

@@ -0,0 +1,191 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "catmullclark_patch.h"
+#include "bezier_curve.h"
+
+namespace embree
+{
+  template<typename Vertex, typename Vertex_t = Vertex>
+    class __aligned(64) BilinearPatchT
+    {
+      typedef CatmullClark1RingT<Vertex,Vertex_t> CatmullClarkRing;
+      typedef CatmullClarkPatchT<Vertex,Vertex_t> CatmullClarkPatch;
+      
+    public:
+      Vertex v[4];
+      
+    public:
+      
+      __forceinline BilinearPatchT () {}
+
+      __forceinline BilinearPatchT (const HalfEdge* edge, const BufferView<Vertex>& vertices) {
+        init(edge,vertices.getPtr(),vertices.getStride());
+      }
+      
+      __forceinline BilinearPatchT (const HalfEdge* edge, const char* vertices, size_t stride) {
+        init(edge,vertices,stride);
+      }
+
+      __forceinline void init (const HalfEdge* edge, const char* vertices, size_t stride)
+      {
+        v[0] = Vertex::loadu(vertices+edge->getStartVertexIndex()*stride); edge = edge->next();
+        v[1] = Vertex::loadu(vertices+edge->getStartVertexIndex()*stride); edge = edge->next();
+        v[2] = Vertex::loadu(vertices+edge->getStartVertexIndex()*stride); edge = edge->next();
+        v[3] = Vertex::loadu(vertices+edge->getStartVertexIndex()*stride); edge = edge->next();
+      }
+
+      __forceinline BilinearPatchT (const CatmullClarkPatch& patch)
+      {
+        v[0] = patch.ring[0].getLimitVertex();
+        v[1] = patch.ring[1].getLimitVertex();
+        v[2] = patch.ring[2].getLimitVertex();
+        v[3] = patch.ring[3].getLimitVertex();
+      }
+
+      __forceinline BBox<Vertex> bounds() const
+      {
+        
+        BBox<Vertex> bounds (v[0]);
+        bounds.extend(v[1]);
+        bounds.extend(v[2]);
+        bounds.extend(v[3]);
+        return bounds;
+      }
+      
+      __forceinline Vertex eval(const float uu, const float vv) const {
+        return lerp(lerp(v[0],v[1],uu),lerp(v[3],v[2],uu),vv);
+      }
+
+      __forceinline Vertex eval_du(const float uu, const float vv) const {
+        return lerp(v[1]-v[0],v[2]-v[3],vv);
+      }
+
+      __forceinline Vertex eval_dv(const float uu, const float vv) const {
+        return lerp(v[3]-v[0],v[2]-v[1],uu);
+      }
+
+      __forceinline Vertex eval_dudu(const float uu, const float vv) const {
+        return Vertex(zero);
+      }
+
+      __forceinline Vertex eval_dvdv(const float uu, const float vv) const {
+        return Vertex(zero);
+      }
+
+      __forceinline Vertex eval_dudv(const float uu, const float vv) const {
+        return (v[2]-v[3]) - (v[1]-v[0]);
+      }
+
+      __forceinline Vertex normal(const float uu, const float vv) const {
+        return cross(eval_du(uu,vv),eval_dv(uu,vv));
+      }
+      
+      __forceinline void eval(const float u, const float v, 
+                              Vertex* P, Vertex* dPdu, Vertex* dPdv, Vertex* ddPdudu, Vertex* ddPdvdv, Vertex* ddPdudv,
+                              const float dscale = 1.0f) const
+      {
+        if (P) {
+          *P = eval(u,v); 
+        }
+        if (dPdu) {
+          assert(dPdu); *dPdu = eval_du(u,v)*dscale; 
+          assert(dPdv); *dPdv = eval_dv(u,v)*dscale; 
+        }
+        if (ddPdudu) {
+          assert(ddPdudu); *ddPdudu = eval_dudu(u,v)*sqr(dscale); 
+          assert(ddPdvdv); *ddPdvdv = eval_dvdv(u,v)*sqr(dscale); 
+          assert(ddPdudv); *ddPdudv = eval_dudv(u,v)*sqr(dscale); 
+        }
+      }
+
+      template<class vfloat>
+      __forceinline Vec3<vfloat> eval(const vfloat& uu, const vfloat& vv) const
+      {
+        const vfloat x = lerp(lerp(v[0].x,v[1].x,uu),lerp(v[3].x,v[2].x,uu),vv);
+        const vfloat y = lerp(lerp(v[0].y,v[1].y,uu),lerp(v[3].y,v[2].y,uu),vv);
+        const vfloat z = lerp(lerp(v[0].z,v[1].z,uu),lerp(v[3].z,v[2].z,uu),vv);
+        return Vec3<vfloat>(x,y,z);
+      }
+
+      template<class vfloat>
+      __forceinline Vec3<vfloat> eval_du(const vfloat& uu, const vfloat& vv) const
+      {
+        const vfloat x = lerp(v[1].x-v[0].x,v[2].x-v[3].x,vv);
+        const vfloat y = lerp(v[1].y-v[0].y,v[2].y-v[3].y,vv);
+        const vfloat z = lerp(v[1].z-v[0].z,v[2].z-v[3].z,vv);
+        return Vec3<vfloat>(x,y,z);
+      }
+
+      template<class vfloat>
+      __forceinline Vec3<vfloat> eval_dv(const vfloat& uu, const vfloat& vv) const
+      {
+        const vfloat x = lerp(v[3].x-v[0].x,v[2].x-v[1].x,uu);
+        const vfloat y = lerp(v[3].y-v[0].y,v[2].y-v[1].y,uu);
+        const vfloat z = lerp(v[3].z-v[0].z,v[2].z-v[1].z,uu);
+        return Vec3<vfloat>(x,y,z);
+      }
+
+      template<typename vfloat>
+      __forceinline Vec3<vfloat> normal(const vfloat& uu, const vfloat& vv) const {
+        return cross(eval_du(uu,vv),eval_dv(uu,vv));
+      }
+
+       template<class vfloat>
+      __forceinline vfloat eval(const size_t i, const vfloat& uu, const vfloat& vv) const {
+        return lerp(lerp(v[0][i],v[1][i],uu),lerp(v[3][i],v[2][i],uu),vv);
+      }
+
+      template<class vfloat>
+      __forceinline vfloat eval_du(const size_t i, const vfloat& uu, const vfloat& vv) const {
+        return lerp(v[1][i]-v[0][i],v[2][i]-v[3][i],vv);
+      }
+
+      template<class vfloat>
+      __forceinline vfloat eval_dv(const size_t i, const vfloat& uu, const vfloat& vv) const {
+        return lerp(v[3][i]-v[0][i],v[2][i]-v[1][i],uu);
+      }
+      
+      template<class vfloat>
+      __forceinline vfloat eval_dudu(const size_t i, const vfloat& uu, const vfloat& vv) const {
+        return vfloat(zero);
+      }
+
+      template<class vfloat>
+      __forceinline vfloat eval_dvdv(const size_t i, const vfloat& uu, const vfloat& vv) const {
+        return vfloat(zero);
+      }
+
+      template<class vfloat>
+      __forceinline vfloat eval_dudv(const size_t i, const vfloat& uu, const vfloat& vv) const {
+        return (v[2][i]-v[3][i]) - (v[1][i]-v[0][i]);
+      }
+
+      template<typename vbool, typename vfloat>
+      __forceinline void eval(const vbool& valid, const vfloat& uu, const vfloat& vv, 
+                              float* P, float* dPdu, float* dPdv, float* ddPdudu, float* ddPdvdv, float* ddPdudv,
+                              const float dscale, const size_t dstride, const size_t N) const
+      {
+        if (P) {
+          for (size_t i=0; i<N; i++) vfloat::store(valid,P+i*dstride,eval(i,uu,vv));
+        }
+        if (dPdu) {
+          for (size_t i=0; i<N; i++) {
+            assert(dPdu); vfloat::store(valid,dPdu+i*dstride,eval_du(i,uu,vv)*dscale);
+            assert(dPdv); vfloat::store(valid,dPdv+i*dstride,eval_dv(i,uu,vv)*dscale);
+          }
+        }
+        if (ddPdudu) {
+          for (size_t i=0; i<N; i++) {
+            assert(ddPdudu); vfloat::store(valid,ddPdudu+i*dstride,eval_dudu(i,uu,vv)*sqr(dscale));
+            assert(ddPdvdv); vfloat::store(valid,ddPdvdv+i*dstride,eval_dvdv(i,uu,vv)*sqr(dscale));
+            assert(ddPdudv); vfloat::store(valid,ddPdudv+i*dstride,eval_dudv(i,uu,vv)*sqr(dscale));
+          }
+        }
+      }
+    };
+  
+  typedef BilinearPatchT<Vec3fa,Vec3fa_t> BilinearPatch3fa;
+}

thirdparty/embree/kernels/subdiv/bspline_curve.h

@@ -0,0 +1,326 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "../common/default.h"
+#include "bezier_curve.h"
+
+namespace embree
+{
+  class BSplineBasis
+  {
+  public:
+
+    template<typename T>
+      static __forceinline Vec4<T> eval(const T& u) 
+    {
+      const T t  = u;
+      const T s  = T(1.0f) - u;
+      const T n0 = s*s*s;
+      const T n1 = (4.0f*(s*s*s)+(t*t*t)) + (12.0f*((s*t)*s) + 6.0f*((t*s)*t));
+      const T n2 = (4.0f*(t*t*t)+(s*s*s)) + (12.0f*((t*s)*t) + 6.0f*((s*t)*s));
+      const T n3 = t*t*t;
+      return T(1.0f/6.0f)*Vec4<T>(n0,n1,n2,n3);
+    }
+    
+    template<typename T>
+      static __forceinline Vec4<T>  derivative(const T& u)
+    {
+      const T t  =  u;
+      const T s  =  1.0f - u;
+      const T n0 = -s*s;
+      const T n1 = -t*t - 4.0f*(t*s);
+      const T n2 =  s*s + 4.0f*(s*t);
+      const T n3 =  t*t;
+      return T(0.5f)*Vec4<T>(n0,n1,n2,n3);
+    }
+
+    template<typename T>
+      static __forceinline Vec4<T>  derivative2(const T& u)
+    {
+      const T t  =  u;
+      const T s  =  1.0f - u;
+      const T n0 = s;
+      const T n1 = t - 2.0f*s;
+      const T n2 = s - 2.0f*t;
+      const T n3 = t;
+      return Vec4<T>(n0,n1,n2,n3);
+    }
+  };
+  
+  struct PrecomputedBSplineBasis
+  {
+    enum { N = 16 };
+  public:
+    PrecomputedBSplineBasis() {}
+    PrecomputedBSplineBasis(int shift);
+
+    /* basis for bspline evaluation */
+  public:
+    float c0[N+1][N+1];
+    float c1[N+1][N+1];
+    float c2[N+1][N+1];
+    float c3[N+1][N+1];
+    
+    /* basis for bspline derivative evaluation */
+  public:
+    float d0[N+1][N+1];
+    float d1[N+1][N+1];
+    float d2[N+1][N+1];
+    float d3[N+1][N+1];
+  };
+  extern PrecomputedBSplineBasis bspline_basis0;
+  extern PrecomputedBSplineBasis bspline_basis1;
+
+  template<typename Vertex>
+    struct BSplineCurveT
+    {
+      Vertex v0,v1,v2,v3;
+      
+      __forceinline BSplineCurveT() {}
+      
+      __forceinline BSplineCurveT(const Vertex& v0, const Vertex& v1, const Vertex& v2, const Vertex& v3)
+        : v0(v0), v1(v1), v2(v2), v3(v3) {}
+
+      __forceinline Vertex begin() const {
+        return madd(1.0f/6.0f,v0,madd(2.0f/3.0f,v1,1.0f/6.0f*v2));
+      }
+
+      __forceinline Vertex end() const {
+        return madd(1.0f/6.0f,v1,madd(2.0f/3.0f,v2,1.0f/6.0f*v3));
+      }
+
+      __forceinline Vertex center() const {
+        return 0.25f*(v0+v1+v2+v3);
+      }
+
+      __forceinline BBox<Vertex> bounds() const {
+        return merge(BBox<Vertex>(v0),BBox<Vertex>(v1),BBox<Vertex>(v2),BBox<Vertex>(v3));
+      }
+      
+      __forceinline friend BSplineCurveT operator -( const BSplineCurveT& a, const Vertex& b ) {
+        return BSplineCurveT(a.v0-b,a.v1-b,a.v2-b,a.v3-b);
+      }
+
+      __forceinline BSplineCurveT<Vec3ff> xfm_pr(const LinearSpace3fa& space, const Vec3fa& p) const
+      {
+        const Vec3ff q0(xfmVector(space,(Vec3fa)v0-p), v0.w);
+        const Vec3ff q1(xfmVector(space,(Vec3fa)v1-p), v1.w);
+        const Vec3ff q2(xfmVector(space,(Vec3fa)v2-p), v2.w);
+        const Vec3ff q3(xfmVector(space,(Vec3fa)v3-p), v3.w);
+        return BSplineCurveT<Vec3ff>(q0,q1,q2,q3);
+      }
+      
+      __forceinline Vertex eval(const float t) const 
+      {
+        const Vec4<float> b = BSplineBasis::eval(t);
+        return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
+      }
+      
+      __forceinline Vertex eval_du(const float t) const
+      {
+        const Vec4<float> b = BSplineBasis::derivative(t);
+        return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
+      }
+      
+      __forceinline Vertex eval_dudu(const float t) const 
+      {
+        const Vec4<float> b = BSplineBasis::derivative2(t);
+        return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
+      }
+
+      __forceinline void eval(const float t, Vertex& p, Vertex& dp) const
+      {
+        p = eval(t);
+        dp = eval_du(t);
+      }
+      
+      __forceinline void eval(const float t, Vertex& p, Vertex& dp, Vertex& ddp) const
+      {
+        p = eval(t);
+        dp = eval_du(t);
+        ddp = eval_dudu(t);
+      }
+
+      template<int M>
+      __forceinline Vec4vf<M> veval(const vfloat<M>& t) const 
+      {
+        const Vec4vf<M> b = BSplineBasis::eval(t);
+        return madd(b.x, Vec4vf<M>(v0), madd(b.y, Vec4vf<M>(v1), madd(b.z, Vec4vf<M>(v2), b.w * Vec4vf<M>(v3))));
+      }
+
+      template<int M>
+      __forceinline Vec4vf<M> veval_du(const vfloat<M>& t) const 
+      {
+        const Vec4vf<M> b = BSplineBasis::derivative(t);
+        return madd(b.x, Vec4vf<M>(v0), madd(b.y, Vec4vf<M>(v1), madd(b.z, Vec4vf<M>(v2), b.w * Vec4vf<M>(v3))));
+      }
+
+      template<int M>
+      __forceinline Vec4vf<M> veval_dudu(const vfloat<M>& t) const 
+      {
+        const Vec4vf<M> b = BSplineBasis::derivative2(t);
+        return madd(b.x, Vec4vf<M>(v0), madd(b.y, Vec4vf<M>(v1), madd(b.z, Vec4vf<M>(v2), b.w * Vec4vf<M>(v3))));
+      }
+
+      template<int M>
+      __forceinline void veval(const vfloat<M>& t, Vec4vf<M>& p, Vec4vf<M>& dp) const
+      {
+        p = veval<M>(t);
+        dp = veval_du<M>(t);
+      }
+      
+      template<int M>
+      __forceinline Vec4vf<M> eval0(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedBSplineBasis::N);
+        assert(ofs <= size);
+        return madd(vfloat<M>::loadu(&bspline_basis0.c0[size][ofs]), Vec4vf<M>(v0),
+                    madd(vfloat<M>::loadu(&bspline_basis0.c1[size][ofs]), Vec4vf<M>(v1),
+                         madd(vfloat<M>::loadu(&bspline_basis0.c2[size][ofs]), Vec4vf<M>(v2),
+                              vfloat<M>::loadu(&bspline_basis0.c3[size][ofs]) * Vec4vf<M>(v3))));
+      }
+      
+      template<int M>
+      __forceinline Vec4vf<M> eval1(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedBSplineBasis::N);
+        assert(ofs <= size);
+        return madd(vfloat<M>::loadu(&bspline_basis1.c0[size][ofs]), Vec4vf<M>(v0), 
+                    madd(vfloat<M>::loadu(&bspline_basis1.c1[size][ofs]), Vec4vf<M>(v1),
+                         madd(vfloat<M>::loadu(&bspline_basis1.c2[size][ofs]), Vec4vf<M>(v2),
+                              vfloat<M>::loadu(&bspline_basis1.c3[size][ofs]) * Vec4vf<M>(v3))));
+      }
+      
+      template<int M>
+      __forceinline Vec4vf<M> derivative0(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedBSplineBasis::N);
+        assert(ofs <= size);
+        return madd(vfloat<M>::loadu(&bspline_basis0.d0[size][ofs]), Vec4vf<M>(v0),
+                    madd(vfloat<M>::loadu(&bspline_basis0.d1[size][ofs]), Vec4vf<M>(v1),
+                         madd(vfloat<M>::loadu(&bspline_basis0.d2[size][ofs]), Vec4vf<M>(v2),
+                              vfloat<M>::loadu(&bspline_basis0.d3[size][ofs]) * Vec4vf<M>(v3))));
+      }
+      
+      template<int M>
+      __forceinline Vec4vf<M> derivative1(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedBSplineBasis::N);
+        assert(ofs <= size);
+        return madd(vfloat<M>::loadu(&bspline_basis1.d0[size][ofs]), Vec4vf<M>(v0),
+                    madd(vfloat<M>::loadu(&bspline_basis1.d1[size][ofs]), Vec4vf<M>(v1),
+                         madd(vfloat<M>::loadu(&bspline_basis1.d2[size][ofs]), Vec4vf<M>(v2),
+                              vfloat<M>::loadu(&bspline_basis1.d3[size][ofs]) * Vec4vf<M>(v3))));
+      }
+      
+      /* calculates bounds of bspline curve geometry */
+      __forceinline BBox3fa accurateRoundBounds() const
+      {
+        const int N = 7;
+        const float scale = 1.0f/(3.0f*(N-1));
+        Vec4vfx pl(pos_inf), pu(neg_inf);
+        for (int i=0; i<=N; i+=VSIZEX)
+        {
+          vintx vi = vintx(i)+vintx(step);
+          vboolx valid = vi <= vintx(N);
+          const Vec4vfx p  = eval0<VSIZEX>(i,N);
+          const Vec4vfx dp = derivative0<VSIZEX>(i,N);
+          const Vec4vfx pm = p-Vec4vfx(scale)*select(vi!=vintx(0),dp,Vec4vfx(zero));
+          const Vec4vfx pp = p+Vec4vfx(scale)*select(vi!=vintx(N),dp,Vec4vfx(zero));
+          pl = select(valid,min(pl,p,pm,pp),pl); // FIXME: use masked min
+          pu = select(valid,max(pu,p,pm,pp),pu); // FIXME: use masked min
+        }
+        const Vec3fa lower(reduce_min(pl.x),reduce_min(pl.y),reduce_min(pl.z));
+        const Vec3fa upper(reduce_max(pu.x),reduce_max(pu.y),reduce_max(pu.z));
+        const float r_min = reduce_min(pl.w);
+        const float r_max = reduce_max(pu.w);
+        const Vec3fa upper_r = Vec3fa(max(abs(r_min),abs(r_max)));
+        return enlarge(BBox3fa(lower,upper),upper_r);
+      }
+      
+      /* calculates bounds when tessellated into N line segments */
+      __forceinline BBox3fa accurateFlatBounds(int N) const
+      {
+        if (likely(N == 4))
+        {
+          const Vec4vf4 pi = eval0<4>(0,4);
+          const Vec3fa lower(reduce_min(pi.x),reduce_min(pi.y),reduce_min(pi.z));
+          const Vec3fa upper(reduce_max(pi.x),reduce_max(pi.y),reduce_max(pi.z));
+          const Vec3fa upper_r = Vec3fa(reduce_max(abs(pi.w)));
+          const Vec3ff pe = end();
+          return enlarge(BBox3fa(min(lower,pe),max(upper,pe)),max(upper_r,Vec3fa(abs(pe.w))));
+        } 
+        else
+        {
+          Vec3vfx pl(pos_inf), pu(neg_inf); vfloatx ru(0.0f);
+          for (int i=0; i<=N; i+=VSIZEX)
+          {
+            vboolx valid = vintx(i)+vintx(step) <= vintx(N);
+            const Vec4vfx pi = eval0<VSIZEX>(i,N);
+            
+            pl.x = select(valid,min(pl.x,pi.x),pl.x); // FIXME: use masked min
+            pl.y = select(valid,min(pl.y,pi.y),pl.y); 
+            pl.z = select(valid,min(pl.z,pi.z),pl.z); 
+            
+            pu.x = select(valid,max(pu.x,pi.x),pu.x); // FIXME: use masked min
+            pu.y = select(valid,max(pu.y,pi.y),pu.y); 
+            pu.z = select(valid,max(pu.z,pi.z),pu.z); 
+            
+            ru = select(valid,max(ru,abs(pi.w)),ru); 
+          }
+          const Vec3fa lower(reduce_min(pl.x),reduce_min(pl.y),reduce_min(pl.z));
+          const Vec3fa upper(reduce_max(pu.x),reduce_max(pu.y),reduce_max(pu.z));
+          const Vec3fa upper_r(reduce_max(ru));
+          return enlarge(BBox3fa(lower,upper),upper_r);
+        }
+      }
+      
+      friend __forceinline embree_ostream operator<<(embree_ostream cout, const BSplineCurveT& curve) {
+        return cout << "BSplineCurve { v0 = " << curve.v0 << ", v1 = " << curve.v1 << ", v2 = " << curve.v2 << ", v3 = " << curve.v3 << " }";
+      }
+    };
+  
+  template<typename Vertex>
+    __forceinline void convert(const BezierCurveT<Vertex>& icurve, BezierCurveT<Vertex>& ocurve) {
+    ocurve = icurve;
+  }
+  
+  template<typename Vertex>
+    __forceinline void convert(const BSplineCurveT<Vertex>& icurve, BSplineCurveT<Vertex>& ocurve) {
+    ocurve = icurve;
+  }
+  
+  template<typename Vertex>
+    __forceinline void convert(const BezierCurveT<Vertex>& icurve, BSplineCurveT<Vertex>& ocurve)
+  {
+    const Vertex v0 = madd(6.0f,icurve.v0,madd(-7.0f,icurve.v1,2.0f*icurve.v2));
+    const Vertex v1 = msub(2.0f,icurve.v1,icurve.v2);
+    const Vertex v2 = msub(2.0f,icurve.v2,icurve.v1);
+    const Vertex v3 = madd(2.0f,icurve.v1,madd(-7.0f,icurve.v2,6.0f*icurve.v3));
+    ocurve = BSplineCurveT<Vertex>(v0,v1,v2,v3);
+  }
+  
+  template<typename Vertex>
+    __forceinline void convert(const BSplineCurveT<Vertex>& icurve, BezierCurveT<Vertex>& ocurve)
+  {
+    const Vertex v0 = madd(1.0f/6.0f,icurve.v0,madd(2.0f/3.0f,icurve.v1,1.0f/6.0f*icurve.v2));
+    const Vertex v1 = madd(2.0f/3.0f,icurve.v1,1.0f/3.0f*icurve.v2);
+    const Vertex v2 = madd(1.0f/3.0f,icurve.v1,2.0f/3.0f*icurve.v2);
+    const Vertex v3 = madd(1.0f/6.0f,icurve.v1,madd(2.0f/3.0f,icurve.v2,1.0f/6.0f*icurve.v3));
+    ocurve = BezierCurveT<Vertex>(v0,v1,v2,v3);
+  }
+
+  template<typename CurveGeometry>
+  __forceinline BSplineCurveT<Vec3ff> enlargeRadiusToMinWidth(const RayQueryContext* context, const CurveGeometry* geom, const Vec3fa& ray_org, const BSplineCurveT<Vec3ff>& curve)
+  {
+    return BSplineCurveT<Vec3ff>(enlargeRadiusToMinWidth(context,geom,ray_org,curve.v0),
+                                 enlargeRadiusToMinWidth(context,geom,ray_org,curve.v1),
+                                 enlargeRadiusToMinWidth(context,geom,ray_org,curve.v2),
+                                 enlargeRadiusToMinWidth(context,geom,ray_org,curve.v3));
+  }
+  
+  typedef BSplineCurveT<Vec3fa> BSplineCurve3fa;
+}
+

thirdparty/embree/kernels/subdiv/bspline_patch.h

@@ -0,0 +1,449 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "catmullclark_patch.h"
+#include "bspline_curve.h"
+
+namespace embree
+{
+  template<typename Vertex, typename Vertex_t = Vertex>
+    class __aligned(64) BSplinePatchT
+    {
+      typedef CatmullClark1RingT<Vertex,Vertex_t> CatmullClarkRing;
+      typedef CatmullClarkPatchT<Vertex,Vertex_t> CatmullClarkPatch;
+      
+    public:
+      
+      __forceinline BSplinePatchT () {}
+
+      __forceinline BSplinePatchT (const CatmullClarkPatch& patch) {
+        init(patch);
+      }
+
+      __forceinline BSplinePatchT(const CatmullClarkPatch& patch,
+                                  const BezierCurveT<Vertex>* border0,
+                                  const BezierCurveT<Vertex>* border1,
+                                  const BezierCurveT<Vertex>* border2,
+                                  const BezierCurveT<Vertex>* border3)
+      {
+        init(patch);
+      }
+
+      __forceinline BSplinePatchT (const HalfEdge* edge, const char* vertices, size_t stride) {
+        init(edge,vertices,stride);
+      }
+
+      __forceinline Vertex hard_corner(const                    Vertex& v01, const Vertex& v02, 
+                                       const Vertex& v10, const Vertex& v11, const Vertex& v12, 
+                                       const Vertex& v20, const Vertex& v21, const Vertex& v22)
+      {
+        return 4.0f*v11 - 2.0f*(v12+v21) + v22;
+      }
+
+      __forceinline Vertex soft_convex_corner( const                    Vertex& v01, const Vertex& v02, 
+                                               const Vertex& v10, const Vertex& v11, const Vertex& v12, 
+                                               const Vertex& v20, const Vertex& v21, const Vertex& v22)
+      {
+        return -8.0f*v11 + 4.0f*(v12+v21) + v22;
+      }
+
+      __forceinline Vertex convex_corner(const float vertex_crease_weight, 
+                                         const                    Vertex& v01, const Vertex& v02, 
+                                         const Vertex& v10, const Vertex& v11, const Vertex& v12, 
+                                         const Vertex& v20, const Vertex& v21, const Vertex& v22)
+      {
+        if (std::isinf(vertex_crease_weight)) return hard_corner(v01,v02,v10,v11,v12,v20,v21,v22);
+        else                                  return soft_convex_corner(v01,v02,v10,v11,v12,v20,v21,v22);
+      }
+
+      __forceinline Vertex load(const HalfEdge* edge, const char* vertices, size_t stride) {
+        return Vertex_t::loadu(vertices+edge->getStartVertexIndex()*stride);
+      }
+
+      __forceinline void init_border(const CatmullClarkRing& edge0,
+                                     Vertex& v01, Vertex& v02,
+                                     const Vertex& v11, const Vertex& v12,
+                                     const Vertex& v21, const Vertex& v22)
+      {
+        if (likely(edge0.has_opposite_back(0)))
+        {
+          v01 = edge0.back(2);
+          v02 = edge0.back(1);
+        } else {
+          v01 = 2.0f*v11-v21;
+          v02 = 2.0f*v12-v22;
+        }
+      }
+
+      __forceinline void init_corner(const CatmullClarkRing& edge0,
+                                     Vertex& v00,       const Vertex& v01, const Vertex& v02, 
+                                     const Vertex& v10, const Vertex& v11, const Vertex& v12, 
+                                     const Vertex& v20, const Vertex& v21, const Vertex& v22)
+      {
+        const bool MAYBE_UNUSED has_back1 = edge0.has_opposite_back(1);
+        const bool has_back0 = edge0.has_opposite_back(0);
+        const bool has_front1 = edge0.has_opposite_front(1);
+        const bool MAYBE_UNUSED has_front2 = edge0.has_opposite_front(2);
+        
+        if (likely(has_back0)) {
+          if (likely(has_front1)) { assert(has_back1 && has_front2); v00 = edge0.back(3); }
+          else { assert(!has_back1); v00 = 2.0f*v01-v02; }
+        }
+        else {
+          if (likely(has_front1)) { assert(!has_front2); v00 = 2.0f*v10-v20; }
+          else v00 = convex_corner(edge0.vertex_crease_weight,v01,v02,v10,v11,v12,v20,v21,v22);
+        }
+      }
+      
+      void init(const CatmullClarkPatch& patch)
+      {
+        /* fill inner vertices */
+        const Vertex v11 = v[1][1] = patch.ring[0].vtx;
+        const Vertex v12 = v[1][2] = patch.ring[1].vtx;
+        const Vertex v22 = v[2][2] = patch.ring[2].vtx; 
+        const Vertex v21 = v[2][1] = patch.ring[3].vtx; 
+        
+        /* fill border vertices */
+        init_border(patch.ring[0],v[0][1],v[0][2],v11,v12,v21,v22);
+        init_border(patch.ring[1],v[1][3],v[2][3],v12,v22,v11,v21);
+        init_border(patch.ring[2],v[3][2],v[3][1],v22,v21,v12,v11);
+        init_border(patch.ring[3],v[2][0],v[1][0],v21,v11,v22,v12);
+        
+        /* fill corner vertices */
+        init_corner(patch.ring[0],v[0][0],v[0][1],v[0][2],v[1][0],v11,v12,v[2][0],v21,v22);
+        init_corner(patch.ring[1],v[0][3],v[1][3],v[2][3],v[0][2],v12,v22,v[0][1],v11,v21);
+        init_corner(patch.ring[2],v[3][3],v[3][2],v[3][1],v[2][3],v22,v21,v[1][3],v12,v11);
+        init_corner(patch.ring[3],v[3][0],v[2][0],v[1][0],v[3][1],v21,v11,v[3][2],v22,v12);
+      }
+      
+      void init_border(const HalfEdge* edge0, const char* vertices, size_t stride,
+                                     Vertex& v01, Vertex& v02,
+                                     const Vertex& v11, const Vertex& v12,
+                                     const Vertex& v21, const Vertex& v22)
+      {
+        if (likely(edge0->hasOpposite())) 
+        {
+          const HalfEdge* e = edge0->opposite()->next()->next(); 
+          v01 = load(e,vertices,stride); 
+          v02 = load(e->next(),vertices,stride);
+        } else {
+          v01 = 2.0f*v11-v21;
+          v02 = 2.0f*v12-v22;
+        }
+      }
+      
+      void init_corner(const HalfEdge* edge0, const char* vertices, size_t stride,
+                       Vertex& v00, const Vertex& v01, const Vertex& v02, 
+                       const Vertex& v10, const Vertex& v11, const Vertex& v12, 
+                       const Vertex& v20, const Vertex& v21, const Vertex& v22)
+      {
+        const bool has_back0 = edge0->hasOpposite();
+        const bool has_front1 = edge0->prev()->hasOpposite();
+
+        if (likely(has_back0))
+        { 
+          const HalfEdge* e = edge0->opposite()->next();
+          if (likely(has_front1))
+          {
+            assert(e->hasOpposite());
+            assert(edge0->prev()->opposite()->prev()->hasOpposite());
+            v00 = load(e->opposite()->prev(),vertices,stride);
+          } 
+          else {
+            assert(!e->hasOpposite());
+            v00 = 2.0f*v01-v02;
+          }
+        }
+        else
+        {
+          if (likely(has_front1)) {
+            assert(!edge0->prev()->opposite()->prev()->hasOpposite());
+            v00 = 2.0f*v10-v20;
+          }
+          else {
+            assert(edge0->vertex_crease_weight == 0.0f || std::isinf(edge0->vertex_crease_weight));
+            v00 = convex_corner(edge0->vertex_crease_weight,v01,v02,v10,v11,v12,v20,v21,v22);
+          }
+        }
+      }
+      
+      void init(const HalfEdge* edge0, const char* vertices, size_t stride)
+      {
+        assert( edge0->isRegularFace() );
+        
+        /* fill inner vertices */
+        const Vertex v11 = v[1][1] = load(edge0,vertices,stride); const HalfEdge* edge1 = edge0->next();
+        const Vertex v12 = v[1][2] = load(edge1,vertices,stride); const HalfEdge* edge2 = edge1->next();
+        const Vertex v22 = v[2][2] = load(edge2,vertices,stride); const HalfEdge* edge3 = edge2->next();
+        const Vertex v21 = v[2][1] = load(edge3,vertices,stride); assert(edge0  == edge3->next());
+        
+        /* fill border vertices */
+        init_border(edge0,vertices,stride,v[0][1],v[0][2],v11,v12,v21,v22);
+        init_border(edge1,vertices,stride,v[1][3],v[2][3],v12,v22,v11,v21);
+        init_border(edge2,vertices,stride,v[3][2],v[3][1],v22,v21,v12,v11);
+        init_border(edge3,vertices,stride,v[2][0],v[1][0],v21,v11,v22,v12);
+        
+        /* fill corner vertices */
+        init_corner(edge0,vertices,stride,v[0][0],v[0][1],v[0][2],v[1][0],v11,v12,v[2][0],v21,v22);
+        init_corner(edge1,vertices,stride,v[0][3],v[1][3],v[2][3],v[0][2],v12,v22,v[0][1],v11,v21);
+        init_corner(edge2,vertices,stride,v[3][3],v[3][2],v[3][1],v[2][3],v22,v21,v[1][3],v12,v11);
+        init_corner(edge3,vertices,stride,v[3][0],v[2][0],v[1][0],v[3][1],v21,v11,v[3][2],v22,v12);
+      }
+      
+      __forceinline BBox<Vertex> bounds() const
+      {
+        const Vertex* const cv = &v[0][0];
+        BBox<Vertex> bounds (cv[0]);
+        for (size_t i=1; i<16 ; i++)
+          bounds.extend( cv[i] );
+        return bounds;
+      }
+      
+      __forceinline Vertex eval(const float uu, const float vv) const
+      {
+        const Vec4f v_n = BSplineBasis::eval(vv);
+        const Vertex_t curve0 = madd(v_n[0],v[0][0],madd(v_n[1],v[1][0],madd(v_n[2],v[2][0],v_n[3] * v[3][0])));
+        const Vertex_t curve1 = madd(v_n[0],v[0][1],madd(v_n[1],v[1][1],madd(v_n[2],v[2][1],v_n[3] * v[3][1])));
+        const Vertex_t curve2 = madd(v_n[0],v[0][2],madd(v_n[1],v[1][2],madd(v_n[2],v[2][2],v_n[3] * v[3][2])));
+        const Vertex_t curve3 = madd(v_n[0],v[0][3],madd(v_n[1],v[1][3],madd(v_n[2],v[2][3],v_n[3] * v[3][3])));
+        
+        const Vec4f u_n = BSplineBasis::eval(uu);
+        return madd(u_n[0],curve0,madd(u_n[1],curve1,madd(u_n[2],curve2,u_n[3] * curve3)));
+      }
+      
+      __forceinline Vertex eval_du(const float uu, const float vv) const
+      {
+        const Vec4f v_n = BSplineBasis::eval(vv);
+        const Vertex_t curve0 = madd(v_n[0],v[0][0],madd(v_n[1],v[1][0],madd(v_n[2],v[2][0],v_n[3] * v[3][0])));
+        const Vertex_t curve1 = madd(v_n[0],v[0][1],madd(v_n[1],v[1][1],madd(v_n[2],v[2][1],v_n[3] * v[3][1])));
+        const Vertex_t curve2 = madd(v_n[0],v[0][2],madd(v_n[1],v[1][2],madd(v_n[2],v[2][2],v_n[3] * v[3][2])));
+        const Vertex_t curve3 = madd(v_n[0],v[0][3],madd(v_n[1],v[1][3],madd(v_n[2],v[2][3],v_n[3] * v[3][3])));
+        
+        const Vec4f u_n = BSplineBasis::derivative(uu);
+        return madd(u_n[0],curve0,madd(u_n[1],curve1,madd(u_n[2],curve2,u_n[3] * curve3)));
+      }
+      
+      __forceinline Vertex eval_dv(const float uu, const float vv) const
+      {
+        const Vec4f v_n = BSplineBasis::derivative(vv);
+        const Vertex_t curve0 = madd(v_n[0],v[0][0],madd(v_n[1],v[1][0],madd(v_n[2],v[2][0],v_n[3] * v[3][0])));
+        const Vertex_t curve1 = madd(v_n[0],v[0][1],madd(v_n[1],v[1][1],madd(v_n[2],v[2][1],v_n[3] * v[3][1])));
+        const Vertex_t curve2 = madd(v_n[0],v[0][2],madd(v_n[1],v[1][2],madd(v_n[2],v[2][2],v_n[3] * v[3][2])));
+        const Vertex_t curve3 = madd(v_n[0],v[0][3],madd(v_n[1],v[1][3],madd(v_n[2],v[2][3],v_n[3] * v[3][3])));
+        
+        const Vec4f u_n = BSplineBasis::eval(uu);
+        return madd(u_n[0],curve0,madd(u_n[1],curve1,madd(u_n[2],curve2,u_n[3] * curve3)));
+      }
+
+      __forceinline Vertex eval_dudu(const float uu, const float vv) const
+      {
+        const Vec4f v_n = BSplineBasis::eval(vv);
+        const Vertex_t curve0 = madd(v_n[0],v[0][0],madd(v_n[1],v[1][0],madd(v_n[2],v[2][0],v_n[3] * v[3][0])));
+        const Vertex_t curve1 = madd(v_n[0],v[0][1],madd(v_n[1],v[1][1],madd(v_n[2],v[2][1],v_n[3] * v[3][1])));
+        const Vertex_t curve2 = madd(v_n[0],v[0][2],madd(v_n[1],v[1][2],madd(v_n[2],v[2][2],v_n[3] * v[3][2])));
+        const Vertex_t curve3 = madd(v_n[0],v[0][3],madd(v_n[1],v[1][3],madd(v_n[2],v[2][3],v_n[3] * v[3][3])));
+        
+        const Vec4f u_n = BSplineBasis::derivative2(uu);
+        return madd(u_n[0],curve0,madd(u_n[1],curve1,madd(u_n[2],curve2,u_n[3] * curve3)));
+      }
+
+      __forceinline Vertex eval_dvdv(const float uu, const float vv) const
+      {
+        const Vec4f v_n = BSplineBasis::derivative2(vv);
+        const Vertex_t curve0 = madd(v_n[0],v[0][0],madd(v_n[1],v[1][0],madd(v_n[2],v[2][0],v_n[3] * v[3][0])));
+        const Vertex_t curve1 = madd(v_n[0],v[0][1],madd(v_n[1],v[1][1],madd(v_n[2],v[2][1],v_n[3] * v[3][1])));
+        const Vertex_t curve2 = madd(v_n[0],v[0][2],madd(v_n[1],v[1][2],madd(v_n[2],v[2][2],v_n[3] * v[3][2])));
+        const Vertex_t curve3 = madd(v_n[0],v[0][3],madd(v_n[1],v[1][3],madd(v_n[2],v[2][3],v_n[3] * v[3][3])));
+        
+        const Vec4f u_n = BSplineBasis::eval(uu);
+        return madd(u_n[0],curve0,madd(u_n[1],curve1,madd(u_n[2],curve2,u_n[3] * curve3)));
+      }
+
+      __forceinline Vertex eval_dudv(const float uu, const float vv) const
+      {
+        const Vec4f v_n = BSplineBasis::derivative(vv);
+        const Vertex_t curve0 = madd(v_n[0],v[0][0],madd(v_n[1],v[1][0],madd(v_n[2],v[2][0],v_n[3] * v[3][0])));
+        const Vertex_t curve1 = madd(v_n[0],v[0][1],madd(v_n[1],v[1][1],madd(v_n[2],v[2][1],v_n[3] * v[3][1])));
+        const Vertex_t curve2 = madd(v_n[0],v[0][2],madd(v_n[1],v[1][2],madd(v_n[2],v[2][2],v_n[3] * v[3][2])));
+        const Vertex_t curve3 = madd(v_n[0],v[0][3],madd(v_n[1],v[1][3],madd(v_n[2],v[2][3],v_n[3] * v[3][3])));
+        
+        const Vec4f u_n = BSplineBasis::derivative(uu);
+        return madd(u_n[0],curve0,madd(u_n[1],curve1,madd(u_n[2],curve2,u_n[3] * curve3)));
+      }
+      
+      __forceinline Vertex normal(const float uu, const float vv) const
+      {
+        const Vertex tu = eval_du(uu,vv);
+        const Vertex tv = eval_dv(uu,vv);
+        return cross(tu,tv);
+      }   
+
+      template<typename T>
+      __forceinline Vec3<T> eval(const T& uu, const T& vv, const Vec4<T>& u_n, const Vec4<T>& v_n) const
+      {
+        const T curve0_x = madd(v_n[0],T(v[0][0].x),madd(v_n[1],T(v[1][0].x),madd(v_n[2],T(v[2][0].x),v_n[3] * T(v[3][0].x))));
+        const T curve1_x = madd(v_n[0],T(v[0][1].x),madd(v_n[1],T(v[1][1].x),madd(v_n[2],T(v[2][1].x),v_n[3] * T(v[3][1].x))));
+        const T curve2_x = madd(v_n[0],T(v[0][2].x),madd(v_n[1],T(v[1][2].x),madd(v_n[2],T(v[2][2].x),v_n[3] * T(v[3][2].x))));
+        const T curve3_x = madd(v_n[0],T(v[0][3].x),madd(v_n[1],T(v[1][3].x),madd(v_n[2],T(v[2][3].x),v_n[3] * T(v[3][3].x))));
+        const T x = madd(u_n[0],curve0_x,madd(u_n[1],curve1_x,madd(u_n[2],curve2_x,u_n[3] * curve3_x)));
+                  
+        const T curve0_y = madd(v_n[0],T(v[0][0].y),madd(v_n[1],T(v[1][0].y),madd(v_n[2],T(v[2][0].y),v_n[3] * T(v[3][0].y))));
+        const T curve1_y = madd(v_n[0],T(v[0][1].y),madd(v_n[1],T(v[1][1].y),madd(v_n[2],T(v[2][1].y),v_n[3] * T(v[3][1].y))));
+        const T curve2_y = madd(v_n[0],T(v[0][2].y),madd(v_n[1],T(v[1][2].y),madd(v_n[2],T(v[2][2].y),v_n[3] * T(v[3][2].y))));
+        const T curve3_y = madd(v_n[0],T(v[0][3].y),madd(v_n[1],T(v[1][3].y),madd(v_n[2],T(v[2][3].y),v_n[3] * T(v[3][3].y))));
+        const T y = madd(u_n[0],curve0_y,madd(u_n[1],curve1_y,madd(u_n[2],curve2_y,u_n[3] * curve3_y)));
+          
+        const T curve0_z = madd(v_n[0],T(v[0][0].z),madd(v_n[1],T(v[1][0].z),madd(v_n[2],T(v[2][0].z),v_n[3] * T(v[3][0].z))));
+        const T curve1_z = madd(v_n[0],T(v[0][1].z),madd(v_n[1],T(v[1][1].z),madd(v_n[2],T(v[2][1].z),v_n[3] * T(v[3][1].z))));
+        const T curve2_z = madd(v_n[0],T(v[0][2].z),madd(v_n[1],T(v[1][2].z),madd(v_n[2],T(v[2][2].z),v_n[3] * T(v[3][2].z))));
+        const T curve3_z = madd(v_n[0],T(v[0][3].z),madd(v_n[1],T(v[1][3].z),madd(v_n[2],T(v[2][3].z),v_n[3] * T(v[3][3].z))));
+        const T z = madd(u_n[0],curve0_z,madd(u_n[1],curve1_z,madd(u_n[2],curve2_z,u_n[3] * curve3_z)));
+        
+        return Vec3<T>(x,y,z);
+      }
+      
+      template<typename T>
+      __forceinline Vec3<T> eval(const T& uu, const T& vv) const
+      {
+        const Vec4<T> u_n = BSplineBasis::eval(uu);
+        const Vec4<T> v_n = BSplineBasis::eval(vv);
+        return eval(uu,vv,u_n,v_n);
+      }
+
+      template<typename T>
+      __forceinline Vec3<T> eval_du(const T& uu, const T& vv) const
+      {
+        const Vec4<T> u_n = BSplineBasis::derivative(uu); 
+        const Vec4<T> v_n = BSplineBasis::eval(vv); 
+        return eval(uu,vv,u_n,v_n);      
+      }
+      
+      template<typename T>
+      __forceinline Vec3<T> eval_dv(const T& uu, const T& vv) const
+      {
+        const Vec4<T> u_n = BSplineBasis::eval(uu); 
+        const Vec4<T> v_n = BSplineBasis::derivative(vv); 
+        return eval(uu,vv,u_n,v_n);      
+      }
+
+      template<typename T>
+      __forceinline Vec3<T> eval_dudu(const T& uu, const T& vv) const
+      {
+        const Vec4<T> u_n = BSplineBasis::derivative2(uu); 
+        const Vec4<T> v_n = BSplineBasis::eval(vv); 
+        return eval(uu,vv,u_n,v_n);      
+      }
+
+      template<typename T>
+      __forceinline Vec3<T> eval_dvdv(const T& uu, const T& vv) const
+      {
+        const Vec4<T> u_n = BSplineBasis::eval(uu); 
+        const Vec4<T> v_n = BSplineBasis::derivative2(vv); 
+        return eval(uu,vv,u_n,v_n);      
+      }
+
+      template<typename T>
+      __forceinline Vec3<T> eval_dudv(const T& uu, const T& vv) const
+      {
+        const Vec4<T> u_n = BSplineBasis::derivative(uu); 
+        const Vec4<T> v_n = BSplineBasis::derivative(vv); 
+        return eval(uu,vv,u_n,v_n);      
+      }
+      
+      template<typename T>
+      __forceinline Vec3<T> normal(const T& uu, const T& vv) const {
+        return cross(eval_du(uu,vv),eval_dv(uu,vv));
+      }
+
+      void eval(const float u, const float v, 
+                Vertex* P, Vertex* dPdu, Vertex* dPdv, Vertex* ddPdudu, Vertex* ddPdvdv, Vertex* ddPdudv, 
+                const float dscale = 1.0f) const
+      {
+        if (P) {
+          *P = eval(u,v); 
+        }
+        if (dPdu) {
+          assert(dPdu); *dPdu = eval_du(u,v)*dscale; 
+          assert(dPdv); *dPdv = eval_dv(u,v)*dscale; 
+        }
+        if (ddPdudu) {
+          assert(ddPdudu); *ddPdudu = eval_dudu(u,v)*sqr(dscale); 
+          assert(ddPdvdv); *ddPdvdv = eval_dvdv(u,v)*sqr(dscale); 
+          assert(ddPdudv); *ddPdudv = eval_dudv(u,v)*sqr(dscale); 
+        }
+      }
+
+      template<class vfloat>
+      __forceinline vfloat eval(const size_t i, const vfloat& uu, const vfloat& vv, const Vec4<vfloat>& u_n, const Vec4<vfloat>& v_n) const
+      {
+        const vfloat curve0_x = madd(v_n[0],vfloat(v[0][0][i]),madd(v_n[1],vfloat(v[1][0][i]),madd(v_n[2],vfloat(v[2][0][i]),v_n[3] * vfloat(v[3][0][i]))));
+        const vfloat curve1_x = madd(v_n[0],vfloat(v[0][1][i]),madd(v_n[1],vfloat(v[1][1][i]),madd(v_n[2],vfloat(v[2][1][i]),v_n[3] * vfloat(v[3][1][i]))));
+        const vfloat curve2_x = madd(v_n[0],vfloat(v[0][2][i]),madd(v_n[1],vfloat(v[1][2][i]),madd(v_n[2],vfloat(v[2][2][i]),v_n[3] * vfloat(v[3][2][i]))));
+        const vfloat curve3_x = madd(v_n[0],vfloat(v[0][3][i]),madd(v_n[1],vfloat(v[1][3][i]),madd(v_n[2],vfloat(v[2][3][i]),v_n[3] * vfloat(v[3][3][i]))));
+        return madd(u_n[0],curve0_x,madd(u_n[1],curve1_x,madd(u_n[2],curve2_x,u_n[3] * curve3_x)));
+      }
+        
+      template<typename vbool, typename vfloat>
+      void eval(const vbool& valid, const vfloat& uu, const vfloat& vv, 
+                float* P, float* dPdu, float* dPdv, float* ddPdudu, float* ddPdvdv, float* ddPdudv, 
+                const float dscale, const size_t dstride, const size_t N) const
+      {
+        if (P) {
+          const Vec4<vfloat> u_n = BSplineBasis::eval(uu); 
+          const Vec4<vfloat> v_n = BSplineBasis::eval(vv); 
+          for (size_t i=0; i<N; i++) vfloat::store(valid,P+i*dstride,eval(i,uu,vv,u_n,v_n));
+        }
+        if (dPdu) 
+        {
+          {
+            assert(dPdu);
+            const Vec4<vfloat> u_n = BSplineBasis::derivative(uu); 
+            const Vec4<vfloat> v_n = BSplineBasis::eval(vv);
+            for (size_t i=0; i<N; i++) vfloat::store(valid,dPdu+i*dstride,eval(i,uu,vv,u_n,v_n)*dscale);
+          }
+          {
+            assert(dPdv);
+            const Vec4<vfloat> u_n = BSplineBasis::eval(uu); 
+            const Vec4<vfloat> v_n = BSplineBasis::derivative(vv);
+            for (size_t i=0; i<N; i++) vfloat::store(valid,dPdv+i*dstride,eval(i,uu,vv,u_n,v_n)*dscale);
+          }
+        }
+        if (ddPdudu) 
+        {
+          {
+            assert(ddPdudu);
+            const Vec4<vfloat> u_n = BSplineBasis::derivative2(uu); 
+            const Vec4<vfloat> v_n = BSplineBasis::eval(vv);
+            for (size_t i=0; i<N; i++) vfloat::store(valid,ddPdudu+i*dstride,eval(i,uu,vv,u_n,v_n)*sqr(dscale));
+          }
+          {
+            assert(ddPdvdv);
+            const Vec4<vfloat> u_n = BSplineBasis::eval(uu); 
+            const Vec4<vfloat> v_n = BSplineBasis::derivative2(vv);
+            for (size_t i=0; i<N; i++) vfloat::store(valid,ddPdvdv+i*dstride,eval(i,uu,vv,u_n,v_n)*sqr(dscale));
+          }
+          {
+            assert(ddPdudv);
+            const Vec4<vfloat> u_n = BSplineBasis::derivative(uu); 
+            const Vec4<vfloat> v_n = BSplineBasis::derivative(vv);
+            for (size_t i=0; i<N; i++) vfloat::store(valid,ddPdudv+i*dstride,eval(i,uu,vv,u_n,v_n)*sqr(dscale));
+          }
+        }
+      }
+
+      friend __forceinline embree_ostream operator<<(embree_ostream o, const BSplinePatchT& p)
+      {
+        for (size_t y=0; y<4; y++)
+          for (size_t x=0; x<4; x++)
+            o << "[" << y << "][" << x << "] " << p.v[y][x] << embree_endl;
+        return o;
+      } 
+
+    public:
+      Vertex v[4][4];
+    };
+  
+  typedef BSplinePatchT<Vec3fa,Vec3fa_t> BSplinePatch3fa;
+}

thirdparty/embree/kernels/subdiv/catmullclark_coefficients.h

@@ -0,0 +1,85 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "../common/geometry.h"
+
+namespace embree
+{
+  static const size_t MAX_PATCH_VALENCE = 16;         //!< maximum number of vertices of a patch
+  static const size_t MAX_RING_FACE_VALENCE = 64;     //!< maximum number of faces per ring
+  static const size_t MAX_RING_EDGE_VALENCE = 2*64;   //!< maximum number of edges per ring
+
+  class CatmullClarkPrecomputedCoefficients 
+  {
+  private:
+    
+    float table_cos_2PI_div_n[MAX_RING_FACE_VALENCE+1];
+
+    float* table_limittangent_a[MAX_RING_FACE_VALENCE+1];
+    float* table_limittangent_b[MAX_RING_FACE_VALENCE+1];
+    float table_limittangent_c[MAX_RING_FACE_VALENCE+1];
+
+    __forceinline float set_cos_2PI_div_n(const size_t n) { 
+      if (unlikely(n == 0)) return 1.0f;
+      return cosf(2.0f*float(pi)/(float)n); 
+    }
+
+    __forceinline float set_limittangent_a(const size_t i, const size_t n)  
+    { 
+      if (unlikely(n == 0)) return 1.0f;
+      const float c0 = 1.0f/(float)n * 1.0f / sqrtf(4.0f + cosf(float(pi)/(float)n)*cosf(float(pi)/(float)n));
+      const float c1 = (1.0f/(float)n + cosf(float(pi)/(float)n) * c0); 
+      return cosf(2.0f*float(pi)*(float)i/(float)n) * c1;
+    }
+
+    __forceinline float set_limittangent_b(const size_t i, const size_t n)  
+    { 
+      if (unlikely(n == 0)) return 1.0f;
+      const float c0 = 1.0f/(float)n * 1.0f / sqrtf(4.0f + cosf(float(pi)/(float)n)*cosf(float(pi)/(float)n));
+      return cosf((2.0f*float(pi)*i+float(pi))/(float)n) * c0;
+    }
+
+    __forceinline float set_limittangent_c(const size_t n)  
+    { 
+      if (unlikely(n == 0)) return 1.0f;
+      return 2.0f/16.0f * (5.0f + cosf(2.0f*float(pi)/(float)n) + cosf(float(pi)/(float)n) * sqrtf(18.0f+2.0f*cosf(2.0f*float(pi)/(float)n)));
+    }
+
+  public:
+
+    __forceinline float cos_2PI_div_n(const size_t n)
+    {
+      if (likely(n <= MAX_RING_FACE_VALENCE))
+        return table_cos_2PI_div_n[n];
+      else
+        return set_cos_2PI_div_n(n);
+    }
+
+    __forceinline float limittangent_a(const size_t i, const size_t n)
+    {
+      assert(n <= MAX_RING_FACE_VALENCE);
+      assert(i < n);
+      return table_limittangent_a[n][i];
+    }
+
+    __forceinline float limittangent_b(const size_t i, const size_t n)
+    {
+      assert(n <= MAX_RING_FACE_VALENCE);
+      assert(i < n);
+      return table_limittangent_b[n][i];
+    }
+
+    __forceinline float limittangent_c(const size_t n)
+    {
+      assert(n <= MAX_RING_FACE_VALENCE);
+      return table_limittangent_c[n];
+    }
+
+    static CatmullClarkPrecomputedCoefficients table;
+ 
+    CatmullClarkPrecomputedCoefficients();    
+    ~CatmullClarkPrecomputedCoefficients();    
+  };
+}

thirdparty/embree/kernels/subdiv/catmullclark_patch.h

@@ -0,0 +1,562 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "catmullclark_ring.h"
+#include "bezier_curve.h"
+
+namespace embree
+{
+  template<typename Vertex, typename Vertex_t = Vertex>
+    class __aligned(64) CatmullClarkPatchT
+    {
+    public:
+    typedef CatmullClark1RingT<Vertex,Vertex_t> CatmullClark1Ring;
+    typedef typename CatmullClark1Ring::Type Type;
+    
+    array_t<CatmullClark1RingT<Vertex,Vertex_t>,4> ring;
+    
+    public:
+    __forceinline CatmullClarkPatchT () {}
+
+    __forceinline CatmullClarkPatchT (const HalfEdge* first_half_edge, const char* vertices, size_t stride) {
+      init(first_half_edge,vertices,stride);
+    }
+    
+    __forceinline CatmullClarkPatchT (const HalfEdge* first_half_edge, const BufferView<Vec3fa>& vertices) {
+      init(first_half_edge,vertices.getPtr(),vertices.getStride());
+    }
+    
+    __forceinline void init (const HalfEdge* first_half_edge, const char* vertices, size_t stride) 
+    {
+      for (unsigned i=0; i<4; i++)
+        ring[i].init(first_half_edge+i,vertices,stride);
+
+      assert(verify());
+    }
+
+    __forceinline size_t bytes() const {
+      return ring[0].bytes()+ring[1].bytes()+ring[2].bytes()+ring[3].bytes();
+    }
+
+    __forceinline void serialize(void* ptr, size_t& ofs) const
+    {
+      for (size_t i=0; i<4; i++)
+        ring[i].serialize((char*)ptr,ofs);
+    }
+
+    __forceinline void deserialize(void* ptr)
+    {
+      size_t ofs = 0;
+      for (size_t i=0; i<4; i++)
+        ring[i].deserialize((char*)ptr,ofs);
+    }
+
+    __forceinline BBox3fa bounds() const
+    {
+      BBox3fa bounds (ring[0].bounds());
+      for (size_t i=1; i<4; i++)
+	bounds.extend(ring[i].bounds());
+      return bounds;
+    }
+    
+    __forceinline Type type() const 
+    {
+      const int ty0 = ring[0].type() ^ CatmullClark1Ring::TYPE_CREASES;
+      const int ty1 = ring[1].type() ^ CatmullClark1Ring::TYPE_CREASES;
+      const int ty2 = ring[2].type() ^ CatmullClark1Ring::TYPE_CREASES;
+      const int ty3 = ring[3].type() ^ CatmullClark1Ring::TYPE_CREASES;
+      return (Type) ((ty0 & ty1 & ty2 & ty3) ^ CatmullClark1Ring::TYPE_CREASES);
+    }
+    
+    __forceinline bool isFinalResolution(float res) const {
+      return ring[0].isFinalResolution(res) && ring[1].isFinalResolution(res) && ring[2].isFinalResolution(res) && ring[3].isFinalResolution(res);
+    }
+    
+    static __forceinline void init_regular(const CatmullClark1RingT<Vertex,Vertex_t>& p0,
+					   const CatmullClark1RingT<Vertex,Vertex_t>& p1,
+					   CatmullClark1RingT<Vertex,Vertex_t>& dest0,
+					   CatmullClark1RingT<Vertex,Vertex_t>& dest1) 
+    {
+      assert(p1.face_valence > 2);
+      dest1.vertex_level = dest0.vertex_level = p0.edge_level;
+      dest1.face_valence = dest0.face_valence = 4;
+      dest1.edge_valence = dest0.edge_valence = 8;
+      dest1.border_index = dest0.border_index = -1;
+      dest1.vtx = dest0.vtx = (Vertex_t)p0.ring[0];
+      dest1.vertex_crease_weight = dest0.vertex_crease_weight = 0.0f;
+      
+      dest1.ring[2] = dest0.ring[0] = (Vertex_t)p0.ring[1];
+      dest1.ring[1] = dest0.ring[7] = (Vertex_t)p1.ring[0];
+      dest1.ring[0] = dest0.ring[6] = (Vertex_t)p1.vtx;
+      dest1.ring[7] = dest0.ring[5] = (Vertex_t)p1.ring[4];
+      dest1.ring[6] = dest0.ring[4] = (Vertex_t)p0.ring[p0.edge_valence-1];
+      dest1.ring[5] = dest0.ring[3] = (Vertex_t)p0.ring[p0.edge_valence-2];
+      dest1.ring[4] = dest0.ring[2] = (Vertex_t)p0.vtx;
+      dest1.ring[3] = dest0.ring[1] = (Vertex_t)p0.ring[2];
+      
+      dest1.crease_weight[1] = dest0.crease_weight[0] = 0.0f;
+      dest1.crease_weight[0] = dest0.crease_weight[3] = p1.crease_weight[1];
+      dest1.crease_weight[3] = dest0.crease_weight[2] = 0.0f;
+      dest1.crease_weight[2] = dest0.crease_weight[1] = p0.crease_weight[0];
+      
+      if (p0.eval_unique_identifier <= p1.eval_unique_identifier)
+      {
+        dest0.eval_start_index = 3;
+        dest1.eval_start_index = 0;
+        dest0.eval_unique_identifier = p0.eval_unique_identifier;
+        dest1.eval_unique_identifier = p0.eval_unique_identifier;
+      }
+      else
+      {
+        dest0.eval_start_index = 1;
+        dest1.eval_start_index = 2;
+        dest0.eval_unique_identifier = p1.eval_unique_identifier;
+        dest1.eval_unique_identifier = p1.eval_unique_identifier;
+      }
+    }    
+    
+    static __forceinline void init_border(const CatmullClark1RingT<Vertex,Vertex_t> &p0,
+                                          const CatmullClark1RingT<Vertex,Vertex_t> &p1,
+                                          CatmullClark1RingT<Vertex,Vertex_t> &dest0,
+                                          CatmullClark1RingT<Vertex,Vertex_t> &dest1) 
+    {
+      dest1.vertex_level = dest0.vertex_level = p0.edge_level;
+      dest1.face_valence = dest0.face_valence = 3;
+      dest1.edge_valence = dest0.edge_valence = 6;
+      dest0.border_index = 2;
+      dest1.border_index = 4;
+      dest1.vtx  = dest0.vtx = (Vertex_t)p0.ring[0];
+      dest1.vertex_crease_weight = dest0.vertex_crease_weight = 0.0f;
+      
+      dest1.ring[2] = dest0.ring[0] = (Vertex_t)p0.ring[1];
+      dest1.ring[1] = dest0.ring[5] = (Vertex_t)p1.ring[0];
+      dest1.ring[0] = dest0.ring[4] = (Vertex_t)p1.vtx;
+      dest1.ring[5] = dest0.ring[3] = (Vertex_t)p0.ring[p0.border_index+1]; // dummy
+      dest1.ring[4] = dest0.ring[2] = (Vertex_t)p0.vtx;
+      dest1.ring[3] = dest0.ring[1] = (Vertex_t)p0.ring[2];
+      
+      dest1.crease_weight[1] = dest0.crease_weight[0] = 0.0f;
+      dest1.crease_weight[0] = dest0.crease_weight[2] = p1.crease_weight[1];
+      dest1.crease_weight[2] = dest0.crease_weight[1] = p0.crease_weight[0];
+      
+      if (p0.eval_unique_identifier <= p1.eval_unique_identifier)
+      {
+        dest0.eval_start_index = 1;
+        dest1.eval_start_index = 2;
+        dest0.eval_unique_identifier = p0.eval_unique_identifier;
+        dest1.eval_unique_identifier = p0.eval_unique_identifier;
+      }
+      else
+      {
+        dest0.eval_start_index = 2;
+        dest1.eval_start_index = 0;
+        dest0.eval_unique_identifier = p1.eval_unique_identifier;
+        dest1.eval_unique_identifier = p1.eval_unique_identifier;
+      }
+    }
+    
+    static __forceinline void init_regular(const Vertex_t &center, const Vertex_t center_ring[8], const unsigned int offset, CatmullClark1RingT<Vertex,Vertex_t> &dest)
+    {
+      dest.vertex_level = 0.0f;
+      dest.face_valence = 4;
+      dest.edge_valence = 8;
+      dest.border_index = -1;
+      dest.vtx     = (Vertex_t)center;
+      dest.vertex_crease_weight = 0.0f;
+      for (size_t i=0; i<8; i++) 
+	dest.ring[i] = (Vertex_t)center_ring[(offset+i)%8];
+      for (size_t i=0; i<4; i++) 
+        dest.crease_weight[i] = 0.0f;
+      
+      dest.eval_start_index = (8-offset)>>1;
+      if (dest.eval_start_index >= dest.face_valence) dest.eval_start_index -= dest.face_valence;
+      assert( dest.eval_start_index < dest.face_valence );
+      dest.eval_unique_identifier = 0;
+    }
+    
+    __noinline void subdivide(array_t<CatmullClarkPatchT,4>& patch) const
+    {
+      ring[0].subdivide(patch[0].ring[0]);
+      ring[1].subdivide(patch[1].ring[1]);
+      ring[2].subdivide(patch[2].ring[2]);
+      ring[3].subdivide(patch[3].ring[3]);
+      
+      patch[0].ring[0].edge_level = 0.5f*ring[0].edge_level;
+      patch[0].ring[1].edge_level = 0.25f*(ring[1].edge_level+ring[3].edge_level);
+      patch[0].ring[2].edge_level = 0.25f*(ring[0].edge_level+ring[2].edge_level);
+      patch[0].ring[3].edge_level = 0.5f*ring[3].edge_level;
+      
+      patch[1].ring[0].edge_level = 0.5f*ring[0].edge_level;
+      patch[1].ring[1].edge_level = 0.5f*ring[1].edge_level;
+      patch[1].ring[2].edge_level = 0.25f*(ring[0].edge_level+ring[2].edge_level);
+      patch[1].ring[3].edge_level = 0.25f*(ring[1].edge_level+ring[3].edge_level);
+      
+      patch[2].ring[0].edge_level = 0.25f*(ring[0].edge_level+ring[2].edge_level);
+      patch[2].ring[1].edge_level = 0.5f*ring[1].edge_level;
+      patch[2].ring[2].edge_level = 0.5f*ring[2].edge_level;
+      patch[2].ring[3].edge_level = 0.25f*(ring[1].edge_level+ring[3].edge_level);
+      
+      patch[3].ring[0].edge_level = 0.25f*(ring[0].edge_level+ring[2].edge_level);
+      patch[3].ring[1].edge_level = 0.25f*(ring[1].edge_level+ring[3].edge_level);
+      patch[3].ring[2].edge_level = 0.5f*ring[2].edge_level;
+      patch[3].ring[3].edge_level = 0.5f*ring[3].edge_level;
+      
+      const bool regular0 = ring[0].has_last_face() && ring[1].face_valence > 2;
+      if (likely(regular0))
+        init_regular(patch[0].ring[0],patch[1].ring[1],patch[0].ring[1],patch[1].ring[0]);
+      else
+        init_border(patch[0].ring[0],patch[1].ring[1],patch[0].ring[1],patch[1].ring[0]);
+      
+      const bool regular1 = ring[1].has_last_face() && ring[2].face_valence > 2;
+      if (likely(regular1))
+        init_regular(patch[1].ring[1],patch[2].ring[2],patch[1].ring[2],patch[2].ring[1]);
+      else
+        init_border(patch[1].ring[1],patch[2].ring[2],patch[1].ring[2],patch[2].ring[1]);
+      
+      const bool regular2 = ring[2].has_last_face() && ring[3].face_valence > 2;
+      if (likely(regular2))
+        init_regular(patch[2].ring[2],patch[3].ring[3],patch[2].ring[3],patch[3].ring[2]);
+      else
+        init_border(patch[2].ring[2],patch[3].ring[3],patch[2].ring[3],patch[3].ring[2]);
+      
+      const bool regular3 = ring[3].has_last_face() && ring[0].face_valence > 2;
+      if (likely(regular3))
+        init_regular(patch[3].ring[3],patch[0].ring[0],patch[3].ring[0],patch[0].ring[3]);
+      else
+        init_border(patch[3].ring[3],patch[0].ring[0],patch[3].ring[0],patch[0].ring[3]);
+      
+      Vertex_t center = (ring[0].vtx + ring[1].vtx + ring[2].vtx + ring[3].vtx) * 0.25f;
+
+      Vertex_t center_ring[8];
+      center_ring[0] = (Vertex_t)patch[3].ring[3].ring[0];
+      center_ring[7] = (Vertex_t)patch[3].ring[3].vtx;
+      center_ring[6] = (Vertex_t)patch[2].ring[2].ring[0];
+      center_ring[5] = (Vertex_t)patch[2].ring[2].vtx;
+      center_ring[4] = (Vertex_t)patch[1].ring[1].ring[0];
+      center_ring[3] = (Vertex_t)patch[1].ring[1].vtx;
+      center_ring[2] = (Vertex_t)patch[0].ring[0].ring[0];
+      center_ring[1] = (Vertex_t)patch[0].ring[0].vtx;
+      
+      init_regular(center,center_ring,0,patch[0].ring[2]);
+      init_regular(center,center_ring,2,patch[1].ring[3]);
+      init_regular(center,center_ring,4,patch[2].ring[0]);
+      init_regular(center,center_ring,6,patch[3].ring[1]);
+      
+      assert(patch[0].verify());
+      assert(patch[1].verify());
+      assert(patch[2].verify());
+      assert(patch[3].verify());
+    }
+    
+    bool verify() const {
+      return ring[0].hasValidPositions() && ring[1].hasValidPositions() && ring[2].hasValidPositions() && ring[3].hasValidPositions();
+    }
+    
+    __forceinline void init( FinalQuad& quad ) const
+    {
+      quad.vtx[0] = (Vertex_t)ring[0].vtx;
+      quad.vtx[1] = (Vertex_t)ring[1].vtx;
+      quad.vtx[2] = (Vertex_t)ring[2].vtx;
+      quad.vtx[3] = (Vertex_t)ring[3].vtx;
+    };
+    
+    friend __forceinline embree_ostream operator<<(embree_ostream o, const CatmullClarkPatchT &p)
+    {
+      o << "CatmullClarkPatch { " << embree_endl;
+      for (size_t i=0; i<4; i++)
+	o << "ring" << i << ": " << p.ring[i] << embree_endl;
+      o << "}" << embree_endl;
+      return o;
+    }
+    };
+  
+  typedef CatmullClarkPatchT<Vec3fa,Vec3fa_t> CatmullClarkPatch3fa;
+  
+  template<typename Vertex, typename Vertex_t = Vertex>
+    class __aligned(64) GeneralCatmullClarkPatchT
+    {
+    public:
+    typedef CatmullClarkPatchT<Vertex,Vertex_t> CatmullClarkPatch;
+    typedef CatmullClark1RingT<Vertex,Vertex_t> CatmullClark1Ring;
+    typedef BezierCurveT<Vertex> BezierCurve;
+
+    static const unsigned SIZE = MAX_PATCH_VALENCE;
+    DynamicStackArray<GeneralCatmullClark1RingT<Vertex,Vertex_t>,8,SIZE> ring;
+    unsigned N;
+    
+    __forceinline GeneralCatmullClarkPatchT () 
+    : N(0) {}
+    
+    GeneralCatmullClarkPatchT (const HalfEdge* h, const char* vertices, size_t stride) {
+      init(h,vertices,stride);
+    }
+
+    __forceinline GeneralCatmullClarkPatchT (const HalfEdge* first_half_edge, const BufferView<Vec3fa>& vertices) {
+      init(first_half_edge,vertices.getPtr(),vertices.getStride());
+    }
+
+    __forceinline void init (const HalfEdge* h, const char* vertices, size_t stride) 
+    {
+      unsigned int i = 0;
+      const HalfEdge* edge = h; 
+      do {
+        ring[i].init(edge,vertices,stride);
+        edge = edge->next();
+        i++;
+      } while ((edge != h) && (i < SIZE));
+      N = i;
+    }
+
+    __forceinline unsigned size() const { 
+      return N; 
+    }
+    
+    __forceinline bool isQuadPatch() const {
+      return (N == 4) && ring[0].only_quads && ring[1].only_quads && ring[2].only_quads && ring[3].only_quads;
+    }
+
+    static __forceinline void init_regular(const CatmullClark1RingT<Vertex,Vertex_t>& p0,
+					   const CatmullClark1RingT<Vertex,Vertex_t>& p1,
+					   CatmullClark1RingT<Vertex,Vertex_t>& dest0,
+					   CatmullClark1RingT<Vertex,Vertex_t>& dest1) 
+    {
+      assert(p1.face_valence > 2);
+      dest1.vertex_level = dest0.vertex_level = p0.edge_level;
+      dest1.face_valence = dest0.face_valence = 4;
+      dest1.edge_valence = dest0.edge_valence = 8;
+      dest1.border_index = dest0.border_index = -1;
+      dest1.vtx = dest0.vtx = (Vertex_t)p0.ring[0];
+      dest1.vertex_crease_weight = dest0.vertex_crease_weight = 0.0f;
+      
+      dest1.ring[2] = dest0.ring[0] = (Vertex_t)p0.ring[1];
+      dest1.ring[1] = dest0.ring[7] = (Vertex_t)p1.ring[0];
+      dest1.ring[0] = dest0.ring[6] = (Vertex_t)p1.vtx;
+      dest1.ring[7] = dest0.ring[5] = (Vertex_t)p1.ring[4];
+      dest1.ring[6] = dest0.ring[4] = (Vertex_t)p0.ring[p0.edge_valence-1];
+      dest1.ring[5] = dest0.ring[3] = (Vertex_t)p0.ring[p0.edge_valence-2];
+      dest1.ring[4] = dest0.ring[2] = (Vertex_t)p0.vtx;
+      dest1.ring[3] = dest0.ring[1] = (Vertex_t)p0.ring[2];
+      
+      dest1.crease_weight[1] = dest0.crease_weight[0] = 0.0f;
+      dest1.crease_weight[0] = dest0.crease_weight[3] = p1.crease_weight[1];
+      dest1.crease_weight[3] = dest0.crease_weight[2] = 0.0f;
+      dest1.crease_weight[2] = dest0.crease_weight[1] = p0.crease_weight[0];
+      
+      if (p0.eval_unique_identifier <= p1.eval_unique_identifier)
+      {
+        dest0.eval_start_index = 3;
+        dest1.eval_start_index = 0;
+        dest0.eval_unique_identifier = p0.eval_unique_identifier;
+        dest1.eval_unique_identifier = p0.eval_unique_identifier;
+      }
+      else
+      {
+        dest0.eval_start_index = 1;
+        dest1.eval_start_index = 2;
+        dest0.eval_unique_identifier = p1.eval_unique_identifier;
+        dest1.eval_unique_identifier = p1.eval_unique_identifier;
+      }      
+    }
+    
+    
+    static __forceinline void init_border(const CatmullClark1RingT<Vertex,Vertex_t> &p0,
+                                          const CatmullClark1RingT<Vertex,Vertex_t> &p1,
+                                          CatmullClark1RingT<Vertex,Vertex_t> &dest0,
+                                          CatmullClark1RingT<Vertex,Vertex_t> &dest1) 
+    {
+      dest1.vertex_level = dest0.vertex_level = p0.edge_level;
+      dest1.face_valence = dest0.face_valence = 3;
+      dest1.edge_valence = dest0.edge_valence = 6;
+      dest0.border_index = 2;
+      dest1.border_index = 4;
+      dest1.vtx  = dest0.vtx = (Vertex_t)p0.ring[0];
+      dest1.vertex_crease_weight = dest0.vertex_crease_weight = 0.0f;
+      
+      dest1.ring[2] = dest0.ring[0] = (Vertex_t)p0.ring[1];
+      dest1.ring[1] = dest0.ring[5] = (Vertex_t)p1.ring[0];
+      dest1.ring[0] = dest0.ring[4] = (Vertex_t)p1.vtx;
+      dest1.ring[5] = dest0.ring[3] = (Vertex_t)p0.ring[p0.border_index+1]; // dummy
+      dest1.ring[4] = dest0.ring[2] = (Vertex_t)p0.vtx;
+      dest1.ring[3] = dest0.ring[1] = (Vertex_t)p0.ring[2];
+      
+      dest1.crease_weight[1] = dest0.crease_weight[0] = 0.0f;
+      dest1.crease_weight[0] = dest0.crease_weight[2] = p1.crease_weight[1];
+      dest1.crease_weight[2] = dest0.crease_weight[1] = p0.crease_weight[0];
+      
+      if (p0.eval_unique_identifier <= p1.eval_unique_identifier)
+      {
+        dest0.eval_start_index = 1;
+        dest1.eval_start_index = 2;
+        dest0.eval_unique_identifier = p0.eval_unique_identifier;
+        dest1.eval_unique_identifier = p0.eval_unique_identifier;
+      }
+      else
+      {
+        dest0.eval_start_index = 2;
+        dest1.eval_start_index = 0;
+        dest0.eval_unique_identifier = p1.eval_unique_identifier;
+        dest1.eval_unique_identifier = p1.eval_unique_identifier;
+      }
+    }
+    
+    static __forceinline void init_regular(const Vertex_t &center, const array_t<Vertex_t,2*SIZE>& center_ring, const float vertex_level, const unsigned int N, const unsigned int offset, CatmullClark1RingT<Vertex,Vertex_t> &dest)
+    {
+      assert(N<(MAX_RING_FACE_VALENCE));
+      assert(2*N<(MAX_RING_EDGE_VALENCE));
+      dest.vertex_level = vertex_level;
+      dest.face_valence = N;
+      dest.edge_valence = 2*N;
+      dest.border_index = -1;
+      dest.vtx     = (Vertex_t)center;
+      dest.vertex_crease_weight = 0.0f;
+      for (unsigned i=0; i<2*N; i++) {
+        dest.ring[i] = (Vertex_t)center_ring[(2*N+offset+i-1)%(2*N)];
+        assert(isvalid(dest.ring[i]));
+      }
+      for (unsigned i=0; i<N; i++) 
+        dest.crease_weight[i] = 0.0f;
+      
+      assert(offset <= 2*N);
+      dest.eval_start_index = (2*N-offset)>>1;
+      if (dest.eval_start_index >= dest.face_valence) dest.eval_start_index -= dest.face_valence;
+      
+      assert( dest.eval_start_index < dest.face_valence );
+      dest.eval_unique_identifier = 0;
+    }
+    
+    __noinline void subdivide(array_t<CatmullClarkPatch,SIZE>& patch, unsigned& N_o) const
+    {
+      N_o = N;
+      assert( N );
+      for (unsigned i=0; i<N; i++) {
+        unsigned ip1 = (i+1)%N; // FIXME: %
+        ring[i].subdivide(patch[i].ring[0]);
+        patch[i]  .ring[0].edge_level = 0.5f*ring[i].edge_level;
+        patch[ip1].ring[3].edge_level = 0.5f*ring[i].edge_level;
+        
+	assert( patch[i].ring[0].hasValidPositions() );
+        
+      }
+      assert(N < 2*SIZE);
+      Vertex_t center = Vertex_t(0.0f);
+      array_t<Vertex_t,2*SIZE> center_ring;
+      float center_vertex_level = 2.0f; // guarantees that irregular vertices get always isolated also for non-quads
+      
+      for (unsigned i=0; i<N; i++)
+      {
+        unsigned ip1 = (i+1)%N; // FIXME: %
+        unsigned im1 = (i+N-1)%N; // FIXME: %
+        bool regular = ring[i].has_last_face() && ring[ip1].face_valence > 2;
+        if (likely(regular)) init_regular(patch[i].ring[0],patch[ip1].ring[0],patch[i].ring[1],patch[ip1].ring[3]); 
+        else                 init_border (patch[i].ring[0],patch[ip1].ring[0],patch[i].ring[1],patch[ip1].ring[3]);
+        
+	assert( patch[i].ring[1].hasValidPositions() );
+	assert( patch[ip1].ring[3].hasValidPositions() );
+        
+	float level = 0.25f*(ring[im1].edge_level+ring[ip1].edge_level);
+        patch[i].ring[1].edge_level = patch[ip1].ring[2].edge_level = level;
+	center_vertex_level = max(center_vertex_level,level);
+        
+        center += ring[i].vtx;
+        center_ring[2*i+0] = (Vertex_t)patch[i].ring[0].vtx;
+        center_ring[2*i+1] = (Vertex_t)patch[i].ring[0].ring[0];
+      }
+      center /= float(N);
+      
+      for (unsigned int i=0; i<N; i++) {
+        init_regular(center,center_ring,center_vertex_level,N,2*i,patch[i].ring[2]);
+        
+	assert( patch[i].ring[2].hasValidPositions() );
+      }
+    }
+    
+    void init(CatmullClarkPatch& patch) const
+    {
+      assert(size() == 4);
+      ring[0].convert(patch.ring[0]);
+      ring[1].convert(patch.ring[1]);
+      ring[2].convert(patch.ring[2]);
+      ring[3].convert(patch.ring[3]);
+    }
+    
+    static void fix_quad_ring_order (array_t<CatmullClarkPatch,GeneralCatmullClarkPatchT::SIZE>& patches)
+    {
+      CatmullClark1Ring patches1ring1 = patches[1].ring[1];
+      patches[1].ring[1] = patches[1].ring[0]; // FIXME: optimize these assignments
+      patches[1].ring[0] = patches[1].ring[3];
+      patches[1].ring[3] = patches[1].ring[2];
+      patches[1].ring[2] = patches1ring1;
+      
+      CatmullClark1Ring patches2ring2 = patches[2].ring[2];
+      patches[2].ring[2] = patches[2].ring[0];
+      patches[2].ring[0] = patches2ring2;
+      CatmullClark1Ring patches2ring3 = patches[2].ring[3];
+      patches[2].ring[3] = patches[2].ring[1];
+      patches[2].ring[1] = patches2ring3;
+      
+      CatmullClark1Ring patches3ring3 = patches[3].ring[3];
+      patches[3].ring[3] = patches[3].ring[0];
+      patches[3].ring[0] = patches[3].ring[1];
+      patches[3].ring[1] = patches[3].ring[2];
+      patches[3].ring[2] = patches3ring3;
+    }
+
+    __forceinline void getLimitBorder(BezierCurve curves[GeneralCatmullClarkPatchT::SIZE]) const
+    {
+      Vertex P0 = ring[0].getLimitVertex();
+      for (unsigned i=0; i<N; i++)
+      {
+        const unsigned i0 = i, i1 = i+1==N ? 0 : i+1;
+        const Vertex P1 = madd(1.0f/3.0f,ring[i0].getLimitTangent(),P0);
+        const Vertex P3 = ring[i1].getLimitVertex();
+        const Vertex P2 = madd(1.0f/3.0f,ring[i1].getSecondLimitTangent(),P3);
+        new (&curves[i]) BezierCurve(P0,P1,P2,P3);
+        P0 = P3;
+      }
+    }
+
+    __forceinline void getLimitBorder(BezierCurve curves[2], const unsigned subPatch) const
+    {
+      const unsigned i0 = subPatch;
+      const Vertex t0_p = ring[i0].getLimitTangent();
+      const Vertex t0_m = ring[i0].getSecondLimitTangent();
+          
+      const unsigned i1 = subPatch+1 == N ? 0 : subPatch+1;
+      const Vertex t1_p = ring[i1].getLimitTangent();
+      const Vertex t1_m = ring[i1].getSecondLimitTangent();
+      
+      const unsigned i2 = subPatch == 0 ? N-1 : subPatch-1;
+      const Vertex t2_p = ring[i2].getLimitTangent();
+      const Vertex t2_m = ring[i2].getSecondLimitTangent();
+      
+      const Vertex b00 = ring[i0].getLimitVertex();
+      const Vertex b03 = ring[i1].getLimitVertex();
+      const Vertex b33 = ring[i2].getLimitVertex();
+      
+      const Vertex b01 = madd(1.0/3.0f,t0_p,b00);
+      const Vertex b11 = madd(1.0/3.0f,t0_m,b00);
+      
+      //const Vertex b13 = madd(1.0/3.0f,t1_p,b03);
+      const Vertex b02 = madd(1.0/3.0f,t1_m,b03);
+          
+      const Vertex b22 = madd(1.0/3.0f,t2_p,b33);
+      const Vertex b23 = madd(1.0/3.0f,t2_m,b33);
+          
+      new (&curves[0]) BezierCurve(b00,b01,b02,b03);
+      new (&curves[1]) BezierCurve(b33,b22,b11,b00);
+    }
+    
+    friend __forceinline embree_ostream operator<<(embree_ostream o, const GeneralCatmullClarkPatchT &p)
+    {
+      o << "GeneralCatmullClarkPatch { " << embree_endl;
+      for (unsigned i=0; i<p.N; i++)
+	o << "ring" << i << ": " << p.ring[i] << embree_endl;
+      o << "}" << embree_endl;
+      return o;
+    }
+    };
+  
+  typedef GeneralCatmullClarkPatchT<Vec3fa,Vec3fa_t> GeneralCatmullClarkPatch3fa;
+}

thirdparty/embree/kernels/subdiv/catmullclark_ring.h

@@ -0,0 +1,826 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "../common/geometry.h"
+#include "../common/buffer.h"
+#include "half_edge.h"
+#include "catmullclark_coefficients.h"
+
+namespace embree
+{
+  struct __aligned(64) FinalQuad {
+    Vec3fa vtx[4];
+  };
+
+  template<typename Vertex, typename Vertex_t = Vertex>
+    struct __aligned(64) CatmullClark1RingT
+  {
+    ALIGNED_STRUCT_(64);
+    
+    int border_index;                                   //!< edge index where border starts
+    unsigned int face_valence;                          //!< number of adjacent quad faces
+    unsigned int edge_valence;                          //!< number of adjacent edges (2*face_valence)
+    float vertex_crease_weight;                         //!< weight of vertex crease (0 if no vertex crease)
+    DynamicStackArray<float,16,MAX_RING_FACE_VALENCE> crease_weight; //!< edge crease weights for each adjacent edge
+    float vertex_level;                                 //!< maximum level of all adjacent edges
+    float edge_level;                                   //!< level of first edge
+    unsigned int eval_start_index;                      //!< topology dependent index to start evaluation
+    unsigned int eval_unique_identifier;                //!< topology dependent unique identifier for this ring 
+    Vertex vtx;                                         //!< center vertex
+    DynamicStackArray<Vertex,32,MAX_RING_EDGE_VALENCE> ring;  //!< ring of neighboring vertices
+   
+  public:
+    CatmullClark1RingT () 
+    : eval_start_index(0), eval_unique_identifier(0) {} // FIXME: default constructor should be empty
+
+    /*! calculates number of bytes required to serialize this structure */
+    __forceinline size_t bytes() const
+    {
+      size_t ofs = 0;
+      ofs += sizeof(border_index);
+      ofs += sizeof(face_valence);
+      assert(2*face_valence == edge_valence);
+      ofs += sizeof(vertex_crease_weight);
+      ofs += face_valence*sizeof(float);
+      ofs += sizeof(vertex_level);
+      ofs += sizeof(edge_level);
+      ofs += sizeof(eval_start_index);
+      ofs += sizeof(eval_unique_identifier);
+      ofs += sizeof(vtx);
+      ofs += edge_valence*sizeof(Vertex);
+      return ofs;
+    }
+
+    template<typename Ty>
+    static __forceinline void store(char* ptr, size_t& ofs, const Ty& v) {
+      *(Ty*)&ptr[ofs] = v; ofs += sizeof(Ty);
+    }
+
+    template<typename Ty>
+    static __forceinline void load(char* ptr, size_t& ofs, Ty& v) {
+      v = *(Ty*)&ptr[ofs]; ofs += sizeof(Ty);
+    }
+
+    /*! serializes the ring to some memory location */
+    __forceinline void serialize(char* ptr, size_t& ofs) const
+    {
+      store(ptr,ofs,border_index);
+      store(ptr,ofs,face_valence);
+      store(ptr,ofs,vertex_crease_weight);
+      for (size_t i=0; i<face_valence; i++)
+        store(ptr,ofs,crease_weight[i]);
+      store(ptr,ofs,vertex_level);
+      store(ptr,ofs,edge_level);
+      store(ptr,ofs,eval_start_index);
+      store(ptr,ofs,eval_unique_identifier);
+      Vertex_t::storeu(&ptr[ofs],vtx); ofs += sizeof(Vertex);
+      for (size_t i=0; i<edge_valence; i++) {
+        Vertex_t::storeu(&ptr[ofs],ring[i]); ofs += sizeof(Vertex);
+      }
+    }
+
+    /*! deserializes the ring from some memory location */
+    __forceinline void deserialize(char* ptr, size_t& ofs)
+    {
+      load(ptr,ofs,border_index);
+      load(ptr,ofs,face_valence);
+      edge_valence = 2*face_valence;
+      load(ptr,ofs,vertex_crease_weight);
+      for (size_t i=0; i<face_valence; i++)
+        load(ptr,ofs,crease_weight[i]);
+      load(ptr,ofs,vertex_level);
+      load(ptr,ofs,edge_level);
+      load(ptr,ofs,eval_start_index);
+      load(ptr,ofs,eval_unique_identifier);
+      vtx = Vertex_t::loadu(&ptr[ofs]); ofs += sizeof(Vertex);
+      for (size_t i=0; i<edge_valence; i++) {
+        ring[i] = Vertex_t::loadu(&ptr[ofs]); ofs += sizeof(Vertex);
+      }
+    }
+
+    __forceinline bool hasBorder() const {
+      return border_index != -1;
+    }
+    
+    __forceinline const Vertex& front(size_t i) const {
+      assert(edge_valence>i);
+      return ring[i];
+    }
+    
+    __forceinline const Vertex& back(size_t i) const {
+      assert(edge_valence>=i);
+      return ring[edge_valence-i];
+    }
+    
+    __forceinline bool has_last_face() const {
+      return (size_t)border_index != (size_t)edge_valence-2;
+    }
+
+    __forceinline bool has_opposite_front(size_t i) const {
+      return (size_t)border_index != 2*i;
+    }
+
+    __forceinline bool has_opposite_back(size_t i) const {
+      return (size_t)border_index != ((size_t)edge_valence-2-2*i);
+    }
+    
+    __forceinline BBox3fa bounds() const
+    {
+      BBox3fa bounds ( vtx );
+      for (size_t i = 0; i<edge_valence ; i++)
+	bounds.extend( ring[i] );
+      return bounds;
+    }
+
+    /*! initializes the ring from the half edge structure */
+    __forceinline void init(const HalfEdge* const h, const char* vertices, size_t stride) 
+    {
+      border_index = -1;
+      vtx = Vertex_t::loadu(vertices+h->getStartVertexIndex()*stride);
+      vertex_crease_weight = h->vertex_crease_weight;
+      
+      HalfEdge* p = (HalfEdge*) h;
+
+      unsigned i=0;
+      unsigned min_vertex_index = (unsigned)-1;
+      unsigned min_vertex_index_face = (unsigned)-1;
+      edge_level = p->edge_level;
+      vertex_level = 0.0f;
+
+      do
+      {
+        vertex_level = max(vertex_level,p->edge_level);
+        crease_weight[i/2] = p->edge_crease_weight;
+        assert(p->hasOpposite() || p->edge_crease_weight == float(inf));
+
+        /* store first two vertices of face */
+        p = p->next();
+        const unsigned index0 = p->getStartVertexIndex();
+        ring[i++] = Vertex_t::loadu(vertices+index0*stride);
+        if (index0 < min_vertex_index) { min_vertex_index = index0; min_vertex_index_face = i>>1; }
+        p = p->next();
+
+        const unsigned index1 = p->getStartVertexIndex();
+        ring[i++] = Vertex_t::loadu(vertices+index1*stride);
+        p = p->next();
+       
+        /* continue with next face */
+        if (likely(p->hasOpposite())) 
+          p = p->opposite();
+        
+        /* if there is no opposite go the long way to the other side of the border */
+        else
+        {
+          /* find minimum start vertex */
+          const unsigned index0 = p->getStartVertexIndex();
+          if (index0 < min_vertex_index) { min_vertex_index = index0; min_vertex_index_face = i>>1; }
+
+          /*! mark first border edge and store dummy vertex for face between the two border edges */
+          border_index = i;
+          crease_weight[i/2] = inf; 
+          ring[i++] = Vertex_t::loadu(vertices+index0*stride);
+          ring[i++] = vtx; // dummy vertex
+          	  
+          /*! goto other side of border */
+          p = (HalfEdge*) h;
+          while (p->hasOpposite()) 
+            p = p->opposite()->next();
+        }
+
+      } while (p != h); 
+
+      edge_valence = i;
+      face_valence = i >> 1;
+      eval_unique_identifier = min_vertex_index;
+      eval_start_index = min_vertex_index_face;
+
+      assert( hasValidPositions() );
+    }
+      
+    __forceinline void subdivide(CatmullClark1RingT& dest) const
+    {
+      dest.edge_level             = 0.5f*edge_level;
+      dest.vertex_level           = 0.5f*vertex_level;
+      dest.face_valence           = face_valence;
+      dest.edge_valence           = edge_valence;
+      dest.border_index           = border_index;
+      dest.vertex_crease_weight   = max(0.0f,vertex_crease_weight-1.0f);
+      dest.eval_start_index       = eval_start_index;
+      dest.eval_unique_identifier = eval_unique_identifier;
+
+      /* calculate face points */
+      Vertex_t S = Vertex_t(0.0f);
+      for (size_t i=0; i<face_valence; i++) 
+      {
+        size_t face_index = i + eval_start_index; if (face_index >= face_valence) face_index -= face_valence; assert(face_index < face_valence);
+        size_t index0 = 2*face_index+0; if (index0 >= edge_valence) index0 -= edge_valence; assert(index0 < edge_valence);
+        size_t index1 = 2*face_index+1; if (index1 >= edge_valence) index1 -= edge_valence; assert(index1 < edge_valence);
+        size_t index2 = 2*face_index+2; if (index2 >= edge_valence) index2 -= edge_valence; assert(index2 < edge_valence);
+        S += dest.ring[index1] = ((vtx + ring[index1]) + (ring[index0] + ring[index2])) * 0.25f;
+      }
+      
+      /* calculate new edge points */
+      size_t num_creases = 0;
+      array_t<size_t,MAX_RING_FACE_VALENCE> crease_id;
+
+      for (size_t i=0; i<face_valence; i++)
+      {
+        size_t face_index = i + eval_start_index;
+        if (face_index >= face_valence) face_index -= face_valence;
+        const float edge_crease = crease_weight[face_index];
+        dest.crease_weight[face_index] = max(edge_crease-1.0f,0.0f);
+      
+        size_t index      = 2*face_index;
+        size_t prev_index = face_index == 0 ? edge_valence-1 : 2*face_index-1;
+        size_t next_index = 2*face_index+1;
+
+        const Vertex_t v = vtx + ring[index];
+        const Vertex_t f = dest.ring[prev_index] + dest.ring[next_index];
+        S += ring[index];
+                
+        /* fast path for regular edge points */
+        if (likely(edge_crease <= 0.0f)) {
+          dest.ring[index] = (v+f) * 0.25f;
+        }
+        
+        /* slower path for hard edge rule */
+        else {
+          crease_id[num_creases++] = face_index;
+          dest.ring[index] = v*0.5f;
+	  
+          /* even slower path for blended edge rule */
+          if (unlikely(edge_crease < 1.0f)) {
+            dest.ring[index] = lerp((v+f)*0.25f,v*0.5f,edge_crease);
+          }
+        }
+      }
+      
+      /* compute new vertex using smooth rule */
+      const float inv_face_valence = 1.0f / (float)face_valence;
+      const Vertex_t v_smooth = (Vertex_t) madd(inv_face_valence,S,(float(face_valence)-2.0f)*vtx)*inv_face_valence;
+      dest.vtx = v_smooth;
+      
+      /* compute new vertex using vertex_crease_weight rule */
+      if (unlikely(vertex_crease_weight > 0.0f)) 
+      {
+        if (vertex_crease_weight >= 1.0f) {
+          dest.vtx = vtx;
+        } else {
+          dest.vtx = lerp(v_smooth,vtx,vertex_crease_weight);
+        }
+        return;
+      }
+      
+      /* no edge crease rule and dart rule */
+      if (likely(num_creases <= 1))
+        return;
+      
+      /* compute new vertex using crease rule */
+      if (likely(num_creases == 2)) 
+      {
+        /* update vertex using crease rule */
+        const size_t crease0 = crease_id[0], crease1 = crease_id[1];
+        const Vertex_t v_sharp = (Vertex_t)(ring[2*crease0] + 6.0f*vtx + ring[2*crease1]) * (1.0f / 8.0f);
+        dest.vtx = v_sharp;
+
+        /* update crease_weights using chaikin rule */
+        const float crease_weight0 = crease_weight[crease0], crease_weight1 = crease_weight[crease1];
+        dest.crease_weight[crease0] = max(0.25f*(3.0f*crease_weight0 + crease_weight1)-1.0f,0.0f);
+        dest.crease_weight[crease1] = max(0.25f*(3.0f*crease_weight1 + crease_weight0)-1.0f,0.0f);
+
+        /* interpolate between sharp and smooth rule */
+        const float v_blend = 0.5f*(crease_weight0+crease_weight1);
+        if (unlikely(v_blend < 1.0f)) {
+          dest.vtx = lerp(v_smooth,v_sharp,v_blend);
+        }
+      }
+      
+      /* compute new vertex using corner rule */
+      else {
+        dest.vtx = vtx;
+      }
+    }
+    
+    __forceinline bool isRegular1() const 
+    {
+      if (border_index == -1) {
+	if (face_valence == 4) return true;
+      } else {
+	if (face_valence < 4) return true;
+      }
+      return false;
+    }
+
+    __forceinline size_t numEdgeCreases() const
+    {
+      ssize_t numCreases = 0;
+      for (size_t i=0; i<face_valence; i++) {
+        numCreases += crease_weight[i] > 0.0f;
+      }
+      return numCreases;
+    }
+
+    enum Type {
+      TYPE_NONE            = 0,      //!< invalid type
+      TYPE_REGULAR         = 1,      //!< regular patch when ignoring creases
+      TYPE_REGULAR_CREASES = 2,      //!< regular patch when considering creases
+      TYPE_GREGORY         = 4,      //!< gregory patch when ignoring creases
+      TYPE_GREGORY_CREASES = 8,      //!< gregory patch when considering creases
+      TYPE_CREASES         = 16      //!< patch has crease features
+    };
+    
+    __forceinline Type type() const
+    {
+      /* check if there is an edge crease anywhere */      
+      const size_t numCreases = numEdgeCreases();
+      const bool noInnerCreases = hasBorder() ? numCreases == 2 : numCreases == 0;
+
+      Type crease_mask = (Type) (TYPE_REGULAR | TYPE_GREGORY);
+      if (noInnerCreases ) crease_mask = (Type) (crease_mask | TYPE_REGULAR_CREASES | TYPE_GREGORY_CREASES);
+      if (numCreases != 0) crease_mask = (Type) (crease_mask | TYPE_CREASES);
+
+      /* calculate if this vertex is regular */
+      bool hasBorder = border_index != -1;
+      if (face_valence == 2 && hasBorder) {
+        if      (vertex_crease_weight == 0.0f      ) return (Type) (crease_mask & (TYPE_REGULAR | TYPE_REGULAR_CREASES | TYPE_GREGORY | TYPE_GREGORY_CREASES | TYPE_CREASES));
+        else if (vertex_crease_weight == float(inf)) return (Type) (crease_mask & (TYPE_REGULAR | TYPE_REGULAR_CREASES | TYPE_GREGORY | TYPE_GREGORY_CREASES | TYPE_CREASES));
+        else                                         return TYPE_CREASES;
+      }
+      else if (vertex_crease_weight != 0.0f)         return TYPE_CREASES;
+      else if (face_valence == 3 &&  hasBorder)      return (Type) (crease_mask & (TYPE_REGULAR | TYPE_REGULAR_CREASES | TYPE_GREGORY | TYPE_GREGORY_CREASES | TYPE_CREASES));
+      else if (face_valence == 4 && !hasBorder)      return (Type) (crease_mask & (TYPE_REGULAR | TYPE_REGULAR_CREASES | TYPE_GREGORY | TYPE_GREGORY_CREASES | TYPE_CREASES));
+      else                                           return (Type) (crease_mask & (TYPE_GREGORY | TYPE_GREGORY_CREASES | TYPE_CREASES));
+    }
+
+    __forceinline bool isFinalResolution(float res) const {
+      return vertex_level <= res;
+    }
+
+    /* computes the limit vertex */
+    __forceinline Vertex getLimitVertex() const
+    {
+      /* return hard corner */ 
+      if (unlikely(std::isinf(vertex_crease_weight)))
+        return vtx;
+
+      /* border vertex rule */
+      if (unlikely(border_index != -1))
+      {
+	const unsigned int second_border_index = border_index+2 >= int(edge_valence) ? 0 : border_index+2;
+	return (4.0f * vtx + (ring[border_index] + ring[second_border_index])) * 1.0f/6.0f;
+      }
+      
+      Vertex_t F( 0.0f );
+      Vertex_t E( 0.0f );
+      
+      assert(eval_start_index < face_valence);
+
+      for (size_t i=0; i<face_valence; i++) {
+        size_t index = i+eval_start_index;
+        if (index >= face_valence) index -= face_valence;
+        F += ring[2*index+1];
+        E += ring[2*index];
+      }
+
+      const float n = (float)face_valence;
+      return (Vertex_t)(n*n*vtx+4.0f*E+F) / ((n+5.0f)*n);      
+    }
+    
+    /* gets limit tangent in the direction of edge vtx -> ring[0] */
+    __forceinline Vertex getLimitTangent() const 
+    {
+      if (unlikely(std::isinf(vertex_crease_weight)))
+        return ring[0] - vtx;
+
+      /* border vertex rule */
+      if (unlikely(border_index != -1))
+      {	
+	if (border_index != (int)edge_valence-2 ) {
+	  return ring[0] - vtx; 
+	}
+	else
+	{
+	  const unsigned int second_border_index = border_index+2 >= int(edge_valence) ? 0 : border_index+2;
+	  return (ring[second_border_index] - ring[border_index]) * 0.5f;
+	}
+      }
+      
+      Vertex_t alpha( 0.0f );
+      Vertex_t beta ( 0.0f );
+      
+      const size_t n = face_valence;
+
+      assert(eval_start_index < face_valence);
+
+      Vertex_t q( 0.0f );
+      for (size_t i=0; i<face_valence; i++)
+      {
+        size_t index = i+eval_start_index;
+        if (index >= face_valence) index -= face_valence;
+        const float a = CatmullClarkPrecomputedCoefficients::table.limittangent_a(index,n);
+        const float b = CatmullClarkPrecomputedCoefficients::table.limittangent_b(index,n);
+	alpha +=  a * ring[2*index];
+	beta  +=  b * ring[2*index+1];
+      }
+
+      const float sigma = CatmullClarkPrecomputedCoefficients::table.limittangent_c(n);
+      return sigma * (alpha + beta);
+    }
+    
+    /* gets limit tangent in the direction of edge vtx -> ring[edge_valence-2] */
+    __forceinline Vertex getSecondLimitTangent() const 
+    {
+      if (unlikely(std::isinf(vertex_crease_weight)))
+        return ring[2] - vtx;
+ 
+      /* border vertex rule */
+      if (unlikely(border_index != -1))
+      {
+        if (border_index != 2) {
+          return ring[2] - vtx;
+        }
+        else {
+          const unsigned int second_border_index = border_index+2 >= int(edge_valence) ? 0 : border_index+2;
+          return (ring[border_index] - ring[second_border_index]) * 0.5f;
+        }
+      }
+      
+      Vertex_t alpha( 0.0f );
+      Vertex_t beta ( 0.0f );
+
+      const size_t n = face_valence;
+
+      assert(eval_start_index < face_valence);
+
+      for (size_t i=0; i<face_valence; i++)
+      {
+        size_t index = i+eval_start_index;
+        if (index >= face_valence) index -= face_valence;
+
+        size_t prev_index = index == 0 ? face_valence-1 : index-1; // need to be bit-wise exact in cosf eval
+        const float a = CatmullClarkPrecomputedCoefficients::table.limittangent_a(prev_index,n);
+        const float b = CatmullClarkPrecomputedCoefficients::table.limittangent_b(prev_index,n);
+	alpha += a * ring[2*index];
+	beta  += b * ring[2*index+1];
+      }
+
+      const float sigma = CatmullClarkPrecomputedCoefficients::table.limittangent_c(n);
+      return sigma* (alpha + beta);      
+    }
+
+    /* gets surface normal */
+    const Vertex getNormal() const  {
+      return cross(getLimitTangent(),getSecondLimitTangent());
+    }
+    
+    /* returns center of the n-th quad in the 1-ring */
+    __forceinline Vertex getQuadCenter(const size_t index) const
+    {
+      const Vertex_t &p0 = vtx;
+      const Vertex_t &p1 = ring[2*index+0];
+      const Vertex_t &p2 = ring[2*index+1];
+      const Vertex_t &p3 = index == face_valence-1 ? ring[0] : ring[2*index+2];
+      const Vertex p = (p0+p1+p2+p3) * 0.25f;
+      return p;
+    }
+    
+    /* returns center of the n-th edge in the 1-ring */
+    __forceinline Vertex getEdgeCenter(const size_t index) const {
+      return (vtx + ring[index*2]) * 0.5f;
+    }
+
+    bool hasValidPositions() const
+    {
+      for (size_t i=0; i<edge_valence; i++) {
+        if (!isvalid(ring[i]))
+          return false;
+      }	
+      return true;
+    }
+
+    friend __forceinline embree_ostream operator<<(embree_ostream o, const CatmullClark1RingT &c)
+    {
+      o << "vtx " << c.vtx << " size = " << c.edge_valence << ", " << 
+	"hard_edge = " << c.border_index << ", face_valence " << c.face_valence << 
+	", edge_level = " << c.edge_level << ", vertex_level = " << c.vertex_level << ", eval_start_index: " << c.eval_start_index << ", ring: " << embree_endl;
+      
+      for (unsigned int i=0; i<min(c.edge_valence,(unsigned int)MAX_RING_FACE_VALENCE); i++) {
+        o << i << " -> " << c.ring[i];
+        if (i % 2 == 0) o << " crease = " << c.crease_weight[i/2];
+        o << embree_endl;
+      }
+      return o;
+    } 
+  };
+
+  typedef CatmullClark1RingT<Vec3fa,Vec3fa_t> CatmullClark1Ring3fa;
+  
+  template<typename Vertex, typename Vertex_t = Vertex>
+    struct __aligned(64) GeneralCatmullClark1RingT
+  {
+    ALIGNED_STRUCT_(64);
+    
+    typedef CatmullClark1RingT<Vertex,Vertex_t> CatmullClark1Ring;
+    
+    struct Face 
+    {
+      __forceinline Face() {}
+      __forceinline Face (int size, float crease_weight)
+        : size(size), crease_weight(crease_weight) {}
+
+      // FIXME: add member that returns total number of vertices
+
+      int size;              // number of vertices-2 of nth face in ring
+      float crease_weight;
+    };
+
+    Vertex vtx;
+    DynamicStackArray<Vertex,32,MAX_RING_EDGE_VALENCE> ring; 
+    DynamicStackArray<Face,16,MAX_RING_FACE_VALENCE> faces;
+    unsigned int face_valence;
+    unsigned int edge_valence;
+    int border_face;
+    float vertex_crease_weight;
+    float vertex_level;                      //!< maximum level of adjacent edges
+    float edge_level;                        // level of first edge
+    bool only_quads;                         // true if all faces are quads
+    unsigned int eval_start_face_index;
+    unsigned int eval_start_vertex_index;
+    unsigned int eval_unique_identifier;
+
+  public:
+    GeneralCatmullClark1RingT() 
+      : eval_start_face_index(0), eval_start_vertex_index(0), eval_unique_identifier(0) {}
+
+    __forceinline bool isRegular() const 
+    {
+      if (border_face == -1 && face_valence == 4) return true;
+      return false;
+    }
+    
+    __forceinline bool has_last_face() const {
+      return border_face != (int)face_valence-1;
+    }
+    
+    __forceinline bool has_second_face() const {
+      return (border_face == -1) || (border_face >= 2);
+    }
+
+    bool hasValidPositions() const
+    {
+      for (size_t i=0; i<edge_valence; i++) {
+        if (!isvalid(ring[i]))
+          return false;
+      }	
+      return true;
+    }
+
+    __forceinline void init(const HalfEdge* const h, const char* vertices, size_t stride)
+    {
+      only_quads = true;
+      border_face = -1;
+      vtx = Vertex_t::loadu(vertices+h->getStartVertexIndex()*stride);
+      vertex_crease_weight = h->vertex_crease_weight;
+      HalfEdge* p = (HalfEdge*) h;
+      
+      unsigned int e=0, f=0;
+      unsigned min_vertex_index = (unsigned)-1;
+      unsigned min_vertex_index_face = (unsigned)-1;
+      unsigned min_vertex_index_vertex = (unsigned)-1;
+      edge_level = p->edge_level;
+      vertex_level = 0.0f;
+      do 
+      {
+        HalfEdge* p_prev = p->prev();
+        HalfEdge* p_next = p->next();
+        const float crease_weight = p->edge_crease_weight;
+         assert(p->hasOpposite() || p->edge_crease_weight == float(inf));
+        vertex_level = max(vertex_level,p->edge_level);
+
+        /* find minimum start vertex */
+        unsigned vertex_index = p_next->getStartVertexIndex();
+        if (vertex_index < min_vertex_index) { min_vertex_index = vertex_index; min_vertex_index_face = f; min_vertex_index_vertex = e; }
+
+	/* store first N-2 vertices of face */
+	unsigned int vn = 0;
+        for (p = p_next; p!=p_prev; p=p->next()) {
+          ring[e++] = Vertex_t::loadu(vertices+p->getStartVertexIndex()*stride);
+          vn++;
+	}
+	faces[f++] = Face(vn,crease_weight);
+	only_quads &= (vn == 2);
+	
+        /* continue with next face */
+        if (likely(p->hasOpposite())) 
+          p = p->opposite();
+        
+        /* if there is no opposite go the long way to the other side of the border */
+        else
+        {
+          /* find minimum start vertex */
+          unsigned vertex_index = p->getStartVertexIndex();
+          if (vertex_index < min_vertex_index) { min_vertex_index = vertex_index; min_vertex_index_face = f; min_vertex_index_vertex = e; }
+
+          /*! mark first border edge and store dummy vertex for face between the two border edges */
+          border_face = f;
+	  faces[f++] = Face(2,inf); 
+          ring[e++] = Vertex_t::loadu(vertices+p->getStartVertexIndex()*stride);
+          ring[e++] = vtx; // dummy vertex
+	  
+          /*! goto other side of border */
+          p = (HalfEdge*) h;
+          while (p->hasOpposite()) 
+            p = p->opposite()->next();
+        }
+	
+      } while (p != h); 
+      
+      edge_valence = e;
+      face_valence = f;
+      eval_unique_identifier = min_vertex_index;
+      eval_start_face_index = min_vertex_index_face;
+      eval_start_vertex_index = min_vertex_index_vertex;
+
+      assert( hasValidPositions() );
+    }
+    
+    __forceinline void subdivide(CatmullClark1Ring& dest) const
+    {
+      dest.edge_level = 0.5f*edge_level;
+      dest.vertex_level = 0.5f*vertex_level;
+      dest.face_valence = face_valence;
+      dest.edge_valence = 2*face_valence;
+      dest.border_index = border_face == -1 ? -1 : 2*border_face; // FIXME:
+      dest.vertex_crease_weight    = max(0.0f,vertex_crease_weight-1.0f);
+      dest.eval_start_index        = eval_start_face_index;
+      dest.eval_unique_identifier  = eval_unique_identifier;
+      assert(dest.face_valence <= MAX_RING_FACE_VALENCE);
+
+      /* calculate face points */
+      Vertex_t S = Vertex_t(0.0f);
+      for (size_t face=0, v=eval_start_vertex_index; face<face_valence; face++) {
+        size_t f = (face + eval_start_face_index)%face_valence;
+
+        Vertex_t F = vtx;
+        for (size_t k=v; k<=v+faces[f].size; k++) F += ring[k%edge_valence]; // FIXME: optimize
+        S += dest.ring[2*f+1] = F/float(faces[f].size+2);
+        v+=faces[f].size;
+        v%=edge_valence;
+      }
+      
+      /* calculate new edge points */
+      size_t num_creases = 0;
+      array_t<size_t,MAX_RING_FACE_VALENCE> crease_id;
+      Vertex_t C = Vertex_t(0.0f);
+      for (size_t face=0, j=eval_start_vertex_index; face<face_valence; face++)
+      {
+        size_t i = (face + eval_start_face_index)%face_valence;
+        
+        const Vertex_t v = vtx + ring[j];
+        Vertex_t f = dest.ring[2*i+1];
+        if (i == 0) f += dest.ring[dest.edge_valence-1]; 
+        else        f += dest.ring[2*i-1];
+        S += ring[j];
+        dest.crease_weight[i] = max(faces[i].crease_weight-1.0f,0.0f);
+        
+        /* fast path for regular edge points */
+        if (likely(faces[i].crease_weight <= 0.0f)) {
+          dest.ring[2*i] = (v+f) * 0.25f;
+        }
+        
+        /* slower path for hard edge rule */
+        else {
+          C += ring[j]; crease_id[num_creases++] = i;
+          dest.ring[2*i] = v*0.5f;
+	  
+          /* even slower path for blended edge rule */
+          if (unlikely(faces[i].crease_weight < 1.0f)) {
+            dest.ring[2*i] = lerp((v+f)*0.25f,v*0.5f,faces[i].crease_weight);
+          }
+        }
+        j+=faces[i].size;
+        j%=edge_valence;
+      }
+      
+      /* compute new vertex using smooth rule */
+      const float inv_face_valence = 1.0f / (float)face_valence;
+      const Vertex_t v_smooth = (Vertex_t) madd(inv_face_valence,S,(float(face_valence)-2.0f)*vtx)*inv_face_valence;
+      dest.vtx = v_smooth;
+      
+      /* compute new vertex using vertex_crease_weight rule */
+      if (unlikely(vertex_crease_weight > 0.0f)) 
+      {
+        if (vertex_crease_weight >= 1.0f) {
+          dest.vtx = vtx;
+        } else {
+          dest.vtx = lerp(vtx,v_smooth,vertex_crease_weight);
+        }
+        return;
+      }
+      
+      if (likely(num_creases <= 1))
+        return;
+      
+      /* compute new vertex using crease rule */
+      if (likely(num_creases == 2)) {
+        const Vertex_t v_sharp = (Vertex_t)(C + 6.0f * vtx) * (1.0f / 8.0f);
+        const float crease_weight0 = faces[crease_id[0]].crease_weight;
+        const float crease_weight1 = faces[crease_id[1]].crease_weight;
+        dest.vtx = v_sharp;
+        dest.crease_weight[crease_id[0]] = max(0.25f*(3.0f*crease_weight0 + crease_weight1)-1.0f,0.0f);
+        dest.crease_weight[crease_id[1]] = max(0.25f*(3.0f*crease_weight1 + crease_weight0)-1.0f,0.0f);
+        const float v_blend = 0.5f*(crease_weight0+crease_weight1);
+        if (unlikely(v_blend < 1.0f)) {
+          dest.vtx = lerp(v_sharp,v_smooth,v_blend);
+        }
+      }
+      
+      /* compute new vertex using corner rule */
+      else {
+        dest.vtx = vtx;
+      }
+    }
+
+    void convert(CatmullClark1Ring& dst) const
+    {
+      dst.edge_level = edge_level;
+      dst.vertex_level = vertex_level;
+      dst.vtx = vtx;
+      dst.face_valence = face_valence;
+      dst.edge_valence = 2*face_valence;
+      dst.border_index = border_face == -1 ? -1 : 2*border_face;
+      for (size_t i=0; i<face_valence; i++) 
+	dst.crease_weight[i] = faces[i].crease_weight;
+      dst.vertex_crease_weight = vertex_crease_weight;
+      for (size_t i=0; i<edge_valence; i++) dst.ring[i] = ring[i];
+
+      dst.eval_start_index = eval_start_face_index;
+      dst.eval_unique_identifier = eval_unique_identifier;
+
+      assert( dst.hasValidPositions() );
+    }
+
+
+    /* gets limit tangent in the direction of edge vtx -> ring[0] */
+    __forceinline Vertex getLimitTangent() const 
+    {
+      CatmullClark1Ring cc_vtx;
+     
+      /* fast path for quad only rings */
+      if (only_quads)
+      {
+        convert(cc_vtx);
+        return cc_vtx.getLimitTangent();
+      }
+      
+      subdivide(cc_vtx);
+      return 2.0f * cc_vtx.getLimitTangent();
+    }
+
+    /* gets limit tangent in the direction of edge vtx -> ring[edge_valence-2] */
+    __forceinline Vertex getSecondLimitTangent() const 
+    {
+      CatmullClark1Ring cc_vtx;
+     
+      /* fast path for quad only rings */
+      if (only_quads)
+      {
+        convert(cc_vtx);
+        return cc_vtx.getSecondLimitTangent();
+      }
+      
+      subdivide(cc_vtx);
+      return 2.0f * cc_vtx.getSecondLimitTangent();
+    }
+
+
+    /* gets limit vertex */
+    __forceinline Vertex getLimitVertex() const 
+    {
+      CatmullClark1Ring cc_vtx;
+     
+      /* fast path for quad only rings */
+      if (only_quads)
+        convert(cc_vtx);
+      else 
+        subdivide(cc_vtx);
+      return cc_vtx.getLimitVertex();
+    }
+
+    friend __forceinline embree_ostream operator<<(embree_ostream o, const GeneralCatmullClark1RingT &c)
+    {
+      o << "vtx " << c.vtx << " size = " << c.edge_valence << ", border_face = " << c.border_face << ", " << " face_valence = " << c.face_valence << 
+	", edge_level = " << c.edge_level << ", vertex_level = " << c.vertex_level << ", ring: " << embree_endl;
+      for (size_t v=0, f=0; f<c.face_valence; v+=c.faces[f++].size) {
+        for (size_t i=v; i<v+c.faces[f].size; i++) {
+          o << i << " -> " << c.ring[i];
+          if (i == v) o << " crease = " << c.faces[f].crease_weight;
+          o << embree_endl;
+        }
+      }
+      return o;
+    } 
+  };  
+}

thirdparty/embree/kernels/subdiv/catmullrom_curve.h

@@ -0,0 +1,314 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "../common/default.h"
+#include "bezier_curve.h"
+#include "../common/scene_curves.h"
+
+/*
+
+  Implements Catmul Rom curves with control points p0, p1, p2, p3. At
+  t=0 the curve goes through p1, with tangent (p2-p0)/2, and for t=1
+  the curve goes through p2 with tangent (p3-p2)/2.
+
+ */
+
+namespace embree
+{
+  class CatmullRomBasis
+  {
+  public:
+
+    template<typename T>
+      static __forceinline Vec4<T> eval(const T& u) 
+    {
+      const T t  = u;
+      const T s  = T(1.0f) - u;
+      const T n0 = - t * s * s;
+      const T n1 = 2.0f + t * t * (3.0f * t - 5.0f);
+      const T n2 = 2.0f + s * s * (3.0f * s - 5.0f);
+      const T n3 = - s * t * t;
+      return T(0.5f) * Vec4<T>(n0, n1, n2, n3);
+    }
+    
+    template<typename T>
+      static __forceinline Vec4<T>  derivative(const T& u)
+    {
+      const T t  =  u;
+      const T s  =  1.0f - u;
+      const T n0 =  - s * s + 2.0f * s * t;
+      const T n1 =  2.0f * t * (3.0f * t - 5.0f) + 3.0f * t * t;
+      const T n2 =  2.0f * s * (3.0f * t + 2.0f) - 3.0f * s * s;
+      const T n3 = -2.0f * s * t + t * t;
+      return T(0.5f) * Vec4<T>(n0, n1, n2, n3);
+    }
+
+    template<typename T>
+      static __forceinline Vec4<T>  derivative2(const T& u)
+    {
+      const T t  =  u;
+      const T n0 = -3.0f * t + 2.0f;
+      const T n1 =  9.0f * t - 5.0f;
+      const T n2 = -9.0f * t + 4.0f;
+      const T n3 =  3.0f * t - 1.0f;
+      return Vec4<T>(n0, n1, n2, n3);
+    }
+  };
+  
+  struct PrecomputedCatmullRomBasis
+  {
+    enum { N = 16 };
+  public:
+    PrecomputedCatmullRomBasis() {}
+    PrecomputedCatmullRomBasis(int shift);
+
+    /* basis for bspline evaluation */
+  public:
+    float c0[N+1][N+1];
+    float c1[N+1][N+1];
+    float c2[N+1][N+1];
+    float c3[N+1][N+1];
+    
+    /* basis for bspline derivative evaluation */
+  public:
+    float d0[N+1][N+1];
+    float d1[N+1][N+1];
+    float d2[N+1][N+1];
+    float d3[N+1][N+1];
+  };
+  extern PrecomputedCatmullRomBasis catmullrom_basis0;
+  extern PrecomputedCatmullRomBasis catmullrom_basis1;
+
+  template<typename Vertex>
+    struct CatmullRomCurveT
+    {
+      Vertex v0,v1,v2,v3;
+      
+      __forceinline CatmullRomCurveT() {}
+      
+      __forceinline CatmullRomCurveT(const Vertex& v0, const Vertex& v1, const Vertex& v2, const Vertex& v3)
+        : v0(v0), v1(v1), v2(v2), v3(v3) {}
+
+      __forceinline Vertex begin() const {
+        return v1;
+      }
+
+      __forceinline Vertex end() const {
+        return v2;
+      }
+
+      __forceinline Vertex center() const {
+        return 0.5f*(v0+v1);
+      }
+
+      __forceinline BBox<Vertex> bounds() const {
+        return merge(BBox<Vertex>(v0),BBox<Vertex>(v1),BBox<Vertex>(v2),BBox<Vertex>(v3));
+      }
+
+      __forceinline friend CatmullRomCurveT operator -( const CatmullRomCurveT& a, const Vertex& b ) {
+        return CatmullRomCurveT(a.v0-b,a.v1-b,a.v2-b,a.v3-b);
+      }
+
+      __forceinline CatmullRomCurveT<Vec3ff> xfm_pr(const LinearSpace3fa& space, const Vec3fa& p) const
+      {
+        const Vec3ff q0(xfmVector(space,v0-p), v0.w);
+        const Vec3ff q1(xfmVector(space,v1-p), v1.w);
+        const Vec3ff q2(xfmVector(space,v2-p), v2.w);
+        const Vec3ff q3(xfmVector(space,v3-p), v3.w);
+        return CatmullRomCurveT<Vec3ff>(q0,q1,q2,q3);
+      }
+      
+      __forceinline Vertex eval(const float t) const 
+      {
+        const Vec4<float> b = CatmullRomBasis::eval(t);
+        return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
+      }
+      
+      __forceinline Vertex eval_du(const float t) const
+      {
+        const Vec4<float> b = CatmullRomBasis::derivative(t);
+        return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
+      }
+      
+      __forceinline Vertex eval_dudu(const float t) const 
+      {
+        const Vec4<float> b = CatmullRomBasis::derivative2(t);
+        return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
+      }
+
+      __forceinline void eval(const float t, Vertex& p, Vertex& dp) const
+      {
+        p = eval(t);
+        dp = eval_du(t);
+      }
+      
+      __forceinline void eval(const float t, Vertex& p, Vertex& dp, Vertex& ddp) const
+      {
+        p = eval(t);
+        dp = eval_du(t);
+        ddp = eval_dudu(t);
+      }
+
+      template<int M>
+      __forceinline Vec4vf<M> veval(const vfloat<M>& t) const 
+      {
+        const Vec4vf<M> b = CatmullRomBasis::eval(t);
+        return madd(b.x, Vec4vf<M>(v0), madd(b.y, Vec4vf<M>(v1), madd(b.z, Vec4vf<M>(v2), b.w * Vec4vf<M>(v3))));
+      }
+
+      template<int M>
+      __forceinline Vec4vf<M> veval_du(const vfloat<M>& t) const 
+      {
+        const Vec4vf<M> b = CatmullRomBasis::derivative(t);
+        return madd(b.x, Vec4vf<M>(v0), madd(b.y, Vec4vf<M>(v1), madd(b.z, Vec4vf<M>(v2), b.w * Vec4vf<M>(v3))));
+      }
+
+      template<int M>
+      __forceinline Vec4vf<M> veval_dudu(const vfloat<M>& t) const 
+      {
+        const Vec4vf<M> b = CatmullRomBasis::derivative2(t);
+        return madd(b.x, Vec4vf<M>(v0), madd(b.y, Vec4vf<M>(v1), madd(b.z, Vec4vf<M>(v2), b.w * Vec4vf<M>(v3))));
+      }
+
+      template<int M>
+      __forceinline void veval(const vfloat<M>& t, Vec4vf<M>& p, Vec4vf<M>& dp) const
+      {
+        p = veval<M>(t);
+        dp = veval_du<M>(t);
+      }
+      
+      template<int M>
+      __forceinline Vec4vf<M> eval0(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedCatmullRomBasis::N);
+        assert(ofs <= size);
+        return madd(vfloat<M>::loadu(&catmullrom_basis0.c0[size][ofs]), Vec4vf<M>(v0),
+                    madd(vfloat<M>::loadu(&catmullrom_basis0.c1[size][ofs]), Vec4vf<M>(v1),
+                         madd(vfloat<M>::loadu(&catmullrom_basis0.c2[size][ofs]), Vec4vf<M>(v2),
+                              vfloat<M>::loadu(&catmullrom_basis0.c3[size][ofs]) * Vec4vf<M>(v3))));
+      }
+      
+      template<int M>
+      __forceinline Vec4vf<M> eval1(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedCatmullRomBasis::N);
+        assert(ofs <= size);
+        return madd(vfloat<M>::loadu(&catmullrom_basis1.c0[size][ofs]), Vec4vf<M>(v0), 
+                    madd(vfloat<M>::loadu(&catmullrom_basis1.c1[size][ofs]), Vec4vf<M>(v1),
+                         madd(vfloat<M>::loadu(&catmullrom_basis1.c2[size][ofs]), Vec4vf<M>(v2),
+                              vfloat<M>::loadu(&catmullrom_basis1.c3[size][ofs]) * Vec4vf<M>(v3))));
+      }
+      
+      template<int M>
+      __forceinline Vec4vf<M> derivative0(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedCatmullRomBasis::N);
+        assert(ofs <= size);
+        return madd(vfloat<M>::loadu(&catmullrom_basis0.d0[size][ofs]), Vec4vf<M>(v0),
+                    madd(vfloat<M>::loadu(&catmullrom_basis0.d1[size][ofs]), Vec4vf<M>(v1),
+                         madd(vfloat<M>::loadu(&catmullrom_basis0.d2[size][ofs]), Vec4vf<M>(v2),
+                              vfloat<M>::loadu(&catmullrom_basis0.d3[size][ofs]) * Vec4vf<M>(v3))));
+      }
+      
+      template<int M>
+      __forceinline Vec4vf<M> derivative1(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedCatmullRomBasis::N);
+        assert(ofs <= size);
+        return madd(vfloat<M>::loadu(&catmullrom_basis1.d0[size][ofs]), Vec4vf<M>(v0),
+                    madd(vfloat<M>::loadu(&catmullrom_basis1.d1[size][ofs]), Vec4vf<M>(v1),
+                         madd(vfloat<M>::loadu(&catmullrom_basis1.d2[size][ofs]), Vec4vf<M>(v2),
+                              vfloat<M>::loadu(&catmullrom_basis1.d3[size][ofs]) * Vec4vf<M>(v3))));
+      }
+      
+      /* calculates bounds of catmull-rom curve geometry */
+      __forceinline BBox3fa accurateRoundBounds() const
+      {
+        const int N = 7;
+        const float scale = 1.0f/(3.0f*(N-1));
+        Vec4vfx pl(pos_inf), pu(neg_inf);
+        for (int i=0; i<=N; i+=VSIZEX)
+        {
+          vintx vi = vintx(i)+vintx(step);
+          vboolx valid = vi <= vintx(N);
+          const Vec4vfx p  = eval0<VSIZEX>(i,N);
+          const Vec4vfx dp = derivative0<VSIZEX>(i,N);
+          const Vec4vfx pm = p-Vec4vfx(scale)*select(vi!=vintx(0),dp,Vec4vfx(zero));
+          const Vec4vfx pp = p+Vec4vfx(scale)*select(vi!=vintx(N),dp,Vec4vfx(zero));
+          pl = select(valid,min(pl,p,pm,pp),pl); // FIXME: use masked min
+          pu = select(valid,max(pu,p,pm,pp),pu); // FIXME: use masked min
+        }
+        const Vec3fa lower(reduce_min(pl.x),reduce_min(pl.y),reduce_min(pl.z));
+        const Vec3fa upper(reduce_max(pu.x),reduce_max(pu.y),reduce_max(pu.z));
+        const float r_min = reduce_min(pl.w);
+        const float r_max = reduce_max(pu.w);
+        const Vec3fa upper_r = Vec3fa(max(abs(r_min),abs(r_max)));
+        return enlarge(BBox3fa(lower,upper),upper_r);
+      }
+      
+      /* calculates bounds when tessellated into N line segments */
+      __forceinline BBox3fa accurateFlatBounds(int N) const
+      {
+        if (likely(N == 4))
+        {
+          const Vec4vf4 pi = eval0<4>(0,4);
+          const Vec3fa lower(reduce_min(pi.x),reduce_min(pi.y),reduce_min(pi.z));
+          const Vec3fa upper(reduce_max(pi.x),reduce_max(pi.y),reduce_max(pi.z));
+          const Vec3fa upper_r = Vec3fa(reduce_max(abs(pi.w)));
+          const Vec3ff pe = end();
+          return enlarge(BBox3fa(min(lower,pe),max(upper,pe)),max(upper_r,Vec3fa(abs(pe.w))));
+        } 
+        else
+        {
+          Vec3vfx pl(pos_inf), pu(neg_inf); vfloatx ru(0.0f);
+          for (int i=0; i<=N; i+=VSIZEX)
+          {
+            vboolx valid = vintx(i)+vintx(step) <= vintx(N);
+            const Vec4vfx pi = eval0<VSIZEX>(i,N);
+            
+            pl.x = select(valid,min(pl.x,pi.x),pl.x); // FIXME: use masked min
+            pl.y = select(valid,min(pl.y,pi.y),pl.y); 
+            pl.z = select(valid,min(pl.z,pi.z),pl.z); 
+            
+            pu.x = select(valid,max(pu.x,pi.x),pu.x); // FIXME: use masked min
+            pu.y = select(valid,max(pu.y,pi.y),pu.y); 
+            pu.z = select(valid,max(pu.z,pi.z),pu.z); 
+            
+            ru = select(valid,max(ru,abs(pi.w)),ru); 
+          }
+          const Vec3fa lower(reduce_min(pl.x),reduce_min(pl.y),reduce_min(pl.z));
+          const Vec3fa upper(reduce_max(pu.x),reduce_max(pu.y),reduce_max(pu.z));
+          const Vec3fa upper_r(reduce_max(ru));
+          return enlarge(BBox3fa(lower,upper),upper_r);
+        }
+      }
+      
+      friend __forceinline embree_ostream operator<<(embree_ostream cout, const CatmullRomCurveT& curve) {
+        return cout << "CatmullRomCurve { v0 = " << curve.v0 << ", v1 = " << curve.v1 << ", v2 = " << curve.v2 << ", v3 = " << curve.v3 << " }";
+      }
+    };
+
+  template<typename Vertex>
+    __forceinline void convert(const CatmullRomCurveT<Vertex>& icurve, BezierCurveT<Vertex>& ocurve)
+  {
+    const Vertex v0 = icurve.v1;
+    const Vertex v1 = icurve.v1+(icurve.v2-icurve.v0)*(1.0f/6.0f);
+    const Vertex v2 = icurve.v2+(icurve.v1-icurve.v3)*(1.0f/6.0f);
+    const Vertex v3 = icurve.v2;
+    ocurve = BezierCurveT<Vertex>(v0,v1,v2,v3);
+  }
+
+  template<typename CurveGeometry>
+  __forceinline CatmullRomCurveT<Vec3ff> enlargeRadiusToMinWidth(const RayQueryContext* context, const CurveGeometry* geom, const Vec3fa& ray_org, const CatmullRomCurveT<Vec3ff>& curve)
+  {
+    return CatmullRomCurveT<Vec3ff>(enlargeRadiusToMinWidth(context,geom,ray_org,curve.v0),
+                                    enlargeRadiusToMinWidth(context,geom,ray_org,curve.v1),
+                                    enlargeRadiusToMinWidth(context,geom,ray_org,curve.v2),
+                                    enlargeRadiusToMinWidth(context,geom,ray_org,curve.v3));
+  }
+  
+  typedef CatmullRomCurveT<Vec3fa> CatmullRomCurve3fa;
+}
+

thirdparty/embree/kernels/subdiv/feature_adaptive_eval.h

@@ -0,0 +1,226 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "patch.h"
+
+namespace embree
+{
+  namespace isa
+  {
+    template<typename Vertex, typename Vertex_t = Vertex>
+      struct FeatureAdaptiveEval
+      {
+      public:
+        
+        typedef PatchT<Vertex,Vertex_t> Patch;
+        typedef typename Patch::Ref Ref;
+        typedef GeneralCatmullClarkPatchT<Vertex,Vertex_t> GeneralCatmullClarkPatch;
+        typedef CatmullClark1RingT<Vertex,Vertex_t> CatmullClarkRing;
+        typedef CatmullClarkPatchT<Vertex,Vertex_t> CatmullClarkPatch;
+        typedef BSplinePatchT<Vertex,Vertex_t> BSplinePatch;
+        typedef BezierPatchT<Vertex,Vertex_t> BezierPatch;
+        typedef GregoryPatchT<Vertex,Vertex_t> GregoryPatch;
+        typedef BilinearPatchT<Vertex,Vertex_t> BilinearPatch;
+        typedef BezierCurveT<Vertex> BezierCurve;
+        
+      public:
+        
+        FeatureAdaptiveEval (const HalfEdge* edge, const char* vertices, size_t stride, const float u, const float v, 
+                             Vertex* P, Vertex* dPdu, Vertex* dPdv, Vertex* ddPdudu, Vertex* ddPdvdv, Vertex* ddPdudv)
+        : P(P), dPdu(dPdu), dPdv(dPdv), ddPdudu(ddPdudu), ddPdvdv(ddPdvdv), ddPdudv(ddPdudv)
+        {
+          switch (edge->patch_type) {
+          case HalfEdge::BILINEAR_PATCH: BilinearPatch(edge,vertices,stride).eval(u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,1.0f); break;
+          case HalfEdge::REGULAR_QUAD_PATCH: RegularPatchT(edge,vertices,stride).eval(u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,1.0f); break;
+#if PATCH_USE_GREGORY == 2
+          case HalfEdge::IRREGULAR_QUAD_PATCH: GregoryPatch(edge,vertices,stride).eval(u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,1.0f); break;
+#endif
+          default: {
+            GeneralCatmullClarkPatch patch(edge,vertices,stride);
+            eval(patch,Vec2f(u,v),0);
+            break;
+          }
+          }
+        }
+
+        FeatureAdaptiveEval (CatmullClarkPatch& patch, const float u, const float v, float dscale, size_t depth, 
+                             Vertex* P, Vertex* dPdu, Vertex* dPdv, Vertex* ddPdudu, Vertex* ddPdvdv, Vertex* ddPdudv)
+        : P(P), dPdu(dPdu), dPdv(dPdv), ddPdudu(ddPdudu), ddPdvdv(ddPdvdv), ddPdudv(ddPdudv)
+        {
+          eval(patch,Vec2f(u,v),dscale,depth);
+        }
+        
+        void eval_general_quad(const GeneralCatmullClarkPatch& patch, array_t<CatmullClarkPatch,GeneralCatmullClarkPatch::SIZE>& patches, const Vec2f& uv, size_t depth)
+        {
+          float u = uv.x, v = uv.y;
+          if (v < 0.5f) {
+            if (u < 0.5f) {
+#if PATCH_USE_GREGORY == 2
+              BezierCurve borders[2]; patch.getLimitBorder(borders,0);
+              BezierCurve border0l,border0r; borders[0].subdivide(border0l,border0r);
+              BezierCurve border2l,border2r; borders[1].subdivide(border2l,border2r);
+              eval(patches[0],Vec2f(2.0f*u,2.0f*v),2.0f,depth+1, &border0l, nullptr, nullptr, &border2r);
+#else
+              eval(patches[0],Vec2f(2.0f*u,2.0f*v),2.0f,depth+1);
+#endif
+              if (dPdu && dPdv) {
+                const Vertex dpdx = *dPdu, dpdy = *dPdv;
+                *dPdu = dpdx; *dPdv = dpdy;
+              }
+            }
+            else {
+#if PATCH_USE_GREGORY == 2
+              BezierCurve borders[2]; patch.getLimitBorder(borders,1);
+              BezierCurve border0l,border0r; borders[0].subdivide(border0l,border0r);
+              BezierCurve border2l,border2r; borders[1].subdivide(border2l,border2r);
+              eval(patches[1],Vec2f(2.0f*v,2.0f-2.0f*u),2.0f,depth+1, &border0l, nullptr, nullptr, &border2r);
+#else
+              eval(patches[1],Vec2f(2.0f*v,2.0f-2.0f*u),2.0f,depth+1);
+#endif
+              if (dPdu && dPdv) {
+                const Vertex dpdx = *dPdu, dpdy = *dPdv;
+                *dPdu = -dpdy; *dPdv = dpdx;
+              }
+            }
+          } else {
+            if (u > 0.5f) {
+#if PATCH_USE_GREGORY == 2
+              BezierCurve borders[2]; patch.getLimitBorder(borders,2);
+              BezierCurve border0l,border0r; borders[0].subdivide(border0l,border0r);
+              BezierCurve border2l,border2r; borders[1].subdivide(border2l,border2r);
+              eval(patches[2],Vec2f(2.0f-2.0f*u,2.0f-2.0f*v),2.0f,depth+1, &border0l, nullptr, nullptr, &border2r);
+#else
+              eval(patches[2],Vec2f(2.0f-2.0f*u,2.0f-2.0f*v),2.0f,depth+1);
+#endif
+              if (dPdu && dPdv) {
+                const Vertex dpdx = *dPdu, dpdy = *dPdv;
+                *dPdu = -dpdx; *dPdv = -dpdy;
+              }
+            }
+            else {
+#if PATCH_USE_GREGORY == 2
+              BezierCurve borders[2]; patch.getLimitBorder(borders,3);
+              BezierCurve border0l,border0r; borders[0].subdivide(border0l,border0r);
+              BezierCurve border2l,border2r; borders[1].subdivide(border2l,border2r);
+              eval(patches[3],Vec2f(2.0f-2.0f*v,2.0f*u),2.0f,depth+1, &border0l, nullptr, nullptr, &border2r);
+#else
+              eval(patches[3],Vec2f(2.0f-2.0f*v,2.0f*u),2.0f,depth+1);
+#endif
+              if (dPdu && dPdv) {
+                const Vertex dpdx = *dPdu, dpdy = *dPdv;
+                *dPdu = dpdy; *dPdv = -dpdx;
+              }
+            }
+          }
+        }
+
+        __forceinline bool final(const CatmullClarkPatch& patch, const typename CatmullClarkRing::Type type, size_t depth) 
+        {
+          const int max_eval_depth = (type & CatmullClarkRing::TYPE_CREASES) ? PATCH_MAX_EVAL_DEPTH_CREASE : PATCH_MAX_EVAL_DEPTH_IRREGULAR;
+//#if PATCH_MIN_RESOLUTION
+//          return patch.isFinalResolution(PATCH_MIN_RESOLUTION) || depth>=(size_t)max_eval_depth;
+//#else
+          return depth>=(size_t)max_eval_depth;
+//#endif
+        }
+        
+        void eval(CatmullClarkPatch& patch, Vec2f uv, float dscale, size_t depth, 
+                  BezierCurve* border0 = nullptr, BezierCurve* border1 = nullptr, BezierCurve* border2 = nullptr, BezierCurve* border3 = nullptr)
+        {
+          while (true) 
+          {
+            typename CatmullClarkPatch::Type ty = patch.type();
+
+            if (unlikely(final(patch,ty,depth)))
+            {
+              if (ty & CatmullClarkRing::TYPE_REGULAR) { 
+                RegularPatch(patch,border0,border1,border2,border3).eval(uv.x,uv.y,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale); 
+                PATCH_DEBUG_SUBDIVISION(234423,c,c,-1);
+                return;
+              } else {
+                IrregularFillPatch(patch,border0,border1,border2,border3).eval(uv.x,uv.y,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale); 
+                PATCH_DEBUG_SUBDIVISION(34534,c,-1,c);
+                return;
+              }
+            }
+            else if (ty & CatmullClarkRing::TYPE_REGULAR_CREASES) { 
+              assert(depth > 0); 
+              RegularPatch(patch,border0,border1,border2,border3).eval(uv.x,uv.y,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale); 
+              PATCH_DEBUG_SUBDIVISION(43524,c,c,-1);
+              return;
+            }
+#if PATCH_USE_GREGORY == 2
+            else if (ty & CatmullClarkRing::TYPE_GREGORY_CREASES) { 
+              assert(depth > 0); 
+              GregoryPatch(patch,border0,border1,border2,border3).eval(uv.x,uv.y,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale); 
+              PATCH_DEBUG_SUBDIVISION(23498,c,-1,c);
+              return;
+            }
+#endif
+            else
+            {
+              array_t<CatmullClarkPatch,4> patches; 
+              patch.subdivide(patches); // FIXME: only have to generate one of the patches
+              
+              const float u = uv.x, v = uv.y;
+              if (v < 0.5f) {
+                if (u < 0.5f) { patch = patches[0]; uv = Vec2f(2.0f*u,2.0f*v); dscale *= 2.0f; }
+                else          { patch = patches[1]; uv = Vec2f(2.0f*u-1.0f,2.0f*v); dscale *= 2.0f; }
+              } else {
+                if (u > 0.5f) { patch = patches[2]; uv = Vec2f(2.0f*u-1.0f,2.0f*v-1.0f); dscale *= 2.0f; }
+                else          { patch = patches[3]; uv = Vec2f(2.0f*u,2.0f*v-1.0f); dscale *= 2.0f; }
+              }
+              depth++;
+            }
+          }
+        }
+        
+        void eval(const GeneralCatmullClarkPatch& patch, const Vec2f& uv, const size_t depth) 
+        {  
+          /* convert into standard quad patch if possible */
+          if (likely(patch.isQuadPatch())) 
+          {
+            CatmullClarkPatch qpatch; patch.init(qpatch);
+            return eval(qpatch,uv,1.0f,depth); 
+          }
+          
+          /* subdivide patch */
+          unsigned N;
+          array_t<CatmullClarkPatch,GeneralCatmullClarkPatch::SIZE> patches; 
+          patch.subdivide(patches,N); // FIXME: only have to generate one of the patches
+          
+          /* parametrization for quads */
+          if (N == 4) 
+            eval_general_quad(patch,patches,uv,depth);
+          
+          /* parametrization for arbitrary polygons */
+          else 
+          {
+            const unsigned l = (unsigned) floor(0.5f*uv.x); const float u = 2.0f*frac(0.5f*uv.x)-0.5f; 
+            const unsigned h = (unsigned) floor(0.5f*uv.y); const float v = 2.0f*frac(0.5f*uv.y)-0.5f; 
+            const unsigned i = 4*h+l; assert(i<N);
+            if (i >= N) return;
+
+#if PATCH_USE_GREGORY == 2
+            BezierCurve borders[2]; patch.getLimitBorder(borders,i);
+            BezierCurve border0l,border0r; borders[0].subdivide(border0l,border0r);
+            BezierCurve border2l,border2r; borders[1].subdivide(border2l,border2r);
+            eval(patches[i],Vec2f(u,v),1.0f,depth+1, &border0l, nullptr, nullptr, &border2r);
+#else
+            eval(patches[i],Vec2f(u,v),1.0f,depth+1);
+#endif
+          }
+        }
+        
+      private:
+        Vertex* const P;
+        Vertex* const dPdu;
+        Vertex* const dPdv;
+        Vertex* const ddPdudu;
+        Vertex* const ddPdvdv;
+        Vertex* const ddPdudv;
+      };
+  }
+}

thirdparty/embree/kernels/subdiv/feature_adaptive_eval_grid.h

@@ -0,0 +1,359 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "patch.h"
+#include "catmullclark_patch.h"
+#include "bspline_patch.h"
+#include "gregory_patch.h"
+#include "tessellation.h"
+
+namespace embree
+{
+  namespace isa 
+  {
+    struct FeatureAdaptiveEvalGrid
+    {
+      typedef CatmullClark1Ring3fa CatmullClarkRing;
+      typedef CatmullClarkPatch3fa CatmullClarkPatch;
+      typedef BilinearPatch3fa BilinearPatch;
+      typedef BSplinePatch3fa BSplinePatch;
+      typedef BezierPatch3fa BezierPatch;
+      typedef GregoryPatch3fa GregoryPatch;
+
+    private:
+      const unsigned x0,x1;
+      const unsigned y0,y1;
+      const unsigned swidth,sheight;
+      const float rcp_swidth, rcp_sheight;
+      float* const Px;
+      float* const Py;
+      float* const Pz;
+      float* const U;
+      float* const V;
+      float* const Nx;
+      float* const Ny;
+      float* const Nz;
+      const unsigned dwidth;
+      //const unsigned dheight;
+      unsigned count;
+      
+
+    public:      
+      FeatureAdaptiveEvalGrid (const GeneralCatmullClarkPatch3fa& patch, unsigned subPatch,
+                               const unsigned x0, const unsigned x1, const unsigned y0, const unsigned y1, const unsigned swidth, const unsigned sheight, 
+                               float* Px, float* Py, float* Pz, float* U, float* V, 
+                               float* Nx, float* Ny, float* Nz,
+                               const unsigned dwidth, const unsigned dheight)
+      : x0(x0), x1(x1), y0(y0), y1(y1), swidth(swidth), sheight(sheight), rcp_swidth(1.0f/(swidth-1.0f)), rcp_sheight(1.0f/(sheight-1.0f)), 
+        Px(Px), Py(Py), Pz(Pz), U(U), V(V), Nx(Nx), Ny(Ny), Nz(Nz), dwidth(dwidth), /*dheight(dheight),*/ count(0)
+      {
+        assert(swidth < (2<<20) && sheight < (2<<20));
+        const BBox2f srange(Vec2f(0.0f,0.0f),Vec2f(float(swidth-1),float(sheight-1)));
+        const BBox2f erange(Vec2f((float)x0,(float)y0),Vec2f((float)x1,(float)y1));
+        
+        /* convert into standard quad patch if possible */
+        if (likely(patch.isQuadPatch())) 
+        {
+          CatmullClarkPatch3fa qpatch; patch.init(qpatch);
+          eval(qpatch, srange, erange, 0);
+          assert(count == (x1-x0+1)*(y1-y0+1));
+          return;
+        }
+        
+        /* subdivide patch */
+        unsigned N;
+        array_t<CatmullClarkPatch3fa,GeneralCatmullClarkPatch3fa::SIZE> patches; 
+        patch.subdivide(patches,N);
+        
+        if (N == 4)
+        {
+          const Vec2f c = srange.center();
+          const BBox2f srange0(srange.lower,c);
+          const BBox2f srange1(Vec2f(c.x,srange.lower.y),Vec2f(srange.upper.x,c.y));
+          const BBox2f srange2(c,srange.upper);
+          const BBox2f srange3(Vec2f(srange.lower.x,c.y),Vec2f(c.x,srange.upper.y));
+
+#if PATCH_USE_GREGORY == 2
+          BezierCurve3fa borders[GeneralCatmullClarkPatch3fa::SIZE]; patch.getLimitBorder(borders);
+          BezierCurve3fa border0l,border0r; borders[0].subdivide(border0l,border0r);
+          BezierCurve3fa border1l,border1r; borders[1].subdivide(border1l,border1r);
+          BezierCurve3fa border2l,border2r; borders[2].subdivide(border2l,border2r);
+          BezierCurve3fa border3l,border3r; borders[3].subdivide(border3l,border3r);
+          GeneralCatmullClarkPatch3fa::fix_quad_ring_order(patches);
+          eval(patches[0],srange0,intersect(srange0,erange),1,&border0l,nullptr,nullptr,&border3r);
+          eval(patches[1],srange1,intersect(srange1,erange),1,&border0r,&border1l,nullptr,nullptr);
+          eval(patches[2],srange2,intersect(srange2,erange),1,nullptr,&border1r,&border2l,nullptr);
+          eval(patches[3],srange3,intersect(srange3,erange),1,nullptr,nullptr,&border2r,&border3l);
+#else
+          GeneralCatmullClarkPatch3fa::fix_quad_ring_order(patches);
+          eval(patches[0],srange0,intersect(srange0,erange),1);
+          eval(patches[1],srange1,intersect(srange1,erange),1);
+          eval(patches[2],srange2,intersect(srange2,erange),1);
+          eval(patches[3],srange3,intersect(srange3,erange),1);
+#endif
+        }
+        else
+        {
+          assert(subPatch < N);
+          
+#if PATCH_USE_GREGORY == 2
+          BezierCurve3fa borders[2]; patch.getLimitBorder(borders,subPatch);
+          BezierCurve3fa border0l,border0r; borders[0].subdivide(border0l,border0r);
+          BezierCurve3fa border2l,border2r; borders[1].subdivide(border2l,border2r);
+          eval(patches[subPatch], srange, erange, 1, &border0l, nullptr, nullptr, &border2r);
+#else
+          eval(patches[subPatch], srange, erange, 1);
+#endif
+          
+        }
+        assert(count == (x1-x0+1)*(y1-y0+1));
+      }
+      
+      FeatureAdaptiveEvalGrid (const CatmullClarkPatch3fa& patch,
+                               const BBox2f& srange, const BBox2f& erange, const unsigned depth,
+                               const unsigned x0, const unsigned x1, const unsigned y0, const unsigned y1, const unsigned swidth, const unsigned sheight, 
+                               float* Px, float* Py, float* Pz, float* U, float* V, 
+                               float* Nx, float* Ny, float* Nz,
+                               const unsigned dwidth, const unsigned dheight)
+      : x0(x0), x1(x1), y0(y0), y1(y1), swidth(swidth), sheight(sheight), rcp_swidth(1.0f/(swidth-1.0f)), rcp_sheight(1.0f/(sheight-1.0f)), 
+        Px(Px), Py(Py), Pz(Pz), U(U), V(V), Nx(Nx), Ny(Ny), Nz(Nz), dwidth(dwidth), /*dheight(dheight),*/ count(0)
+      {
+        eval(patch,srange,erange,depth);
+      }
+
+      template<typename Patch>
+      void evalLocalGrid(const Patch& patch, const BBox2f& srange, const int lx0, const int lx1, const int ly0, const int ly1)
+      {
+        const float scale_x = rcp(srange.upper.x-srange.lower.x);
+        const float scale_y = rcp(srange.upper.y-srange.lower.y);
+        count += (lx1-lx0)*(ly1-ly0);
+        
+#if 0
+        for (unsigned iy=ly0; iy<ly1; iy++) {
+          for (unsigned ix=lx0; ix<lx1; ix++) {
+            const float lu = select(ix == swidth -1, float(1.0f), (float(ix)-srange.lower.x)*scale_x);
+            const float lv = select(iy == sheight-1, float(1.0f), (float(iy)-srange.lower.y)*scale_y);
+            const Vec3fa p = patch.eval(lu,lv);
+            const float u = float(ix)*rcp_swidth;
+            const float v = float(iy)*rcp_sheight;
+            const int ofs = (iy-y0)*dwidth+(ix-x0);
+            Px[ofs] = p.x;
+            Py[ofs] = p.y;
+            Pz[ofs] = p.z;
+            U[ofs] = u;
+            V[ofs] = v;
+          }
+        }
+#else
+        foreach2(lx0,lx1,ly0,ly1,[&](const vboolx& valid, const vintx& ix, const vintx& iy) {
+            const vfloatx lu = select(ix == swidth -1, vfloatx(1.0f), (vfloatx(ix)-srange.lower.x)*scale_x);
+            const vfloatx lv = select(iy == sheight-1, vfloatx(1.0f), (vfloatx(iy)-srange.lower.y)*scale_y);
+            const Vec3vfx p = patch.eval(lu,lv);
+            Vec3vfx n = zero;
+            if (unlikely(Nx != nullptr)) n = normalize_safe(patch.normal(lu,lv));
+            const vfloatx u = vfloatx(ix)*rcp_swidth;
+            const vfloatx v = vfloatx(iy)*rcp_sheight;
+            const vintx ofs = (iy-y0)*dwidth+(ix-x0);
+            if (likely(all(valid)) && all(iy==iy[0])) {
+              const unsigned ofs2 = ofs[0];
+              vfloatx::storeu(Px+ofs2,p.x);
+              vfloatx::storeu(Py+ofs2,p.y);
+              vfloatx::storeu(Pz+ofs2,p.z);
+              vfloatx::storeu(U+ofs2,u);
+              vfloatx::storeu(V+ofs2,v);
+              if (unlikely(Nx != nullptr)) {
+                vfloatx::storeu(Nx+ofs2,n.x);
+                vfloatx::storeu(Ny+ofs2,n.y);
+                vfloatx::storeu(Nz+ofs2,n.z);
+              }
+            } else {
+              foreach_unique_index(valid,iy,[&](const vboolx& valid, const int iy0, const int j) {
+                  const unsigned ofs2 = ofs[j]-j;
+                  vfloatx::storeu(valid,Px+ofs2,p.x);
+                  vfloatx::storeu(valid,Py+ofs2,p.y);
+                  vfloatx::storeu(valid,Pz+ofs2,p.z);
+                  vfloatx::storeu(valid,U+ofs2,u);
+                  vfloatx::storeu(valid,V+ofs2,v);
+                  if (unlikely(Nx != nullptr)) {
+                    vfloatx::storeu(valid,Nx+ofs2,n.x);
+                    vfloatx::storeu(valid,Ny+ofs2,n.y);
+                    vfloatx::storeu(valid,Nz+ofs2,n.z);
+                  }
+                });
+            }
+          });
+#endif
+      }
+      
+      __forceinline bool final(const CatmullClarkPatch3fa& patch, const CatmullClarkRing::Type type, unsigned depth) 
+      {
+        const unsigned max_eval_depth = (type & CatmullClarkRing::TYPE_CREASES) ? PATCH_MAX_EVAL_DEPTH_CREASE : PATCH_MAX_EVAL_DEPTH_IRREGULAR;
+//#if PATCH_MIN_RESOLUTION
+//        return patch.isFinalResolution(PATCH_MIN_RESOLUTION) || depth>=max_eval_depth;
+//#else
+        return depth>=max_eval_depth;
+//#endif
+      }
+      
+      void eval(const CatmullClarkPatch3fa& patch, const BBox2f& srange, const BBox2f& erange, const unsigned depth, 
+                const BezierCurve3fa* border0 = nullptr, const BezierCurve3fa* border1 = nullptr, const BezierCurve3fa* border2 = nullptr, const BezierCurve3fa* border3 = nullptr)
+      {
+        if (erange.empty())
+          return;
+        
+        int lx0 = (int) ceilf(erange.lower.x);
+        int lx1 = (int) ceilf(erange.upper.x) + (erange.upper.x == x1 && (srange.lower.x < erange.upper.x || erange.upper.x == 0));
+        int ly0 = (int) ceilf(erange.lower.y);
+        int ly1 = (int) ceilf(erange.upper.y) + (erange.upper.y == y1 && (srange.lower.y < erange.upper.y || erange.upper.y == 0));
+        if (lx0 >= lx1 || ly0 >= ly1) return;
+
+        CatmullClarkPatch::Type ty = patch.type();
+
+        if (unlikely(final(patch,ty,depth)))
+        {
+          if (ty & CatmullClarkRing::TYPE_REGULAR) {
+            RegularPatch rpatch(patch,border0,border1,border2,border3);
+            evalLocalGrid(rpatch,srange,lx0,lx1,ly0,ly1);
+            return;
+          } else {
+            IrregularFillPatch ipatch(patch,border0,border1,border2,border3);
+            evalLocalGrid(ipatch,srange,lx0,lx1,ly0,ly1);
+            return;
+          }
+        }
+        else if (ty & CatmullClarkRing::TYPE_REGULAR_CREASES) { 
+          assert(depth > 0); 
+          RegularPatch rpatch(patch,border0,border1,border2,border3);
+          evalLocalGrid(rpatch,srange,lx0,lx1,ly0,ly1);
+          return;
+        }
+#if PATCH_USE_GREGORY == 2
+        else if (ty & CatmullClarkRing::TYPE_GREGORY_CREASES) { 
+          assert(depth > 0); 
+          GregoryPatch gpatch(patch,border0,border1,border2,border3);
+          evalLocalGrid(gpatch,srange,lx0,lx1,ly0,ly1);
+        }
+#endif
+        else
+        {
+          array_t<CatmullClarkPatch3fa,4> patches; 
+          patch.subdivide(patches);
+          
+          const Vec2f c = srange.center();
+          const BBox2f srange0(srange.lower,c);
+          const BBox2f srange1(Vec2f(c.x,srange.lower.y),Vec2f(srange.upper.x,c.y));
+          const BBox2f srange2(c,srange.upper);
+          const BBox2f srange3(Vec2f(srange.lower.x,c.y),Vec2f(c.x,srange.upper.y));
+          
+          eval(patches[0],srange0,intersect(srange0,erange),depth+1);
+          eval(patches[1],srange1,intersect(srange1,erange),depth+1);
+          eval(patches[2],srange2,intersect(srange2,erange),depth+1);
+          eval(patches[3],srange3,intersect(srange3,erange),depth+1);
+        }
+      }
+    };
+    
+    template<typename Eval, typename Patch>
+      bool stitch_col(const Patch& patch, int subPatch,
+                      const bool right, const unsigned y0, const unsigned y1, const int fine_y, const int coarse_y, 
+                      float* Px, float* Py, float* Pz, float* U, float* V, float* Nx, float* Ny, float* Nz, const unsigned dx0, const unsigned dwidth, const unsigned dheight)
+    {
+      assert(coarse_y <= fine_y);
+      if (likely(fine_y == coarse_y))
+        return false;
+      
+      const unsigned y0s = stitch(y0,fine_y,coarse_y);
+      const unsigned y1s = stitch(y1,fine_y,coarse_y);
+      const unsigned M = y1s-y0s+1 + VSIZEX;
+      
+      dynamic_large_stack_array(float,px,M,64*sizeof(float));
+      dynamic_large_stack_array(float,py,M,64*sizeof(float));
+      dynamic_large_stack_array(float,pz,M,64*sizeof(float));
+      dynamic_large_stack_array(float,u,M,64*sizeof(float));
+      dynamic_large_stack_array(float,v,M,64*sizeof(float));
+      dynamic_large_stack_array(float,nx,M,64*sizeof(float));
+      dynamic_large_stack_array(float,ny,M,64*sizeof(float));
+      dynamic_large_stack_array(float,nz,M,64*sizeof(float));
+      const bool has_Nxyz = Nx; assert(!Nx || (Ny && Nz));
+      Eval(patch,subPatch, right,right, y0s,y1s, 2,coarse_y+1, px,py,pz,u,v, 
+           has_Nxyz ? (float*)nx : nullptr,has_Nxyz ? (float*)ny : nullptr ,has_Nxyz ? (float*)nz : nullptr, 1,4097);
+      
+      for (unsigned y=y0; y<=y1; y++) 
+      {
+        const unsigned ys = stitch(y,fine_y,coarse_y)-y0s;
+        Px[(y-y0)*dwidth+dx0] = px[ys];
+        Py[(y-y0)*dwidth+dx0] = py[ys];
+        Pz[(y-y0)*dwidth+dx0] = pz[ys];
+        U [(y-y0)*dwidth+dx0] = u[ys];
+        V [(y-y0)*dwidth+dx0] = v[ys];
+        if (unlikely(has_Nxyz)) {
+          Nx[(y-y0)*dwidth+dx0] = nx[ys];
+          Ny[(y-y0)*dwidth+dx0] = ny[ys];
+          Nz[(y-y0)*dwidth+dx0] = nz[ys];
+        }
+      }
+      return true;
+    }
+    
+    template<typename Eval, typename Patch>
+      bool stitch_row(const Patch& patch, int subPatch, 
+                      const bool bottom, const unsigned x0, const unsigned x1, const int fine_x, const int coarse_x, 
+                      float* Px, float* Py, float* Pz, float* U, float* V, float* Nx, float* Ny, float* Nz, const unsigned dy0, const unsigned dwidth, const unsigned dheight)
+    {
+      assert(coarse_x <= fine_x);
+      if (likely(fine_x == coarse_x))
+	return false;
+      
+      const unsigned x0s = stitch(x0,fine_x,coarse_x);
+      const unsigned x1s = stitch(x1,fine_x,coarse_x);
+      const unsigned M = x1s-x0s+1 + VSIZEX;
+
+      dynamic_large_stack_array(float,px,M,32*sizeof(float));
+      dynamic_large_stack_array(float,py,M,32*sizeof(float));
+      dynamic_large_stack_array(float,pz,M,32*sizeof(float));
+      dynamic_large_stack_array(float,u,M,32*sizeof(float));
+      dynamic_large_stack_array(float,v,M,32*sizeof(float));
+      dynamic_large_stack_array(float,nx,M,32*sizeof(float));
+      dynamic_large_stack_array(float,ny,M,32*sizeof(float));
+      dynamic_large_stack_array(float,nz,M,32*sizeof(float));
+      const bool has_Nxyz = Nx; assert(!Nx || (Ny && Nz));
+      Eval(patch,subPatch, x0s,x1s, bottom,bottom, coarse_x+1,2, px,py,pz,u,v, 
+           has_Nxyz ? (float*)nx :nullptr, has_Nxyz ? (float*)ny : nullptr , has_Nxyz ? (float*)nz : nullptr, 4097,1);
+      
+      for (unsigned x=x0; x<=x1; x++) 
+      {
+	const unsigned xs = stitch(x,fine_x,coarse_x)-x0s;
+	Px[dy0*dwidth+x-x0] = px[xs];
+        Py[dy0*dwidth+x-x0] = py[xs];
+        Pz[dy0*dwidth+x-x0] = pz[xs];
+        U [dy0*dwidth+x-x0] = u[xs];
+        V [dy0*dwidth+x-x0] = v[xs];
+        if (unlikely(has_Nxyz)) {
+          Nx[dy0*dwidth+x-x0] = nx[xs];
+          Ny[dy0*dwidth+x-x0] = ny[xs];
+          Nz[dy0*dwidth+x-x0] = nz[xs];
+        }
+      }
+      return true;
+    }
+    
+    template<typename Eval, typename Patch>
+    void feature_adaptive_eval_grid (const Patch& patch, unsigned subPatch, const float levels[4],
+                                     const unsigned x0, const unsigned x1, const unsigned y0, const unsigned y1, const unsigned swidth, const unsigned sheight, 
+                                     float* Px, float* Py, float* Pz, float* U, float* V, float* Nx, float* Ny, float* Nz, const unsigned dwidth, const unsigned dheight)
+    {
+      bool sl = false, sr = false, st = false, sb = false;
+      if (levels) {
+        sl = x0 == 0         && stitch_col<Eval,Patch>(patch,subPatch,0,y0,y1,sheight-1,int(levels[3]), Px,Py,Pz,U,V,Nx,Ny,Nz, 0    ,dwidth,dheight);
+        sr = x1 == swidth-1  && stitch_col<Eval,Patch>(patch,subPatch,1,y0,y1,sheight-1,int(levels[1]), Px,Py,Pz,U,V,Nx,Ny,Nz, x1-x0,dwidth,dheight);
+        st = y0 == 0         && stitch_row<Eval,Patch>(patch,subPatch,0,x0,x1,swidth-1,int(levels[0]), Px,Py,Pz,U,V,Nx,Ny,Nz, 0    ,dwidth,dheight);
+        sb = y1 == sheight-1 && stitch_row<Eval,Patch>(patch,subPatch,1,x0,x1,swidth-1,int(levels[2]), Px,Py,Pz,U,V,Nx,Ny,Nz, y1-y0,dwidth,dheight);
+      }
+      const unsigned ofs = st*dwidth+sl;
+      Eval(patch,subPatch,x0+sl,x1-sr,y0+st,y1-sb, swidth,sheight, Px+ofs,Py+ofs,Pz+ofs,U+ofs,V+ofs,Nx?Nx+ofs:nullptr,Ny?Ny+ofs:nullptr,Nz?Nz+ofs:nullptr, dwidth,dheight);
+    }
+  }
+}
+

thirdparty/embree/kernels/subdiv/feature_adaptive_eval_simd.h

@@ -0,0 +1,186 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "patch.h"
+
+namespace embree
+{
+  namespace isa
+  {
+    template<typename vbool, typename vint, typename vfloat, typename Vertex, typename Vertex_t = Vertex>
+      struct FeatureAdaptiveEvalSimd
+      {
+      public:
+        
+        typedef PatchT<Vertex,Vertex_t> Patch;
+        typedef typename Patch::Ref Ref;
+        typedef GeneralCatmullClarkPatchT<Vertex,Vertex_t> GeneralCatmullClarkPatch;
+        typedef CatmullClark1RingT<Vertex,Vertex_t> CatmullClarkRing;
+        typedef CatmullClarkPatchT<Vertex,Vertex_t> CatmullClarkPatch;
+        typedef BSplinePatchT<Vertex,Vertex_t> BSplinePatch;
+        typedef BezierPatchT<Vertex,Vertex_t> BezierPatch;
+        typedef GregoryPatchT<Vertex,Vertex_t> GregoryPatch;
+        typedef BilinearPatchT<Vertex,Vertex_t> BilinearPatch;
+        typedef BezierCurveT<Vertex> BezierCurve;
+
+        FeatureAdaptiveEvalSimd (const HalfEdge* edge, const char* vertices, size_t stride, const vbool& valid, const vfloat& u, const vfloat& v, 
+                                 float* P, float* dPdu, float* dPdv, float* ddPdudu, float* ddPdvdv, float* ddPdudv, const size_t dstride, const size_t N)
+        : P(P), dPdu(dPdu), dPdv(dPdv), ddPdudu(ddPdudu), ddPdvdv(ddPdvdv), ddPdudv(ddPdudv), dstride(dstride), N(N)
+        {
+          switch (edge->patch_type) {
+          case HalfEdge::BILINEAR_PATCH: BilinearPatch(edge,vertices,stride).eval(valid,u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,1.0f,dstride,N); break;
+          case HalfEdge::REGULAR_QUAD_PATCH: RegularPatchT(edge,vertices,stride).eval(valid,u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,1.0f,dstride,N); break;
+#if PATCH_USE_GREGORY == 2
+          case HalfEdge::IRREGULAR_QUAD_PATCH: GregoryPatchT<Vertex,Vertex_t>(edge,vertices,stride).eval(valid,u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,1.0f,dstride,N); break;
+#endif
+          default: {
+            GeneralCatmullClarkPatch patch(edge,vertices,stride);
+            eval_direct(valid,patch,Vec2<vfloat>(u,v),0);
+            break;
+          }
+          }
+        }
+
+        FeatureAdaptiveEvalSimd (const CatmullClarkPatch& patch, const vbool& valid, const vfloat& u, const vfloat& v, float dscale, size_t depth, 
+                                 float* P, float* dPdu, float* dPdv, float* ddPdudu, float* ddPdvdv, float* ddPdudv, const size_t dstride, const size_t N)
+        : P(P), dPdu(dPdu), dPdv(dPdv), ddPdudu(ddPdudu), ddPdvdv(ddPdvdv), ddPdudv(ddPdudv), dstride(dstride), N(N)
+        {
+          eval_direct(valid,patch,Vec2<vfloat>(u,v),dscale,depth);
+        }
+
+        template<size_t N>
+        __forceinline void eval_quad_direct(const vbool& valid, array_t<CatmullClarkPatch,N>& patches, const Vec2<vfloat>& uv, float dscale, size_t depth)
+        {
+          const vfloat u = uv.x, v = uv.y;
+          const vbool u0_mask = u < 0.5f, u1_mask = u >= 0.5f;
+          const vbool v0_mask = v < 0.5f, v1_mask = v >= 0.5f;
+          const vbool u0v0_mask = valid & u0_mask & v0_mask;
+          const vbool u0v1_mask = valid & u0_mask & v1_mask;
+          const vbool u1v0_mask = valid & u1_mask & v0_mask;
+          const vbool u1v1_mask = valid & u1_mask & v1_mask;
+          if (any(u0v0_mask)) eval_direct(u0v0_mask,patches[0],Vec2<vfloat>(2.0f*u,2.0f*v),2.0f*dscale,depth+1);
+          if (any(u1v0_mask)) eval_direct(u1v0_mask,patches[1],Vec2<vfloat>(2.0f*u-1.0f,2.0f*v),2.0f*dscale,depth+1);
+          if (any(u1v1_mask)) eval_direct(u1v1_mask,patches[2],Vec2<vfloat>(2.0f*u-1.0f,2.0f*v-1.0f),2.0f*dscale,depth+1);
+          if (any(u0v1_mask)) eval_direct(u0v1_mask,patches[3],Vec2<vfloat>(2.0f*u,2.0f*v-1.0f),2.0f*dscale,depth+1);
+        }
+        
+        template<size_t N>
+        __forceinline void eval_general_quad_direct(const vbool& valid, const GeneralCatmullClarkPatch& patch, array_t<CatmullClarkPatch,N>& patches, const Vec2<vfloat>& uv, float dscale, size_t depth)
+        {
+#if PATCH_USE_GREGORY == 2
+          BezierCurve borders[GeneralCatmullClarkPatch::SIZE]; patch.getLimitBorder(borders);
+          BezierCurve border0l,border0r; borders[0].subdivide(border0l,border0r);
+          BezierCurve border1l,border1r; borders[1].subdivide(border1l,border1r);
+          BezierCurve border2l,border2r; borders[2].subdivide(border2l,border2r);
+          BezierCurve border3l,border3r; borders[3].subdivide(border3l,border3r);
+#endif
+          GeneralCatmullClarkPatch::fix_quad_ring_order(patches);
+          const vfloat u = uv.x, v = uv.y;
+          const vbool u0_mask = u < 0.5f, u1_mask = u >= 0.5f;
+          const vbool v0_mask = v < 0.5f, v1_mask = v >= 0.5f;
+          const vbool u0v0_mask = valid & u0_mask & v0_mask;
+          const vbool u0v1_mask = valid & u0_mask & v1_mask;
+          const vbool u1v0_mask = valid & u1_mask & v0_mask;
+          const vbool u1v1_mask = valid & u1_mask & v1_mask;
+#if PATCH_USE_GREGORY == 2
+          if (any(u0v0_mask)) eval_direct(u0v0_mask,patches[0],Vec2<vfloat>(2.0f*u,2.0f*v),2.0f*dscale,depth+1,&border0l,nullptr,nullptr,&border3r);
+          if (any(u1v0_mask)) eval_direct(u1v0_mask,patches[1],Vec2<vfloat>(2.0f*u-1.0f,2.0f*v),2.0f*dscale,depth+1,&border0r,&border1l,nullptr,nullptr);
+          if (any(u1v1_mask)) eval_direct(u1v1_mask,patches[2],Vec2<vfloat>(2.0f*u-1.0f,2.0f*v-1.0f),2.0f*dscale,depth+1,nullptr,&border1r,&border2l,nullptr);
+          if (any(u0v1_mask)) eval_direct(u0v1_mask,patches[3],Vec2<vfloat>(2.0f*u,2.0f*v-1.0f),2.0f*dscale,depth+1,nullptr,nullptr,&border2r,&border3l);
+#else
+          if (any(u0v0_mask)) eval_direct(u0v0_mask,patches[0],Vec2<vfloat>(2.0f*u,2.0f*v),2.0f*dscale,depth+1);
+          if (any(u1v0_mask)) eval_direct(u1v0_mask,patches[1],Vec2<vfloat>(2.0f*u-1.0f,2.0f*v),2.0f*dscale,depth+1);
+          if (any(u1v1_mask)) eval_direct(u1v1_mask,patches[2],Vec2<vfloat>(2.0f*u-1.0f,2.0f*v-1.0f),2.0f*dscale,depth+1);
+          if (any(u0v1_mask)) eval_direct(u0v1_mask,patches[3],Vec2<vfloat>(2.0f*u,2.0f*v-1.0f),2.0f*dscale,depth+1);
+#endif
+        }
+        
+        __forceinline bool final(const CatmullClarkPatch& patch, const typename CatmullClarkRing::Type type, size_t depth) 
+        {
+          const size_t max_eval_depth = (type & CatmullClarkRing::TYPE_CREASES) ? PATCH_MAX_EVAL_DEPTH_CREASE : PATCH_MAX_EVAL_DEPTH_IRREGULAR;
+//#if PATCH_MIN_RESOLUTION
+//          return patch.isFinalResolution(PATCH_MIN_RESOLUTION) || depth>=max_eval_depth;
+//#else
+          return depth>=max_eval_depth;
+//#endif
+        }
+
+        void eval_direct(const vbool& valid, const CatmullClarkPatch& patch, const Vec2<vfloat>& uv, float dscale, size_t depth,
+                         BezierCurve* border0 = nullptr, BezierCurve* border1 = nullptr, BezierCurve* border2 = nullptr, BezierCurve* border3 = nullptr)
+        {
+          typename CatmullClarkPatch::Type ty = patch.type();
+
+          if (unlikely(final(patch,ty,depth)))
+          {
+            if (ty & CatmullClarkRing::TYPE_REGULAR) { 
+              RegularPatch(patch,border0,border1,border2,border3).eval(valid,uv.x,uv.y,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale,dstride,N);
+            } else {
+              IrregularFillPatch(patch,border0,border1,border2,border3).eval(valid,uv.x,uv.y,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale,dstride,N);
+            }
+          }
+          else if (ty & CatmullClarkRing::TYPE_REGULAR_CREASES) { 
+            assert(depth > 0); RegularPatch(patch,border0,border1,border2,border3).eval(valid,uv.x,uv.y,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale,dstride,N);
+          }
+#if PATCH_USE_GREGORY == 2
+          else if (ty & CatmullClarkRing::TYPE_GREGORY_CREASES) { 
+            assert(depth > 0); GregoryPatch(patch,border0,border1,border2,border3).eval(valid,uv.x,uv.y,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale,dstride,N);
+          }
+#endif
+          else
+          {
+            array_t<CatmullClarkPatch,4> patches; 
+            patch.subdivide(patches); // FIXME: only have to generate one of the patches
+            eval_quad_direct(valid,patches,uv,dscale,depth);
+          }
+        }  
+
+        void eval_direct(const vbool& valid, const GeneralCatmullClarkPatch& patch, const Vec2<vfloat>& uv, const size_t depth) 
+        {
+          /* convert into standard quad patch if possible */
+          if (likely(patch.isQuadPatch())) {
+            CatmullClarkPatch qpatch; patch.init(qpatch);
+            return eval_direct(valid,qpatch,uv,1.0f,depth);
+          }
+          
+          /* subdivide patch */
+          unsigned Nc;
+          array_t<CatmullClarkPatch,GeneralCatmullClarkPatch::SIZE> patches; 
+          patch.subdivide(patches,Nc); // FIXME: only have to generate one of the patches
+          
+          /* parametrization for quads */
+          if (Nc == 4) 
+            eval_general_quad_direct(valid,patch,patches,uv,1.0f,depth);
+          
+          /* parametrization for arbitrary polygons */
+          else 
+          {
+            const vint l = (vint)floor(0.5f*uv.x); const vfloat u = 2.0f*frac(0.5f*uv.x)-0.5f; 
+            const vint h = (vint)floor(0.5f*uv.y); const vfloat v = 2.0f*frac(0.5f*uv.y)-0.5f; 
+            const vint i = (h<<2)+l; assert(all(valid,i<Nc));
+            foreach_unique(valid,i,[&](const vbool& valid, const int i) {
+#if PATCH_USE_GREGORY == 2
+                BezierCurve borders[2]; patch.getLimitBorder(borders,i);
+                BezierCurve border0l,border0r; borders[0].subdivide(border0l,border0r);
+                BezierCurve border2l,border2r; borders[1].subdivide(border2l,border2r);
+                eval_direct(valid,patches[i],Vec2<vfloat>(u,v),1.0f,depth+1, &border0l, nullptr, nullptr, &border2r);
+#else
+                eval_direct(valid,patches[i],Vec2<vfloat>(u,v),1.0f,depth+1);
+#endif
+              });
+          }
+        }
+
+      private:
+        float* const P;
+        float* const dPdu;
+        float* const dPdv;
+        float* const ddPdudu;
+        float* const ddPdvdv;
+        float* const ddPdudv;
+        const size_t dstride;
+        const size_t N;
+      };
+  }
+}

thirdparty/embree/kernels/subdiv/gregory_patch.h

@@ -0,0 +1,893 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "catmullclark_patch.h"
+#include "bezier_patch.h"
+#include "bezier_curve.h"
+#include "catmullclark_coefficients.h"
+
+namespace embree
+{  
+  template<typename Vertex, typename Vertex_t = Vertex>
+  class __aligned(64) GregoryPatchT
+  {
+    typedef CatmullClarkPatchT<Vertex,Vertex_t> CatmullClarkPatch;
+    typedef GeneralCatmullClarkPatchT<Vertex,Vertex_t> GeneralCatmullClarkPatch;
+    typedef CatmullClark1RingT<Vertex,Vertex_t> CatmullClark1Ring;
+    typedef BezierCurveT<Vertex> BezierCurve;
+
+  public:
+    Vertex v[4][4];
+    Vertex f[2][2];
+
+    __forceinline GregoryPatchT() {}
+
+    __forceinline GregoryPatchT(const CatmullClarkPatch& patch) {
+      init(patch);
+    }
+
+    __forceinline GregoryPatchT(const CatmullClarkPatch& patch, 
+                                const BezierCurve* border0, const BezierCurve* border1, const BezierCurve* border2, const BezierCurve* border3) 
+    {
+      init_crackfix(patch,border0,border1,border2,border3);
+    }
+
+    __forceinline GregoryPatchT (const HalfEdge* edge, const char* vertices, size_t stride) { 
+      init(CatmullClarkPatch(edge,vertices,stride));
+    }
+      
+    __forceinline Vertex& p0() { return v[0][0]; }
+    __forceinline Vertex& p1() { return v[0][3]; }
+    __forceinline Vertex& p2() { return v[3][3]; }
+    __forceinline Vertex& p3() { return v[3][0]; }
+    
+    __forceinline Vertex& e0_p() { return v[0][1]; }
+    __forceinline Vertex& e0_m() { return v[1][0]; }
+    __forceinline Vertex& e1_p() { return v[1][3]; }
+    __forceinline Vertex& e1_m() { return v[0][2]; }
+    __forceinline Vertex& e2_p() { return v[3][2]; }
+    __forceinline Vertex& e2_m() { return v[2][3]; }
+    __forceinline Vertex& e3_p() { return v[2][0]; }
+    __forceinline Vertex& e3_m() { return v[3][1]; }
+    
+    __forceinline Vertex& f0_p() { return v[1][1]; }
+    __forceinline Vertex& f1_p() { return v[1][2]; }
+    __forceinline Vertex& f2_p() { return v[2][2]; }
+    __forceinline Vertex& f3_p() { return v[2][1]; }
+    __forceinline Vertex& f0_m() { return f[0][0]; }
+    __forceinline Vertex& f1_m() { return f[0][1]; }
+    __forceinline Vertex& f2_m() { return f[1][1]; }
+    __forceinline Vertex& f3_m() { return f[1][0]; }
+    
+    __forceinline const Vertex& p0() const { return v[0][0]; }
+    __forceinline const Vertex& p1() const { return v[0][3]; }
+    __forceinline const Vertex& p2() const { return v[3][3]; }
+    __forceinline const Vertex& p3() const { return v[3][0]; }
+    
+    __forceinline const Vertex& e0_p() const { return v[0][1]; }
+    __forceinline const Vertex& e0_m() const { return v[1][0]; }
+    __forceinline const Vertex& e1_p() const { return v[1][3]; }
+    __forceinline const Vertex& e1_m() const { return v[0][2]; }
+    __forceinline const Vertex& e2_p() const { return v[3][2]; }
+    __forceinline const Vertex& e2_m() const { return v[2][3]; }
+    __forceinline const Vertex& e3_p() const { return v[2][0]; }
+    __forceinline const Vertex& e3_m() const { return v[3][1]; }
+    
+    __forceinline const Vertex& f0_p() const { return v[1][1]; }
+    __forceinline const Vertex& f1_p() const { return v[1][2]; }
+    __forceinline const Vertex& f2_p() const { return v[2][2]; }
+    __forceinline const Vertex& f3_p() const { return v[2][1]; }
+    __forceinline const Vertex& f0_m() const { return f[0][0]; }
+    __forceinline const Vertex& f1_m() const { return f[0][1]; }
+    __forceinline const Vertex& f2_m() const { return f[1][1]; }
+    __forceinline const Vertex& f3_m() const { return f[1][0]; }
+    
+    __forceinline Vertex initCornerVertex(const CatmullClarkPatch& irreg_patch, const size_t index) {
+      return irreg_patch.ring[index].getLimitVertex();
+    }
+    
+    __forceinline Vertex initPositiveEdgeVertex(const CatmullClarkPatch& irreg_patch, const size_t index, const Vertex& p_vtx) {
+      return madd(1.0f/3.0f,irreg_patch.ring[index].getLimitTangent(),p_vtx);
+    }
+    
+    __forceinline Vertex initNegativeEdgeVertex(const CatmullClarkPatch& irreg_patch, const size_t index, const Vertex& p_vtx) {
+      return madd(1.0f/3.0f,irreg_patch.ring[index].getSecondLimitTangent(),p_vtx);
+    }
+
+    __forceinline Vertex initPositiveEdgeVertex2(const CatmullClarkPatch& irreg_patch, const size_t index, const Vertex& p_vtx) 
+    {
+      CatmullClark1Ring3fa r0,r1,r2;
+      irreg_patch.ring[index].subdivide(r0);
+      r0.subdivide(r1);
+      r1.subdivide(r2);
+      return madd(8.0f/3.0f,r2.getLimitTangent(),p_vtx);
+    }
+    
+    __forceinline Vertex initNegativeEdgeVertex2(const CatmullClarkPatch& irreg_patch, const size_t index, const Vertex& p_vtx) 
+    {
+      CatmullClark1Ring3fa r0,r1,r2;
+      irreg_patch.ring[index].subdivide(r0);
+      r0.subdivide(r1);
+      r1.subdivide(r2);
+      return madd(8.0f/3.0f,r2.getSecondLimitTangent(),p_vtx);
+    }
+    
+    void initFaceVertex(const CatmullClarkPatch& irreg_patch, 
+			const size_t index, 
+			const Vertex& p_vtx, 
+                        const Vertex& e0_p_vtx, 
+			const Vertex& e1_m_vtx, 
+			const unsigned int face_valence_p1,
+ 			const Vertex& e0_m_vtx,	
+			const Vertex& e3_p_vtx,	
+			const unsigned int face_valence_p3,
+			Vertex& f_p_vtx, 
+			Vertex& f_m_vtx)
+    {
+      const unsigned int face_valence = irreg_patch.ring[index].face_valence;
+      const unsigned int edge_valence = irreg_patch.ring[index].edge_valence;
+      const unsigned int border_index = irreg_patch.ring[index].border_index;
+      
+      const Vertex& vtx     = irreg_patch.ring[index].vtx;
+      const Vertex e_i      = irreg_patch.ring[index].getEdgeCenter(0);
+      const Vertex c_i_m_1  = irreg_patch.ring[index].getQuadCenter(0);
+      const Vertex e_i_m_1  = irreg_patch.ring[index].getEdgeCenter(1);
+      
+      Vertex c_i, e_i_p_1;
+      const bool hasHardEdge0 =
+        std::isinf(irreg_patch.ring[index].vertex_crease_weight) &&
+        std::isinf(irreg_patch.ring[index].crease_weight[0]);
+                
+      if (unlikely((border_index == edge_valence-2) || hasHardEdge0))
+      {
+        /* mirror quad center and edge mid-point */
+        c_i     = madd(2.0f, e_i - c_i_m_1, c_i_m_1);
+        e_i_p_1 = madd(2.0f, vtx - e_i_m_1, e_i_m_1);
+      }
+      else
+      {
+        c_i     = irreg_patch.ring[index].getQuadCenter( face_valence-1 );
+        e_i_p_1 = irreg_patch.ring[index].getEdgeCenter( face_valence-1 );
+      }
+      
+      Vertex c_i_m_2, e_i_m_2;
+      const bool hasHardEdge1 =
+        std::isinf(irreg_patch.ring[index].vertex_crease_weight) &&
+        std::isinf(irreg_patch.ring[index].crease_weight[1]);
+      
+      if (unlikely(border_index == 2 || hasHardEdge1))
+      {
+        /* mirror quad center and edge mid-point */
+        c_i_m_2  = madd(2.0f, e_i_m_1 - c_i_m_1, c_i_m_1);
+        e_i_m_2  = madd(2.0f, vtx - e_i, + e_i);
+      }
+      else
+      {
+        c_i_m_2  = irreg_patch.ring[index].getQuadCenter( 1 );
+        e_i_m_2  = irreg_patch.ring[index].getEdgeCenter( 2 );
+      }      
+      
+      const float d = 3.0f;
+      //const float c     = cosf(2.0f*M_PI/(float)face_valence);
+      //const float c_e_p = cosf(2.0f*M_PI/(float)face_valence_p1);
+      //const float c_e_m = cosf(2.0f*M_PI/(float)face_valence_p3);
+      
+      const float c     = CatmullClarkPrecomputedCoefficients::table.cos_2PI_div_n(face_valence);
+      const float c_e_p = CatmullClarkPrecomputedCoefficients::table.cos_2PI_div_n(face_valence_p1);
+      const float c_e_m = CatmullClarkPrecomputedCoefficients::table.cos_2PI_div_n(face_valence_p3);
+
+      const Vertex r_e_p = 1.0f/3.0f * (e_i_m_1 - e_i_p_1) + 2.0f/3.0f * (c_i_m_1 - c_i);
+      const Vertex r_e_m = 1.0f/3.0f * (e_i     - e_i_m_2) + 2.0f/3.0f * (c_i_m_1 - c_i_m_2);
+
+      f_p_vtx = 1.0f / d * (c_e_p * p_vtx + (d - 2.0f*c - c_e_p) * e0_p_vtx + 2.0f*c* e1_m_vtx + r_e_p);      
+      f_m_vtx = 1.0f / d * (c_e_m * p_vtx + (d - 2.0f*c - c_e_m) * e0_m_vtx + 2.0f*c* e3_p_vtx + r_e_m);     
+    }
+
+    __noinline void init(const CatmullClarkPatch& patch)
+    {
+      assert( patch.ring[0].hasValidPositions() );
+      assert( patch.ring[1].hasValidPositions() );
+      assert( patch.ring[2].hasValidPositions() );
+      assert( patch.ring[3].hasValidPositions() );
+      
+      p0() = initCornerVertex(patch,0);
+      p1() = initCornerVertex(patch,1);
+      p2() = initCornerVertex(patch,2);
+      p3() = initCornerVertex(patch,3);
+
+      e0_p() = initPositiveEdgeVertex(patch,0, p0());
+      e1_p() = initPositiveEdgeVertex(patch,1, p1());
+      e2_p() = initPositiveEdgeVertex(patch,2, p2());
+      e3_p() = initPositiveEdgeVertex(patch,3, p3());
+
+      e0_m() = initNegativeEdgeVertex(patch,0, p0());
+      e1_m() = initNegativeEdgeVertex(patch,1, p1());
+      e2_m() = initNegativeEdgeVertex(patch,2, p2());
+      e3_m() = initNegativeEdgeVertex(patch,3, p3());
+
+      const unsigned int face_valence_p0 = patch.ring[0].face_valence;
+      const unsigned int face_valence_p1 = patch.ring[1].face_valence;
+      const unsigned int face_valence_p2 = patch.ring[2].face_valence;
+      const unsigned int face_valence_p3 = patch.ring[3].face_valence;
+      
+      initFaceVertex(patch,0,p0(),e0_p(),e1_m(),face_valence_p1,e0_m(),e3_p(),face_valence_p3,f0_p(),f0_m() );
+      initFaceVertex(patch,1,p1(),e1_p(),e2_m(),face_valence_p2,e1_m(),e0_p(),face_valence_p0,f1_p(),f1_m() );
+      initFaceVertex(patch,2,p2(),e2_p(),e3_m(),face_valence_p3,e2_m(),e1_p(),face_valence_p1,f2_p(),f2_m() );
+      initFaceVertex(patch,3,p3(),e3_p(),e0_m(),face_valence_p0,e3_m(),e2_p(),face_valence_p3,f3_p(),f3_m() );
+
+    }
+
+    __noinline void init_crackfix(const CatmullClarkPatch& patch, 
+                                  const BezierCurve* border0, 
+                                  const BezierCurve* border1,
+                                  const BezierCurve* border2, 
+                                  const BezierCurve* border3)
+    {
+      assert( patch.ring[0].hasValidPositions() );
+      assert( patch.ring[1].hasValidPositions() );
+      assert( patch.ring[2].hasValidPositions() );
+      assert( patch.ring[3].hasValidPositions() );
+      
+      p0() = initCornerVertex(patch,0);
+      p1() = initCornerVertex(patch,1);
+      p2() = initCornerVertex(patch,2);
+      p3() = initCornerVertex(patch,3);
+
+      e0_p() = initPositiveEdgeVertex(patch,0, p0());
+      e1_p() = initPositiveEdgeVertex(patch,1, p1());
+      e2_p() = initPositiveEdgeVertex(patch,2, p2());
+      e3_p() = initPositiveEdgeVertex(patch,3, p3());
+
+      e0_m() = initNegativeEdgeVertex(patch,0, p0());
+      e1_m() = initNegativeEdgeVertex(patch,1, p1());
+      e2_m() = initNegativeEdgeVertex(patch,2, p2());
+      e3_m() = initNegativeEdgeVertex(patch,3, p3());
+
+      if (unlikely(border0 != nullptr)) 
+      {         
+        p0()   = border0->v0;
+        e0_p() = border0->v1; 
+        e1_m() = border0->v2; 
+        p1()   = border0->v3;
+      }
+      
+      if (unlikely(border1 != nullptr))
+      {          
+        p1()   = border1->v0; 
+        e1_p() = border1->v1; 
+        e2_m() = border1->v2; 
+        p2()   = border1->v3; 
+      }
+
+      if (unlikely(border2 != nullptr))
+      {          
+        p2()   = border2->v0; 
+        e2_p() = border2->v1; 
+        e3_m() = border2->v2; 
+        p3()   = border2->v3; 
+      }
+
+      if (unlikely(border3 != nullptr))
+      {          
+        p3()   = border3->v0; 
+        e3_p() = border3->v1; 
+        e0_m() = border3->v2; 
+        p0()   = border3->v3; 
+      }
+
+      const unsigned int face_valence_p0 = patch.ring[0].face_valence;
+      const unsigned int face_valence_p1 = patch.ring[1].face_valence;
+      const unsigned int face_valence_p2 = patch.ring[2].face_valence;
+      const unsigned int face_valence_p3 = patch.ring[3].face_valence;
+      
+      initFaceVertex(patch,0,p0(),e0_p(),e1_m(),face_valence_p1,e0_m(),e3_p(),face_valence_p3,f0_p(),f0_m() );
+      initFaceVertex(patch,1,p1(),e1_p(),e2_m(),face_valence_p2,e1_m(),e0_p(),face_valence_p0,f1_p(),f1_m() );
+      initFaceVertex(patch,2,p2(),e2_p(),e3_m(),face_valence_p3,e2_m(),e1_p(),face_valence_p1,f2_p(),f2_m() );
+      initFaceVertex(patch,3,p3(),e3_p(),e0_m(),face_valence_p0,e3_m(),e2_p(),face_valence_p3,f3_p(),f3_m() );
+    }
+
+    
+    void computeGregoryPatchFacePoints(const unsigned int face_valence,
+				       const Vertex& r_e_p, 
+				       const Vertex& r_e_m, 					 
+				       const Vertex& p_vtx, 
+				       const Vertex& e0_p_vtx, 
+				       const Vertex& e1_m_vtx, 
+				       const unsigned int face_valence_p1,
+				       const Vertex& e0_m_vtx,	
+				       const Vertex& e3_p_vtx,	
+				       const unsigned int face_valence_p3,
+				       Vertex& f_p_vtx, 
+				       Vertex& f_m_vtx,
+                                       const float d = 3.0f)
+    {
+      //const float c     = cosf(2.0*M_PI/(float)face_valence);
+      //const float c_e_p = cosf(2.0*M_PI/(float)face_valence_p1);
+      //const float c_e_m = cosf(2.0*M_PI/(float)face_valence_p3);
+
+      const float c     = CatmullClarkPrecomputedCoefficients::table.cos_2PI_div_n(face_valence);
+      const float c_e_p = CatmullClarkPrecomputedCoefficients::table.cos_2PI_div_n(face_valence_p1);
+      const float c_e_m = CatmullClarkPrecomputedCoefficients::table.cos_2PI_div_n(face_valence_p3);
+
+
+      f_p_vtx = 1.0f / d * (c_e_p * p_vtx + (d - 2.0f*c - c_e_p) * e0_p_vtx + 2.0f*c* e1_m_vtx + r_e_p);      
+      f_m_vtx = 1.0f / d * (c_e_m * p_vtx + (d - 2.0f*c - c_e_m) * e0_m_vtx + 2.0f*c* e3_p_vtx + r_e_m);      
+      f_p_vtx = 1.0f / d * (c_e_p * p_vtx + (d - 2.0f*c - c_e_p) * e0_p_vtx + 2.0f*c* e1_m_vtx + r_e_p);      
+      f_m_vtx = 1.0f / d * (c_e_m * p_vtx + (d - 2.0f*c - c_e_m) * e0_m_vtx + 2.0f*c* e3_p_vtx + r_e_m);
+    }
+
+    __noinline void init(const GeneralCatmullClarkPatch& patch)
+    {
+      assert(patch.size() == 4);
+#if 0
+      CatmullClarkPatch qpatch; patch.init(qpatch);
+      init(qpatch);
+#else
+      const float face_valence_p0 = patch.ring[0].face_valence;
+      const float face_valence_p1 = patch.ring[1].face_valence;
+      const float face_valence_p2 = patch.ring[2].face_valence;
+      const float face_valence_p3 = patch.ring[3].face_valence;
+
+      Vertex p0_r_p, p0_r_m;
+      patch.ring[0].computeGregoryPatchEdgePoints( p0(), e0_p(), e0_m(), p0_r_p, p0_r_m );
+
+      Vertex p1_r_p, p1_r_m;
+      patch.ring[1].computeGregoryPatchEdgePoints( p1(), e1_p(), e1_m(), p1_r_p, p1_r_m );
+      
+      Vertex p2_r_p, p2_r_m;
+      patch.ring[2].computeGregoryPatchEdgePoints( p2(), e2_p(), e2_m(), p2_r_p, p2_r_m );
+
+      Vertex p3_r_p, p3_r_m;
+      patch.ring[3].computeGregoryPatchEdgePoints( p3(), e3_p(), e3_m(), p3_r_p, p3_r_m );
+
+      computeGregoryPatchFacePoints(face_valence_p0, p0_r_p, p0_r_m, p0(), e0_p(), e1_m(), face_valence_p1, e0_m(), e3_p(), face_valence_p3, f0_p(), f0_m() );
+      computeGregoryPatchFacePoints(face_valence_p1, p1_r_p, p1_r_m, p1(), e1_p(), e2_m(), face_valence_p2, e1_m(), e0_p(), face_valence_p0, f1_p(), f1_m() );
+      computeGregoryPatchFacePoints(face_valence_p2, p2_r_p, p2_r_m, p2(), e2_p(), e3_m(), face_valence_p3, e2_m(), e1_p(), face_valence_p1, f2_p(), f2_m() );
+      computeGregoryPatchFacePoints(face_valence_p3, p3_r_p, p3_r_m, p3(), e3_p(), e0_m(), face_valence_p0, e3_m(), e2_p(), face_valence_p3, f3_p(), f3_m() );
+
+#endif
+    }
+   
+    
+    __forceinline void convert_to_bezier()
+    {
+      f0_p() = (f0_p() + f0_m()) * 0.5f;
+      f1_p() = (f1_p() + f1_m()) * 0.5f;
+      f2_p() = (f2_p() + f2_m()) * 0.5f;
+      f3_p() = (f3_p() + f3_m()) * 0.5f;
+      f0_m() = Vertex( zero );
+      f1_m() = Vertex( zero );
+      f2_m() = Vertex( zero );
+      f3_m() = Vertex( zero );      
+    }
+    
+    static __forceinline void computeInnerVertices(const Vertex matrix[4][4], const Vertex f_m[2][2], const float uu, const float vv,
+						   Vertex_t& matrix_11, Vertex_t& matrix_12, Vertex_t& matrix_22, Vertex_t& matrix_21)
+    {
+      if (unlikely(uu == 0.0f || uu == 1.0f || vv == 0.0f || vv == 1.0f)) 
+      {
+	matrix_11 = matrix[1][1];
+	matrix_12 = matrix[1][2];
+	matrix_22 = matrix[2][2];
+	matrix_21 = matrix[2][1];	 
+      }
+      else
+      {
+	const Vertex_t f0_p = matrix[1][1];
+	const Vertex_t f1_p = matrix[1][2];
+	const Vertex_t f2_p = matrix[2][2];
+	const Vertex_t f3_p = matrix[2][1];
+        
+	const Vertex_t f0_m = f_m[0][0];
+	const Vertex_t f1_m = f_m[0][1];
+	const Vertex_t f2_m = f_m[1][1];
+	const Vertex_t f3_m = f_m[1][0];
+        
+	matrix_11 = (      uu  * f0_p +       vv  * f0_m)*rcp(uu+vv);
+	matrix_12 = ((1.0f-uu) * f1_m +       vv  * f1_p)*rcp(1.0f-uu+vv);
+	matrix_22 = ((1.0f-uu) * f2_p + (1.0f-vv) * f2_m)*rcp(2.0f-uu-vv);
+	matrix_21 = (      uu  * f3_m + (1.0f-vv) * f3_p)*rcp(1.0f+uu-vv);
+      }
+    } 
+
+    template<typename vfloat>
+    static __forceinline void computeInnerVertices(const Vertex v[4][4], const Vertex f[2][2], 
+                                                   size_t i, const vfloat& uu, const vfloat& vv, vfloat& matrix_11, vfloat& matrix_12, vfloat& matrix_22, vfloat& matrix_21) 
+    {
+      const auto m_border = (uu == 0.0f) | (uu == 1.0f) | (vv == 0.0f) | (vv == 1.0f);
+
+      const vfloat f0_p = v[1][1][i];
+      const vfloat f1_p = v[1][2][i];
+      const vfloat f2_p = v[2][2][i];
+      const vfloat f3_p = v[2][1][i];
+      
+      const vfloat f0_m = f[0][0][i];
+      const vfloat f1_m = f[0][1][i];
+      const vfloat f2_m = f[1][1][i];
+      const vfloat f3_m = f[1][0][i];
+      
+      const vfloat one_minus_uu = vfloat(1.0f) - uu;
+      const vfloat one_minus_vv = vfloat(1.0f) - vv;      
+      
+      const vfloat f0_i = (          uu * f0_p +           vv * f0_m) * rcp(uu+vv);
+      const vfloat f1_i = (one_minus_uu * f1_m +           vv * f1_p) * rcp(one_minus_uu+vv);
+      const vfloat f2_i = (one_minus_uu * f2_p + one_minus_vv * f2_m) * rcp(one_minus_uu+one_minus_vv);
+      const vfloat f3_i = (          uu * f3_m + one_minus_vv * f3_p) * rcp(uu+one_minus_vv);
+      
+      matrix_11 = select(m_border,f0_p,f0_i);
+      matrix_12 = select(m_border,f1_p,f1_i);
+      matrix_22 = select(m_border,f2_p,f2_i);
+      matrix_21 = select(m_border,f3_p,f3_i);
+    }
+
+    static __forceinline Vertex eval(const Vertex matrix[4][4], const Vertex f[2][2], const float& uu, const float& vv) 
+    {
+      Vertex_t v_11, v_12, v_22, v_21;
+      computeInnerVertices(matrix,f,uu,vv,v_11, v_12, v_22, v_21);
+      
+      const Vec4<float> Bu = BezierBasis::eval(uu);
+      const Vec4<float> Bv = BezierBasis::eval(vv);
+      
+      return madd(Bv.x,madd(Bu.x,matrix[0][0],madd(Bu.y,matrix[0][1],madd(Bu.z,matrix[0][2],Bu.w * matrix[0][3]))), 
+                  madd(Bv.y,madd(Bu.x,matrix[1][0],madd(Bu.y,v_11        ,madd(Bu.z,v_12        ,Bu.w * matrix[1][3]))), 
+                       madd(Bv.z,madd(Bu.x,matrix[2][0],madd(Bu.y,v_21        ,madd(Bu.z,v_22        ,Bu.w * matrix[2][3]))), 
+                            Bv.w*madd(Bu.x,matrix[3][0],madd(Bu.y,matrix[3][1],madd(Bu.z,matrix[3][2],Bu.w * matrix[3][3])))))); 
+    }
+
+    static __forceinline Vertex eval_du(const Vertex matrix[4][4], const Vertex f[2][2], const float uu, const float vv) // approximative derivative
+    {
+      Vertex_t v_11, v_12, v_22, v_21;
+      computeInnerVertices(matrix,f,uu,vv,v_11, v_12, v_22, v_21);
+      
+      const Vec4<float> Bu = BezierBasis::derivative(uu);
+      const Vec4<float> Bv = BezierBasis::eval(vv);
+
+      return madd(Bv.x,madd(Bu.x,matrix[0][0],madd(Bu.y,matrix[0][1],madd(Bu.z,matrix[0][2],Bu.w * matrix[0][3]))), 
+                  madd(Bv.y,madd(Bu.x,matrix[1][0],madd(Bu.y,v_11        ,madd(Bu.z,v_12        ,Bu.w * matrix[1][3]))), 
+                       madd(Bv.z,madd(Bu.x,matrix[2][0],madd(Bu.y,v_21        ,madd(Bu.z,v_22        ,Bu.w * matrix[2][3]))), 
+                            Bv.w*madd(Bu.x,matrix[3][0],madd(Bu.y,matrix[3][1],madd(Bu.z,matrix[3][2],Bu.w * matrix[3][3])))))); 
+    }
+
+    static __forceinline Vertex eval_dv(const Vertex matrix[4][4], const Vertex f[2][2], const float uu, const float vv) // approximative derivative
+    {
+      Vertex_t v_11, v_12, v_22, v_21;
+      computeInnerVertices(matrix,f,uu,vv,v_11, v_12, v_22, v_21);
+      
+      const Vec4<float> Bu = BezierBasis::eval(uu);
+      const Vec4<float> Bv = BezierBasis::derivative(vv);
+ 
+      return madd(Bv.x,madd(Bu.x,matrix[0][0],madd(Bu.y,matrix[0][1],madd(Bu.z,matrix[0][2],Bu.w * matrix[0][3]))), 
+                  madd(Bv.y,madd(Bu.x,matrix[1][0],madd(Bu.y,v_11        ,madd(Bu.z,v_12        ,Bu.w * matrix[1][3]))), 
+                       madd(Bv.z,madd(Bu.x,matrix[2][0],madd(Bu.y,v_21        ,madd(Bu.z,v_22        ,Bu.w * matrix[2][3]))), 
+                            Bv.w*madd(Bu.x,matrix[3][0],madd(Bu.y,matrix[3][1],madd(Bu.z,matrix[3][2],Bu.w * matrix[3][3])))))); 
+    }
+
+    static __forceinline Vertex eval_dudu(const Vertex matrix[4][4], const Vertex f[2][2], const float uu, const float vv) // approximative derivative
+    {
+      Vertex_t v_11, v_12, v_22, v_21;
+      computeInnerVertices(matrix,f,uu,vv,v_11, v_12, v_22, v_21);
+      
+      const Vec4<float> Bu = BezierBasis::derivative2(uu);
+      const Vec4<float> Bv = BezierBasis::eval(vv);
+ 
+      return madd(Bv.x,madd(Bu.x,matrix[0][0],madd(Bu.y,matrix[0][1],madd(Bu.z,matrix[0][2],Bu.w * matrix[0][3]))), 
+                  madd(Bv.y,madd(Bu.x,matrix[1][0],madd(Bu.y,v_11        ,madd(Bu.z,v_12        ,Bu.w * matrix[1][3]))), 
+                       madd(Bv.z,madd(Bu.x,matrix[2][0],madd(Bu.y,v_21        ,madd(Bu.z,v_22        ,Bu.w * matrix[2][3]))), 
+                            Bv.w*madd(Bu.x,matrix[3][0],madd(Bu.y,matrix[3][1],madd(Bu.z,matrix[3][2],Bu.w * matrix[3][3])))))); 
+     }
+
+    static __forceinline Vertex eval_dvdv(const Vertex matrix[4][4], const Vertex f[2][2], const float uu, const float vv) // approximative derivative
+    {
+      Vertex_t v_11, v_12, v_22, v_21;
+      computeInnerVertices(matrix,f,uu,vv,v_11, v_12, v_22, v_21);
+      
+      const Vec4<float> Bu = BezierBasis::eval(uu);
+      const Vec4<float> Bv = BezierBasis::derivative2(vv);
+
+      return madd(Bv.x,madd(Bu.x,matrix[0][0],madd(Bu.y,matrix[0][1],madd(Bu.z,matrix[0][2],Bu.w * matrix[0][3]))), 
+                  madd(Bv.y,madd(Bu.x,matrix[1][0],madd(Bu.y,v_11        ,madd(Bu.z,v_12        ,Bu.w * matrix[1][3]))), 
+                       madd(Bv.z,madd(Bu.x,matrix[2][0],madd(Bu.y,v_21        ,madd(Bu.z,v_22        ,Bu.w * matrix[2][3]))), 
+                            Bv.w*madd(Bu.x,matrix[3][0],madd(Bu.y,matrix[3][1],madd(Bu.z,matrix[3][2],Bu.w * matrix[3][3])))))); 
+    }
+
+    static __forceinline Vertex eval_dudv(const Vertex matrix[4][4], const Vertex f[2][2], const float uu, const float vv) // approximative derivative
+    {
+      Vertex_t v_11, v_12, v_22, v_21;
+      computeInnerVertices(matrix,f,uu,vv,v_11, v_12, v_22, v_21);
+      
+      const Vec4<float> Bu = BezierBasis::derivative(uu);
+      const Vec4<float> Bv = BezierBasis::derivative(vv);
+
+      return madd(Bv.x,madd(Bu.x,matrix[0][0],madd(Bu.y,matrix[0][1],madd(Bu.z,matrix[0][2],Bu.w * matrix[0][3]))), 
+                  madd(Bv.y,madd(Bu.x,matrix[1][0],madd(Bu.y,v_11        ,madd(Bu.z,v_12        ,Bu.w * matrix[1][3]))), 
+                       madd(Bv.z,madd(Bu.x,matrix[2][0],madd(Bu.y,v_21        ,madd(Bu.z,v_22        ,Bu.w * matrix[2][3]))), 
+                            Bv.w*madd(Bu.x,matrix[3][0],madd(Bu.y,matrix[3][1],madd(Bu.z,matrix[3][2],Bu.w * matrix[3][3])))))); 
+    }
+
+    __forceinline Vertex eval(const float uu, const float vv) const {
+      return eval(v,f,uu,vv);
+    }
+
+    __forceinline Vertex eval_du( const float uu, const float vv) const {
+      return eval_du(v,f,uu,vv);
+    }
+
+    __forceinline Vertex eval_dv( const float uu, const float vv) const {
+      return eval_dv(v,f,uu,vv);
+    }
+
+    __forceinline Vertex eval_dudu( const float uu, const float vv) const {
+      return eval_dudu(v,f,uu,vv);
+    }
+
+    __forceinline Vertex eval_dvdv( const float uu, const float vv) const {
+      return eval_dvdv(v,f,uu,vv);
+    }
+
+    __forceinline Vertex eval_dudv( const float uu, const float vv) const {
+      return eval_dudv(v,f,uu,vv);
+    }
+
+    static __forceinline Vertex normal(const Vertex matrix[4][4], const Vertex f_m[2][2], const float uu, const float vv)  // FIXME: why not using basis functions
+    {
+      /* interpolate inner vertices */
+      Vertex_t matrix_11, matrix_12, matrix_22, matrix_21;
+      computeInnerVertices(matrix,f_m,uu,vv,matrix_11, matrix_12, matrix_22, matrix_21);
+      
+      /* tangentU */
+      const Vertex_t col0 = deCasteljau(vv, (Vertex_t)matrix[0][0], (Vertex_t)matrix[1][0], (Vertex_t)matrix[2][0], (Vertex_t)matrix[3][0]);
+      const Vertex_t col1 = deCasteljau(vv, (Vertex_t)matrix[0][1], (Vertex_t)matrix_11   , (Vertex_t)matrix_21   , (Vertex_t)matrix[3][1]);
+      const Vertex_t col2 = deCasteljau(vv, (Vertex_t)matrix[0][2], (Vertex_t)matrix_12   , (Vertex_t)matrix_22   , (Vertex_t)matrix[3][2]);
+      const Vertex_t col3 = deCasteljau(vv, (Vertex_t)matrix[0][3], (Vertex_t)matrix[1][3], (Vertex_t)matrix[2][3], (Vertex_t)matrix[3][3]);
+      
+      const Vertex_t tangentU = deCasteljau_tangent(uu, col0, col1, col2, col3);
+      
+      /* tangentV */
+      const Vertex_t row0 = deCasteljau(uu, (Vertex_t)matrix[0][0], (Vertex_t)matrix[0][1], (Vertex_t)matrix[0][2], (Vertex_t)matrix[0][3]);
+      const Vertex_t row1 = deCasteljau(uu, (Vertex_t)matrix[1][0], (Vertex_t)matrix_11   , (Vertex_t)matrix_12   , (Vertex_t)matrix[1][3]);
+      const Vertex_t row2 = deCasteljau(uu, (Vertex_t)matrix[2][0], (Vertex_t)matrix_21   , (Vertex_t)matrix_22   , (Vertex_t)matrix[2][3]);
+      const Vertex_t row3 = deCasteljau(uu, (Vertex_t)matrix[3][0], (Vertex_t)matrix[3][1], (Vertex_t)matrix[3][2], (Vertex_t)matrix[3][3]);
+      
+      const Vertex_t tangentV = deCasteljau_tangent(vv, row0, row1, row2, row3);
+      
+      /* normal = tangentU x tangentV */
+      const Vertex_t n = cross(tangentU,tangentV);
+      
+      return n;     
+    }
+   
+    __forceinline Vertex normal( const float uu, const float vv) const {
+      return normal(v,f,uu,vv);
+    }    
+    
+    __forceinline void eval(const float u, const float v, 
+                            Vertex* P, Vertex* dPdu, Vertex* dPdv, 
+                            Vertex* ddPdudu, Vertex* ddPdvdv, Vertex* ddPdudv,
+                            const float dscale = 1.0f) const
+    {
+      if (P) {
+        *P = eval(u,v); 
+      }
+      if (dPdu) {
+        assert(dPdu); *dPdu = eval_du(u,v)*dscale; 
+        assert(dPdv); *dPdv = eval_dv(u,v)*dscale; 
+      }
+      if (ddPdudu) {
+        assert(ddPdudu); *ddPdudu = eval_dudu(u,v)*sqr(dscale); 
+        assert(ddPdvdv); *ddPdvdv = eval_dvdv(u,v)*sqr(dscale); 
+        assert(ddPdudv); *ddPdudv = eval_dudv(u,v)*sqr(dscale); 
+      }
+    }
+
+    template<class vfloat>
+    static __forceinline vfloat eval(const Vertex v[4][4], const Vertex f[2][2], 
+                                     const size_t i, const vfloat& uu, const vfloat& vv, const Vec4<vfloat>& u_n, const Vec4<vfloat>& v_n,
+                                     vfloat& matrix_11, vfloat& matrix_12, vfloat& matrix_22, vfloat& matrix_21)
+    {
+      const vfloat curve0_x = madd(v_n[0],vfloat(v[0][0][i]),madd(v_n[1],vfloat(v[1][0][i]),madd(v_n[2],vfloat(v[2][0][i]),v_n[3] * vfloat(v[3][0][i]))));
+      const vfloat curve1_x = madd(v_n[0],vfloat(v[0][1][i]),madd(v_n[1],vfloat(matrix_11 ),madd(v_n[2],vfloat(matrix_21 ),v_n[3] * vfloat(v[3][1][i]))));
+      const vfloat curve2_x = madd(v_n[0],vfloat(v[0][2][i]),madd(v_n[1],vfloat(matrix_12 ),madd(v_n[2],vfloat(matrix_22 ),v_n[3] * vfloat(v[3][2][i]))));
+      const vfloat curve3_x = madd(v_n[0],vfloat(v[0][3][i]),madd(v_n[1],vfloat(v[1][3][i]),madd(v_n[2],vfloat(v[2][3][i]),v_n[3] * vfloat(v[3][3][i]))));
+      return madd(u_n[0],curve0_x,madd(u_n[1],curve1_x,madd(u_n[2],curve2_x,u_n[3] * curve3_x)));
+    }
+    
+    template<typename vbool, typename vfloat>
+    static __forceinline void eval(const Vertex v[4][4], const Vertex f[2][2], 
+                                   const vbool& valid, const vfloat& uu, const vfloat& vv, 
+                                   float* P, float* dPdu, float* dPdv, float* ddPdudu, float* ddPdvdv, float* ddPdudv,
+                                   const float dscale, const size_t dstride, const size_t N) 
+    {
+      if (P) {
+        const Vec4<vfloat> u_n = BezierBasis::eval(uu); 
+        const Vec4<vfloat> v_n = BezierBasis::eval(vv); 
+        for (size_t i=0; i<N; i++) {
+          vfloat matrix_11, matrix_12, matrix_22, matrix_21;
+          computeInnerVertices(v,f,i,uu,vv,matrix_11,matrix_12,matrix_22,matrix_21); // FIXME: calculated multiple times
+          vfloat::store(valid,P+i*dstride,eval(v,f,i,uu,vv,u_n,v_n,matrix_11,matrix_12,matrix_22,matrix_21));
+        }
+      }
+      if (dPdu)
+      {
+        {
+          assert(dPdu);
+          const Vec4<vfloat> u_n = BezierBasis::derivative(uu); 
+          const Vec4<vfloat> v_n = BezierBasis::eval(vv);
+          for (size_t i=0; i<N; i++) {
+            vfloat matrix_11, matrix_12, matrix_22, matrix_21;
+            computeInnerVertices(v,f,i,uu,vv,matrix_11,matrix_12,matrix_22,matrix_21);  // FIXME: calculated multiple times
+            vfloat::store(valid,dPdu+i*dstride,eval(v,f,i,uu,vv,u_n,v_n,matrix_11,matrix_12,matrix_22,matrix_21)*dscale);
+          }
+        }
+        {
+          assert(dPdv);
+          const Vec4<vfloat> u_n = BezierBasis::eval(uu); 
+          const Vec4<vfloat> v_n = BezierBasis::derivative(vv);
+          for (size_t i=0; i<N; i++) {
+            vfloat matrix_11, matrix_12, matrix_22, matrix_21;
+            computeInnerVertices(v,f,i,uu,vv,matrix_11,matrix_12,matrix_22,matrix_21);  // FIXME: calculated multiple times
+            vfloat::store(valid,dPdv+i*dstride,eval(v,f,i,uu,vv,u_n,v_n,matrix_11,matrix_12,matrix_22,matrix_21)*dscale);
+          }
+        }
+      }
+      if (ddPdudu)
+      {
+        {
+          assert(ddPdudu);
+          const Vec4<vfloat> u_n = BezierBasis::derivative2(uu); 
+          const Vec4<vfloat> v_n = BezierBasis::eval(vv);
+          for (size_t i=0; i<N; i++) {
+            vfloat matrix_11, matrix_12, matrix_22, matrix_21;
+            computeInnerVertices(v,f,i,uu,vv,matrix_11,matrix_12,matrix_22,matrix_21);  // FIXME: calculated multiple times
+            vfloat::store(valid,ddPdudu+i*dstride,eval(v,f,i,uu,vv,u_n,v_n,matrix_11,matrix_12,matrix_22,matrix_21)*sqr(dscale));
+          }
+        }
+        {
+          assert(ddPdvdv);
+          const Vec4<vfloat> u_n = BezierBasis::eval(uu); 
+          const Vec4<vfloat> v_n = BezierBasis::derivative2(vv);
+          for (size_t i=0; i<N; i++) {
+            vfloat matrix_11, matrix_12, matrix_22, matrix_21;
+            computeInnerVertices(v,f,i,uu,vv,matrix_11,matrix_12,matrix_22,matrix_21);  // FIXME: calculated multiple times
+            vfloat::store(valid,ddPdvdv+i*dstride,eval(v,f,i,uu,vv,u_n,v_n,matrix_11,matrix_12,matrix_22,matrix_21)*sqr(dscale));
+          }
+        }
+        {
+          assert(ddPdudv);
+          const Vec4<vfloat> u_n = BezierBasis::derivative(uu); 
+          const Vec4<vfloat> v_n = BezierBasis::derivative(vv);
+          for (size_t i=0; i<N; i++) {
+            vfloat matrix_11, matrix_12, matrix_22, matrix_21;
+            computeInnerVertices(v,f,i,uu,vv,matrix_11,matrix_12,matrix_22,matrix_21);  // FIXME: calculated multiple times
+            vfloat::store(valid,ddPdudv+i*dstride,eval(v,f,i,uu,vv,u_n,v_n,matrix_11,matrix_12,matrix_22,matrix_21)*sqr(dscale));
+          }
+        }
+      }
+    }
+
+    template<typename vbool, typename vfloat>
+    __forceinline void eval(const vbool& valid, const vfloat& uu, const vfloat& vv, 
+                            float* P, float* dPdu, float* dPdv, float* ddPdudu, float* ddPdvdv, float* ddPdudv,
+                            const float dscale, const size_t dstride, const size_t N) const {
+      eval(v,f,valid,uu,vv,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale,dstride,N);
+    }
+
+    template<class T>
+      static __forceinline Vec3<T> eval_t(const Vertex matrix[4][4], const Vec3<T> f[2][2], const T& uu, const T& vv) 
+    {
+      typedef typename T::Bool M;
+      const M m_border = (uu == 0.0f) | (uu == 1.0f) | (vv == 0.0f) | (vv == 1.0f);
+
+      const Vec3<T> f0_p = Vec3<T>(matrix[1][1].x,matrix[1][1].y,matrix[1][1].z);
+      const Vec3<T> f1_p = Vec3<T>(matrix[1][2].x,matrix[1][2].y,matrix[1][2].z);
+      const Vec3<T> f2_p = Vec3<T>(matrix[2][2].x,matrix[2][2].y,matrix[2][2].z);
+      const Vec3<T> f3_p = Vec3<T>(matrix[2][1].x,matrix[2][1].y,matrix[2][1].z);
+      
+      const Vec3<T> f0_m = f[0][0];
+      const Vec3<T> f1_m = f[0][1];
+      const Vec3<T> f2_m = f[1][1];
+      const Vec3<T> f3_m = f[1][0];
+      
+      const T one_minus_uu = T(1.0f) - uu;
+      const T one_minus_vv = T(1.0f) - vv;      
+      
+      const Vec3<T> f0_i = (          uu * f0_p +           vv * f0_m) * rcp(uu+vv);
+      const Vec3<T> f1_i = (one_minus_uu * f1_m +           vv * f1_p) * rcp(one_minus_uu+vv);
+      const Vec3<T> f2_i = (one_minus_uu * f2_p + one_minus_vv * f2_m) * rcp(one_minus_uu+one_minus_vv);
+      const Vec3<T> f3_i = (          uu * f3_m + one_minus_vv * f3_p) * rcp(uu+one_minus_vv);
+      
+      const Vec3<T> F0( select(m_border,f0_p.x,f0_i.x), select(m_border,f0_p.y,f0_i.y), select(m_border,f0_p.z,f0_i.z) );
+      const Vec3<T> F1( select(m_border,f1_p.x,f1_i.x), select(m_border,f1_p.y,f1_i.y), select(m_border,f1_p.z,f1_i.z) );
+      const Vec3<T> F2( select(m_border,f2_p.x,f2_i.x), select(m_border,f2_p.y,f2_i.y), select(m_border,f2_p.z,f2_i.z) );
+      const Vec3<T> F3( select(m_border,f3_p.x,f3_i.x), select(m_border,f3_p.y,f3_i.y), select(m_border,f3_p.z,f3_i.z) );
+
+      const T B0_u = one_minus_uu * one_minus_uu * one_minus_uu;
+      const T B0_v = one_minus_vv * one_minus_vv * one_minus_vv;
+      const T B1_u = 3.0f * (one_minus_uu * uu * one_minus_uu);
+      const T B1_v = 3.0f * (one_minus_vv * vv * one_minus_vv);
+      const T B2_u = 3.0f * (uu * one_minus_uu * uu);
+      const T B2_v = 3.0f * (vv * one_minus_vv * vv);
+      const T B3_u = uu * uu * uu;
+      const T B3_v = vv * vv * vv;
+
+      const T x = madd(B0_v,madd(B0_u,matrix[0][0].x,madd(B1_u,matrix[0][1].x,madd(B2_u,matrix[0][2].x,B3_u * matrix[0][3].x))), 
+                  madd(B1_v,madd(B0_u,matrix[1][0].x,madd(B1_u,F0.x          ,madd(B2_u,F1.x          ,B3_u * matrix[1][3].x))), 
+                  madd(B2_v,madd(B0_u,matrix[2][0].x,madd(B1_u,F3.x          ,madd(B2_u,F2.x          ,B3_u * matrix[2][3].x))), 
+                       B3_v*madd(B0_u,matrix[3][0].x,madd(B1_u,matrix[3][1].x,madd(B2_u,matrix[3][2].x,B3_u * matrix[3][3].x)))))); 
+
+      const T y = madd(B0_v,madd(B0_u,matrix[0][0].y,madd(B1_u,matrix[0][1].y,madd(B2_u,matrix[0][2].y,B3_u * matrix[0][3].y))),
+                  madd(B1_v,madd(B0_u,matrix[1][0].y,madd(B1_u,F0.y          ,madd(B2_u,F1.y          ,B3_u * matrix[1][3].y))),
+                  madd(B2_v,madd(B0_u,matrix[2][0].y,madd(B1_u,F3.y          ,madd(B2_u,F2.y          ,B3_u * matrix[2][3].y))),
+                       B3_v*madd(B0_u,matrix[3][0].y,madd(B1_u,matrix[3][1].y,madd(B2_u,matrix[3][2].y,B3_u * matrix[3][3].y))))));
+      
+      const T z = madd(B0_v,madd(B0_u,matrix[0][0].z,madd(B1_u,matrix[0][1].z,madd(B2_u,matrix[0][2].z,B3_u * matrix[0][3].z))),
+                  madd(B1_v,madd(B0_u,matrix[1][0].z,madd(B1_u,F0.z          ,madd(B2_u,F1.z          ,B3_u * matrix[1][3].z))),
+                  madd(B2_v,madd(B0_u,matrix[2][0].z,madd(B1_u,F3.z          ,madd(B2_u,F2.z          ,B3_u * matrix[2][3].z))),
+                       B3_v*madd(B0_u,matrix[3][0].z,madd(B1_u,matrix[3][1].z,madd(B2_u,matrix[3][2].z,B3_u * matrix[3][3].z))))));
+      
+      return Vec3<T>(x,y,z);
+    }
+
+    template<class T>
+    __forceinline Vec3<T> eval(const T& uu, const T& vv) const 
+    {
+      Vec3<T> ff[2][2];
+      ff[0][0] = Vec3<T>(f[0][0]);
+      ff[0][1] = Vec3<T>(f[0][1]);
+      ff[1][1] = Vec3<T>(f[1][1]);
+      ff[1][0] = Vec3<T>(f[1][0]);
+      return eval_t(v,ff,uu,vv);
+    }
+
+    template<class T>
+      static __forceinline Vec3<T> normal_t(const Vertex matrix[4][4], const Vec3<T> f[2][2], const T& uu, const T& vv) 
+    {
+      typedef typename T::Bool M;
+      
+      const Vec3<T> f0_p = Vec3<T>(matrix[1][1].x,matrix[1][1].y,matrix[1][1].z);
+      const Vec3<T> f1_p = Vec3<T>(matrix[1][2].x,matrix[1][2].y,matrix[1][2].z);
+      const Vec3<T> f2_p = Vec3<T>(matrix[2][2].x,matrix[2][2].y,matrix[2][2].z);
+      const Vec3<T> f3_p = Vec3<T>(matrix[2][1].x,matrix[2][1].y,matrix[2][1].z);
+
+      const Vec3<T> f0_m = f[0][0];
+      const Vec3<T> f1_m = f[0][1];
+      const Vec3<T> f2_m = f[1][1];
+      const Vec3<T> f3_m = f[1][0];
+      
+      const T one_minus_uu = T(1.0f) - uu;
+      const T one_minus_vv = T(1.0f) - vv;      
+      
+      const Vec3<T> f0_i = (          uu * f0_p +           vv * f0_m) * rcp(uu+vv);
+      const Vec3<T> f1_i = (one_minus_uu * f1_m +           vv * f1_p) * rcp(one_minus_uu+vv);
+      const Vec3<T> f2_i = (one_minus_uu * f2_p + one_minus_vv * f2_m) * rcp(one_minus_uu+one_minus_vv);
+      const Vec3<T> f3_i = (          uu * f3_m + one_minus_vv * f3_p) * rcp(uu+one_minus_vv);
+
+#if 1
+      const M m_corner0 = (uu == 0.0f) & (vv == 0.0f);
+      const M m_corner1 = (uu == 1.0f) & (vv == 0.0f);
+      const M m_corner2 = (uu == 1.0f) & (vv == 1.0f);
+      const M m_corner3 = (uu == 0.0f) & (vv == 1.0f);      
+      const Vec3<T> matrix_11( select(m_corner0,f0_p.x,f0_i.x), select(m_corner0,f0_p.y,f0_i.y), select(m_corner0,f0_p.z,f0_i.z) );
+      const Vec3<T> matrix_12( select(m_corner1,f1_p.x,f1_i.x), select(m_corner1,f1_p.y,f1_i.y), select(m_corner1,f1_p.z,f1_i.z) );
+      const Vec3<T> matrix_22( select(m_corner2,f2_p.x,f2_i.x), select(m_corner2,f2_p.y,f2_i.y), select(m_corner2,f2_p.z,f2_i.z) );
+      const Vec3<T> matrix_21( select(m_corner3,f3_p.x,f3_i.x), select(m_corner3,f3_p.y,f3_i.y), select(m_corner3,f3_p.z,f3_i.z) );
+#else
+      const M m_border = (uu == 0.0f) | (uu == 1.0f) | (vv == 0.0f) | (vv == 1.0f);
+      const Vec3<T> matrix_11( select(m_border,f0_p.x,f0_i.x), select(m_border,f0_p.y,f0_i.y), select(m_border,f0_p.z,f0_i.z) );
+      const Vec3<T> matrix_12( select(m_border,f1_p.x,f1_i.x), select(m_border,f1_p.y,f1_i.y), select(m_border,f1_p.z,f1_i.z) );
+      const Vec3<T> matrix_22( select(m_border,f2_p.x,f2_i.x), select(m_border,f2_p.y,f2_i.y), select(m_border,f2_p.z,f2_i.z) );
+      const Vec3<T> matrix_21( select(m_border,f3_p.x,f3_i.x), select(m_border,f3_p.y,f3_i.y), select(m_border,f3_p.z,f3_i.z) );
+#endif
+      
+      const Vec3<T> matrix_00 = Vec3<T>(matrix[0][0].x,matrix[0][0].y,matrix[0][0].z);
+      const Vec3<T> matrix_10 = Vec3<T>(matrix[1][0].x,matrix[1][0].y,matrix[1][0].z);
+      const Vec3<T> matrix_20 = Vec3<T>(matrix[2][0].x,matrix[2][0].y,matrix[2][0].z);
+      const Vec3<T> matrix_30 = Vec3<T>(matrix[3][0].x,matrix[3][0].y,matrix[3][0].z);
+      
+      const Vec3<T> matrix_01 = Vec3<T>(matrix[0][1].x,matrix[0][1].y,matrix[0][1].z);
+      const Vec3<T> matrix_02 = Vec3<T>(matrix[0][2].x,matrix[0][2].y,matrix[0][2].z);
+      const Vec3<T> matrix_03 = Vec3<T>(matrix[0][3].x,matrix[0][3].y,matrix[0][3].z);
+      
+      const Vec3<T> matrix_31 = Vec3<T>(matrix[3][1].x,matrix[3][1].y,matrix[3][1].z);
+      const Vec3<T> matrix_32 = Vec3<T>(matrix[3][2].x,matrix[3][2].y,matrix[3][2].z);
+      const Vec3<T> matrix_33 = Vec3<T>(matrix[3][3].x,matrix[3][3].y,matrix[3][3].z);
+      
+      const Vec3<T> matrix_13 = Vec3<T>(matrix[1][3].x,matrix[1][3].y,matrix[1][3].z);
+      const Vec3<T> matrix_23 = Vec3<T>(matrix[2][3].x,matrix[2][3].y,matrix[2][3].z);
+      
+      /* tangentU */
+      const Vec3<T> col0 = deCasteljau(vv, matrix_00, matrix_10, matrix_20, matrix_30);
+      const Vec3<T> col1 = deCasteljau(vv, matrix_01, matrix_11, matrix_21, matrix_31);
+      const Vec3<T> col2 = deCasteljau(vv, matrix_02, matrix_12, matrix_22, matrix_32);
+      const Vec3<T> col3 = deCasteljau(vv, matrix_03, matrix_13, matrix_23, matrix_33);
+      
+      const Vec3<T> tangentU = deCasteljau_tangent(uu, col0, col1, col2, col3);
+      
+      /* tangentV */
+      const Vec3<T> row0 = deCasteljau(uu, matrix_00, matrix_01, matrix_02, matrix_03);
+      const Vec3<T> row1 = deCasteljau(uu, matrix_10, matrix_11, matrix_12, matrix_13);
+      const Vec3<T> row2 = deCasteljau(uu, matrix_20, matrix_21, matrix_22, matrix_23);
+      const Vec3<T> row3 = deCasteljau(uu, matrix_30, matrix_31, matrix_32, matrix_33);
+      
+      const Vec3<T> tangentV = deCasteljau_tangent(vv, row0, row1, row2, row3);
+      
+      /* normal = tangentU x tangentV */
+      const Vec3<T> n = cross(tangentU,tangentV);
+      return n;
+    }
+
+     template<class T>
+    __forceinline Vec3<T> normal(const T& uu, const T& vv) const 
+    {
+      Vec3<T> ff[2][2];
+      ff[0][0] = Vec3<T>(f[0][0]);
+      ff[0][1] = Vec3<T>(f[0][1]);
+      ff[1][1] = Vec3<T>(f[1][1]);
+      ff[1][0] = Vec3<T>(f[1][0]);
+      return normal_t(v,ff,uu,vv);
+    }
+
+    __forceinline BBox<Vertex> bounds() const
+    {
+      const Vertex *const cv = &v[0][0];
+      BBox<Vertex> bounds (cv[0]);
+      for (size_t i=1; i<16; i++) 
+        bounds.extend( cv[i] );
+      bounds.extend(f[0][0]);
+      bounds.extend(f[1][0]);
+      bounds.extend(f[1][1]);
+      bounds.extend(f[1][1]);
+      return bounds;
+    }
+    
+    friend embree_ostream operator<<(embree_ostream o, const GregoryPatchT& p)
+    {
+      for (size_t y=0; y<4; y++)
+	for (size_t x=0; x<4; x++)
+	  o << "v[" << y << "][" << x << "] " << p.v[y][x] << embree_endl;
+      
+      for (size_t y=0; y<2; y++)
+	for (size_t x=0; x<2; x++)
+	  o << "f[" << y << "][" << x << "] " << p.f[y][x] << embree_endl;
+      return o;
+    } 
+  };
+
+  typedef GregoryPatchT<Vec3fa,Vec3fa_t> GregoryPatch3fa;
+
+  template<typename Vertex, typename Vertex_t>
+    __forceinline  BezierPatchT<Vertex,Vertex_t>::BezierPatchT (const HalfEdge* edge, const char* vertices, size_t stride) 
+  {
+    CatmullClarkPatchT<Vertex,Vertex_t> patch(edge,vertices,stride);
+    GregoryPatchT<Vertex,Vertex_t> gpatch(patch); 
+    gpatch.convert_to_bezier(); 
+    for (size_t y=0; y<4; y++)
+      for (size_t x=0; x<4; x++)
+        matrix[y][x] = (Vertex_t)gpatch.v[y][x];
+  }
+  
+   template<typename Vertex, typename Vertex_t>
+    __forceinline BezierPatchT<Vertex,Vertex_t>::BezierPatchT(const CatmullClarkPatchT<Vertex,Vertex_t>& patch) 
+    {
+      GregoryPatchT<Vertex,Vertex_t> gpatch(patch); 
+      gpatch.convert_to_bezier(); 
+      for (size_t y=0; y<4; y++)
+	for (size_t x=0; x<4; x++)
+	  matrix[y][x] = (Vertex_t)gpatch.v[y][x];
+    }
+
+   template<typename Vertex, typename Vertex_t>
+     __forceinline BezierPatchT<Vertex,Vertex_t>::BezierPatchT(const CatmullClarkPatchT<Vertex,Vertex_t>& patch, 
+                                                               const BezierCurveT<Vertex>* border0,
+                                                               const BezierCurveT<Vertex>* border1,
+                                                               const BezierCurveT<Vertex>* border2,
+                                                               const BezierCurveT<Vertex>* border3) 
+    {
+      GregoryPatchT<Vertex,Vertex_t> gpatch(patch,border0,border1,border2,border3); 
+      gpatch.convert_to_bezier(); 
+      for (size_t y=0; y<4; y++)
+	for (size_t x=0; x<4; x++)
+	  matrix[y][x] = (Vertex_t)gpatch.v[y][x];
+    }
+}

thirdparty/embree/kernels/subdiv/gregory_patch_dense.h

@@ -0,0 +1,113 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "gregory_patch.h"
+
+namespace embree
+{  
+  class __aligned(64) DenseGregoryPatch3fa
+  {
+    typedef Vec3fa Vec3fa_4x4[4][4];
+  public:
+
+    __forceinline DenseGregoryPatch3fa (const GregoryPatch3fa& patch)
+    {
+      for (size_t y=0; y<4; y++)
+	for (size_t x=0; x<4; x++)
+	  matrix[y][x] = Vec3ff(patch.v[y][x], 0.0f);
+      
+      matrix[0][0].w = patch.f[0][0].x;
+      matrix[0][1].w = patch.f[0][0].y;
+      matrix[0][2].w = patch.f[0][0].z;
+      matrix[0][3].w = 0.0f;
+      
+      matrix[1][0].w = patch.f[0][1].x;
+      matrix[1][1].w = patch.f[0][1].y;
+      matrix[1][2].w = patch.f[0][1].z;
+      matrix[1][3].w = 0.0f;
+      
+      matrix[2][0].w = patch.f[1][1].x;
+      matrix[2][1].w = patch.f[1][1].y;
+      matrix[2][2].w = patch.f[1][1].z;
+      matrix[2][3].w = 0.0f;
+      
+      matrix[3][0].w = patch.f[1][0].x;
+      matrix[3][1].w = patch.f[1][0].y;
+      matrix[3][2].w = patch.f[1][0].z;
+      matrix[3][3].w = 0.0f;
+    }
+
+    __forceinline void extract_f_m(Vec3fa f_m[2][2]) const
+    {
+      f_m[0][0] = Vec3fa( matrix[0][0].w, matrix[0][1].w, matrix[0][2].w );
+      f_m[0][1] = Vec3fa( matrix[1][0].w, matrix[1][1].w, matrix[1][2].w );
+      f_m[1][1] = Vec3fa( matrix[2][0].w, matrix[2][1].w, matrix[2][2].w );
+      f_m[1][0] = Vec3fa( matrix[3][0].w, matrix[3][1].w, matrix[3][2].w );      
+    }
+
+    __forceinline Vec3fa eval(const float uu, const float vv) const
+    {
+      __aligned(64) Vec3fa f_m[2][2]; extract_f_m(f_m);
+      return GregoryPatch3fa::eval(*(Vec3fa_4x4*)&matrix,f_m,uu,vv);
+    }
+
+    __forceinline Vec3fa normal(const float uu, const float vv) const
+    {
+      __aligned(64) Vec3fa f_m[2][2]; extract_f_m(f_m);
+      return GregoryPatch3fa::normal(*(Vec3fa_4x4*)&matrix,f_m,uu,vv);
+    }
+
+    template<class T>
+      __forceinline Vec3<T> eval(const T &uu, const T &vv) const 
+    {
+      Vec3<T> f_m[2][2];
+      f_m[0][0] = Vec3<T>( matrix[0][0].w, matrix[0][1].w, matrix[0][2].w );
+      f_m[0][1] = Vec3<T>( matrix[1][0].w, matrix[1][1].w, matrix[1][2].w );
+      f_m[1][1] = Vec3<T>( matrix[2][0].w, matrix[2][1].w, matrix[2][2].w );
+      f_m[1][0] = Vec3<T>( matrix[3][0].w, matrix[3][1].w, matrix[3][2].w );
+      return GregoryPatch3fa::eval_t(*(Vec3fa_4x4*)&matrix,f_m,uu,vv);
+    }
+    
+    template<class T>
+      __forceinline Vec3<T> normal(const T &uu, const T &vv) const 
+    {
+      Vec3<T> f_m[2][2];
+      f_m[0][0] = Vec3<T>( matrix[0][0].w, matrix[0][1].w, matrix[0][2].w );
+      f_m[0][1] = Vec3<T>( matrix[1][0].w, matrix[1][1].w, matrix[1][2].w );
+      f_m[1][1] = Vec3<T>( matrix[2][0].w, matrix[2][1].w, matrix[2][2].w );
+      f_m[1][0] = Vec3<T>( matrix[3][0].w, matrix[3][1].w, matrix[3][2].w );
+      return GregoryPatch3fa::normal_t(*(Vec3fa_4x4*)&matrix,f_m,uu,vv);
+    }
+
+    __forceinline void eval(const float u, const float v, 
+                            Vec3fa* P, Vec3fa* dPdu, Vec3fa* dPdv, Vec3fa* ddPdudu, Vec3fa* ddPdvdv, Vec3fa* ddPdudv,
+                            const float dscale = 1.0f) const
+    {
+      __aligned(64) Vec3fa f_m[2][2]; extract_f_m(f_m);
+      if (P) {
+        *P    = GregoryPatch3fa::eval(*(Vec3fa_4x4*)&matrix,f_m,u,v); 
+      }
+      if (dPdu) {
+        assert(dPdu); *dPdu = GregoryPatch3fa::eval_du(*(Vec3fa_4x4*)&matrix,f_m,u,v)*dscale; 
+        assert(dPdv); *dPdv = GregoryPatch3fa::eval_dv(*(Vec3fa_4x4*)&matrix,f_m,u,v)*dscale; 
+      }
+      if (ddPdudu) {
+        assert(ddPdudu); *ddPdudu = GregoryPatch3fa::eval_dudu(*(Vec3fa_4x4*)&matrix,f_m,u,v)*sqr(dscale); 
+        assert(ddPdvdv); *ddPdvdv = GregoryPatch3fa::eval_dvdv(*(Vec3fa_4x4*)&matrix,f_m,u,v)*sqr(dscale); 
+        assert(ddPdudv); *ddPdudv = GregoryPatch3fa::eval_dudv(*(Vec3fa_4x4*)&matrix,f_m,u,v)*sqr(dscale); 
+      }
+    }
+
+    template<typename vbool, typename vfloat>
+    __forceinline void eval(const vbool& valid, const vfloat& uu, const vfloat& vv, float* P, float* dPdu, float* dPdv, const float dscale, const size_t dstride, const size_t N) const 
+    {
+      __aligned(64) Vec3fa f_m[2][2]; extract_f_m(f_m);
+      GregoryPatch3fa::eval(matrix,f_m,valid,uu,vv,P,dPdu,dPdv,dscale,dstride,N);
+    }
+
+  private:
+    Vec3ff matrix[4][4]; // f_p/m points are stored in 4th component
+  };
+}

thirdparty/embree/kernels/subdiv/gridrange.h

@@ -0,0 +1,96 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "../common/default.h"
+
+namespace embree
+{
+  struct __aligned(16) GridRange
+  {
+    unsigned int u_start;
+    unsigned int u_end;
+    unsigned int v_start;
+    unsigned int v_end;
+
+    __forceinline GridRange() {}
+
+    __forceinline GridRange(unsigned int u_start, unsigned int u_end, unsigned int v_start, unsigned int v_end) 
+      : u_start(u_start), u_end(u_end), v_start(v_start), v_end(v_end) {}
+
+    __forceinline unsigned int width() const {
+      return u_end-u_start+1;
+    }
+
+    __forceinline unsigned int height() const {
+      return v_end-v_start+1;
+    }
+
+    __forceinline bool hasLeafSize() const
+    {
+      const unsigned int u_size = u_end-u_start+1;
+      const unsigned int v_size = v_end-v_start+1;
+      assert(u_size >= 1);
+      assert(v_size >= 1);
+      return u_size <= 3 && v_size <= 3;
+    }
+
+    static __forceinline unsigned int split(unsigned int start,unsigned int end)
+    {
+      const unsigned int center = (start+end)/2;
+      assert (center > start);
+      assert (center < end);
+      return center;
+    }
+
+    __forceinline void split(GridRange& r0, GridRange& r1) const
+    {
+      assert( hasLeafSize() == false );
+      const unsigned int u_size = u_end-u_start+1;
+      const unsigned int v_size = v_end-v_start+1;
+      r0 = *this;
+      r1 = *this;
+
+      if (u_size >= v_size)
+      {
+        const unsigned int u_mid = split(u_start,u_end);
+        r0.u_end   = u_mid;
+        r1.u_start = u_mid;
+      }
+      else
+      {
+        const unsigned int v_mid = split(v_start,v_end);
+        r0.v_end   = v_mid;
+        r1.v_start = v_mid;
+      }
+    }
+
+    __forceinline unsigned int splitIntoSubRanges(GridRange r[4]) const
+    {
+      assert( !hasLeafSize() );
+      unsigned int children = 0;
+      GridRange first,second;
+      split(first,second);
+
+      if (first.hasLeafSize()) {
+        r[0] = first;
+        children++;
+      } 
+      else {
+        first.split(r[0],r[1]);
+        children += 2;
+      }
+
+      if (second.hasLeafSize())	{
+        r[children] = second;
+        children++;
+      }
+      else {
+        second.split(r[children+0],r[children+1]);
+        children += 2;
+      }
+      return children;      
+    }
+  };
+}

thirdparty/embree/kernels/subdiv/half_edge.h

@@ -0,0 +1,371 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "catmullclark_coefficients.h"
+
+namespace embree
+{
+  class __aligned(32) HalfEdge
+  {
+    friend class SubdivMesh;
+    public:
+
+    enum PatchType : char { 
+      BILINEAR_PATCH        = 0, //!< a bilinear patch
+      REGULAR_QUAD_PATCH    = 1, //!< a regular quad patch can be represented as a B-Spline
+      IRREGULAR_QUAD_PATCH  = 2, //!< an irregular quad patch can be represented as a Gregory patch
+      COMPLEX_PATCH         = 3  //!< these patches need subdivision and cannot be processed by the above fast code paths
+    };
+    
+    enum VertexType : char { 
+      REGULAR_VERTEX           = 0, //!< regular vertex
+      NON_MANIFOLD_EDGE_VERTEX = 1, //!< vertex of a non-manifold edge
+    };
+    
+    __forceinline friend PatchType max( const PatchType& ty0, const PatchType& ty1) {
+      return (PatchType) max((int)ty0,(int)ty1);
+    }
+    
+    struct Edge 
+    {
+      /*! edge constructor */
+      __forceinline Edge(const uint32_t v0, const uint32_t v1)
+	: v0(v0), v1(v1) {}
+
+      /*! create an 64 bit identifier that is unique for the not oriented edge */
+      __forceinline operator uint64_t() const       
+      {
+	uint32_t p0 = v0, p1 = v1;
+	if (p0<p1) std::swap(p0,p1);
+	return (((uint64_t)p0) << 32) | (uint64_t)p1;
+      }
+
+    public:
+      uint32_t v0,v1;    //!< start and end vertex of the edge
+    };
+
+    HalfEdge () 
+      : vtx_index(-1), next_half_edge_ofs(0), prev_half_edge_ofs(0), opposite_half_edge_ofs(0), edge_crease_weight(0), 
+      vertex_crease_weight(0), edge_level(0), patch_type(COMPLEX_PATCH), vertex_type(REGULAR_VERTEX)
+    {
+      static_assert(sizeof(HalfEdge) == 32, "invalid half edge size");
+    }
+ 
+    __forceinline bool hasOpposite() const { return opposite_half_edge_ofs != 0; }
+    __forceinline void setOpposite(HalfEdge* opposite) { opposite_half_edge_ofs = int(opposite-this); }
+    
+    __forceinline       HalfEdge* next()       { assert( next_half_edge_ofs != 0 ); return &this[next_half_edge_ofs]; }
+    __forceinline const HalfEdge* next() const { assert( next_half_edge_ofs != 0 ); return &this[next_half_edge_ofs]; }
+    
+    __forceinline       HalfEdge* prev()       { assert( prev_half_edge_ofs != 0 ); return &this[prev_half_edge_ofs]; }
+    __forceinline const HalfEdge* prev() const { assert( prev_half_edge_ofs != 0 ); return &this[prev_half_edge_ofs]; }
+    
+    __forceinline       HalfEdge* opposite()       { assert( opposite_half_edge_ofs != 0 ); return &this[opposite_half_edge_ofs]; }
+    __forceinline const HalfEdge* opposite() const { assert( opposite_half_edge_ofs != 0 ); return &this[opposite_half_edge_ofs]; }
+    
+    __forceinline       HalfEdge* rotate()       { return opposite()->next(); }
+    __forceinline const HalfEdge* rotate() const { return opposite()->next(); }
+    
+    __forceinline unsigned int getStartVertexIndex() const { return vtx_index; }
+    __forceinline unsigned int getEndVertexIndex  () const { return next()->vtx_index; }
+    __forceinline Edge         getEdge            () const { return Edge(getStartVertexIndex(),getEndVertexIndex()); }
+   
+    
+    /*! tests if the start vertex of the edge is regular */
+    __forceinline PatchType vertexType() const
+    {
+      const HalfEdge* p = this;
+      size_t face_valence = 0;
+      bool hasBorder = false;
+      
+      do
+      {
+        /* we need subdivision to handle edge creases */
+        if (p->hasOpposite() && p->edge_crease_weight > 0.0f) 
+          return COMPLEX_PATCH;
+        
+        face_valence++;
+        
+        /* test for quad */
+        const HalfEdge* pp = p;
+        pp = pp->next(); if (pp == p) return COMPLEX_PATCH;
+        pp = pp->next(); if (pp == p) return COMPLEX_PATCH;
+        pp = pp->next(); if (pp == p) return COMPLEX_PATCH;
+        pp = pp->next(); if (pp != p) return COMPLEX_PATCH;
+        
+        /* continue with next face */
+        p = p->prev();
+        if (likely(p->hasOpposite())) 
+          p = p->opposite();
+        
+        /* if there is no opposite go the long way to the other side of the border */
+        else
+        {
+          face_valence++;
+          hasBorder = true;
+          p = this;
+          while (p->hasOpposite()) 
+            p = p->rotate();
+        }
+      } while (p != this); 
+      
+      /* calculate vertex type */
+      if (face_valence == 2 && hasBorder) {
+        if      (vertex_crease_weight == 0.0f      ) return REGULAR_QUAD_PATCH;
+        else if (vertex_crease_weight == float(inf)) return REGULAR_QUAD_PATCH;
+        else                                         return COMPLEX_PATCH;
+      }
+      else if (vertex_crease_weight != 0.0f)         return COMPLEX_PATCH;
+      else if (face_valence == 3 &&  hasBorder)      return REGULAR_QUAD_PATCH;
+      else if (face_valence == 4 && !hasBorder)      return REGULAR_QUAD_PATCH;
+      else                                           return IRREGULAR_QUAD_PATCH;
+    }
+
+    /*! tests if this edge is part of a bilinear patch */
+    __forceinline bool bilinearVertex() const {
+      return vertex_crease_weight == float(inf) && edge_crease_weight == float(inf);
+    }
+    
+    /*! calculates the type of the patch */
+    __forceinline PatchType patchType() const 
+    {
+      const HalfEdge* p = this;
+      PatchType ret = REGULAR_QUAD_PATCH;
+      bool bilinear = true;
+      
+      ret = max(ret,p->vertexType());
+      bilinear &= p->bilinearVertex();
+      if ((p = p->next()) == this) return COMPLEX_PATCH;
+      
+      ret = max(ret,p->vertexType());
+      bilinear &= p->bilinearVertex();
+      if ((p = p->next()) == this) return COMPLEX_PATCH;
+      
+      ret = max(ret,p->vertexType());
+      bilinear &= p->bilinearVertex();
+      if ((p = p->next()) == this) return COMPLEX_PATCH;
+      
+      ret = max(ret,p->vertexType());
+      bilinear &= p->bilinearVertex();
+      if ((p = p->next()) != this) return COMPLEX_PATCH;
+      
+      if (bilinear) return BILINEAR_PATCH;
+      return ret;
+    }
+    
+    /*! tests if the face is a regular b-spline face */
+    __forceinline bool isRegularFace() const {
+      return patch_type == REGULAR_QUAD_PATCH;
+    }
+    
+    /*! tests if the face can be diced (using bspline or gregory patch) */
+    __forceinline bool isGregoryFace() const {
+      return patch_type == IRREGULAR_QUAD_PATCH || patch_type == REGULAR_QUAD_PATCH;
+    }
+    
+    /*! tests if the base vertex of this half edge is a corner vertex */
+    __forceinline bool isCorner() const {
+      return !hasOpposite() && !prev()->hasOpposite();
+    }
+
+    /*! tests if the vertex is attached to any border */
+    __forceinline bool vertexHasBorder() const 
+    {
+      const HalfEdge* p = this;
+      do {
+        if (!p->hasOpposite()) return true;
+        p = p->rotate();
+      } while (p != this);
+      return false;
+    }
+    
+    /*! tests if the face this half edge belongs to has some border */
+    __forceinline bool faceHasBorder() const 
+    {
+      const HalfEdge* p = this;
+      do {
+        if (p->vertexHasBorder() && (p->vertex_type != HalfEdge::NON_MANIFOLD_EDGE_VERTEX)) return true;
+        p = p->next();
+      } while (p != this);
+      return false;
+    }
+    
+    /*! calculates conservative bounds of a catmull clark subdivision face */
+    __forceinline BBox3fa bounds(const BufferView<Vec3fa>& vertices) const
+    {
+      BBox3fa bounds = this->get1RingBounds(vertices);
+      for (const HalfEdge* p=this->next(); p!=this; p=p->next())
+        bounds.extend(p->get1RingBounds(vertices));
+      return bounds;
+    }
+    
+    /*! tests if this is a valid patch */
+    __forceinline bool valid(const BufferView<Vec3fa>& vertices) const
+    {
+      size_t N = 1;
+      if (!this->validRing(vertices)) return false;
+      for (const HalfEdge* p=this->next(); p!=this; p=p->next(), N++) {
+        if (!p->validRing(vertices)) return false;
+      }
+      return N >= 3 && N <= MAX_PATCH_VALENCE;
+    }
+    
+    /*! counts number of polygon edges  */
+    __forceinline unsigned int numEdges() const
+    {
+      unsigned int N = 1;
+      for (const HalfEdge* p=this->next(); p!=this; p=p->next(), N++);
+      return N;
+    }
+
+    /*! calculates face and edge valence */
+    __forceinline void calculateFaceValenceAndEdgeValence(size_t& faceValence, size_t& edgeValence) const 
+    {
+      faceValence = 0;
+      edgeValence = 0;
+      
+      const HalfEdge* p = this;
+      do 
+      {
+         /* calculate bounds of current face */
+        unsigned int numEdges = p->numEdges();
+        assert(numEdges >= 3);
+        edgeValence += numEdges-2;
+        
+        faceValence++;
+        p = p->prev();
+        
+        /* continue with next face */
+        if (likely(p->hasOpposite())) 
+          p = p->opposite();
+        
+        /* if there is no opposite go the long way to the other side of the border */
+        else {
+          faceValence++;
+          edgeValence++;
+          p = this;
+          while (p->hasOpposite()) 
+            p = p->opposite()->next();
+        }
+        
+      } while (p != this); 
+    }
+
+    /*! stream output */
+    friend __forceinline std::ostream &operator<<(std::ostream &o, const HalfEdge &h)
+    {
+      return o << "{ " << 
+        "vertex = " << h.vtx_index << ", " << //" -> " << h.next()->vtx_index << ", " << 
+        "prev = " << h.prev_half_edge_ofs << ", " << 
+        "next = " << h.next_half_edge_ofs << ", " << 
+        "opposite = " << h.opposite_half_edge_ofs << ", " << 
+        "edge_crease = " << h.edge_crease_weight << ", " << 
+        "vertex_crease = " << h.vertex_crease_weight << ", " << 
+        //"edge_level = " << h.edge_level << 
+        " }";
+    } 
+    
+  private:
+    
+    /*! calculates the bounds of the face associated with the half-edge */
+    __forceinline BBox3fa getFaceBounds(const BufferView<Vec3fa>& vertices) const 
+    {
+      BBox3fa b = vertices[getStartVertexIndex()];
+      for (const HalfEdge* p = next(); p!=this; p=p->next()) {
+        b.extend(vertices[p->getStartVertexIndex()]);
+      }
+      return b;
+    }
+    
+    /*! calculates the bounds of the 1-ring associated with the vertex of the half-edge */
+    __forceinline BBox3fa get1RingBounds(const BufferView<Vec3fa>& vertices) const 
+    {
+      BBox3fa bounds = empty;
+      const HalfEdge* p = this;
+      do 
+      {
+        /* calculate bounds of current face */
+        bounds.extend(p->getFaceBounds(vertices));
+        p = p->prev();
+        
+        /* continue with next face */
+        if (likely(p->hasOpposite())) 
+          p = p->opposite();
+        
+        /* if there is no opposite go the long way to the other side of the border */
+        else {
+          p = this;
+          while (p->hasOpposite()) 
+            p = p->opposite()->next();
+        }
+        
+      } while (p != this); 
+      
+      return bounds;
+    }
+    
+    /*! tests if this is a valid face */
+    __forceinline bool validFace(const BufferView<Vec3fa>& vertices, size_t& N) const 
+    {
+      const Vec3fa v = vertices[getStartVertexIndex()];
+      if (!isvalid(v)) return false;
+      size_t n = 1;
+      for (const HalfEdge* p = next(); p!=this; p=p->next(), n++) {
+        const Vec3fa v = vertices[p->getStartVertexIndex()];
+        if (!isvalid(v)) return false;
+      }
+      N += n-2;
+      return n >= 3 && n <= MAX_PATCH_VALENCE;
+    }
+    
+    /*! tests if this is a valid ring */
+    __forceinline bool validRing(const BufferView<Vec3fa>& vertices) const 
+    {
+      size_t faceValence = 0;
+      size_t edgeValence = 0;
+      
+      const HalfEdge* p = this;
+      do 
+      {
+        /* calculate bounds of current face */
+        if (!p->validFace(vertices,edgeValence)) 
+          return false;
+        
+        faceValence++;
+        p = p->prev();
+        
+        /* continue with next face */
+        if (likely(p->hasOpposite())) 
+          p = p->opposite();
+        
+        /* if there is no opposite go the long way to the other side of the border */
+        else {
+          faceValence++;
+          edgeValence++;
+          p = this;
+          while (p->hasOpposite()) 
+            p = p->opposite()->next();
+        }
+        
+      } while (p != this); 
+      
+      return faceValence <= MAX_RING_FACE_VALENCE && edgeValence <= MAX_RING_EDGE_VALENCE;
+    }
+    
+  private:
+    unsigned int vtx_index;         //!< index of edge start vertex
+    int next_half_edge_ofs;         //!< relative offset to next half edge of face
+    int prev_half_edge_ofs;         //!< relative offset to previous half edge of face
+    int opposite_half_edge_ofs;     //!< relative offset to opposite half edge
+    
+  public:
+    float edge_crease_weight;       //!< crease weight attached to edge
+    float vertex_crease_weight;     //!< crease weight attached to start vertex
+    float edge_level;               //!< subdivision factor for edge
+    PatchType patch_type;           //!< stores type of subdiv patch
+    VertexType vertex_type;         //!< stores type of the start vertex
+    char align[2];
+  };
+}

thirdparty/embree/kernels/subdiv/hermite_curve.h

@@ -0,0 +1,45 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "../common/default.h"
+#include "bezier_curve.h"
+
+namespace embree
+{
+  template<typename Vertex>
+    struct HermiteCurveT : BezierCurveT<Vertex>
+    {
+      __forceinline HermiteCurveT() {}
+
+      __forceinline HermiteCurveT(const BezierCurveT<Vertex>& curve)
+        : BezierCurveT<Vertex>(curve) {}
+      
+      __forceinline HermiteCurveT(const Vertex& v0, const Vertex& t0, const Vertex& v1, const Vertex& t1)
+        : BezierCurveT<Vertex>(v0,madd(1.0f/3.0f,t0,v0),nmadd(1.0f/3.0f,t1,v1),v1) {}
+
+      __forceinline HermiteCurveT<Vec3ff> xfm_pr(const LinearSpace3fa& space, const Vec3fa& p) const
+      {
+        const Vec3ff q0(xfmVector(space,this->v0-p), this->v0.w);
+        const Vec3ff q1(xfmVector(space,this->v1-p), this->v1.w);
+        const Vec3ff q2(xfmVector(space,this->v2-p), this->v2.w);
+        const Vec3ff q3(xfmVector(space,this->v3-p), this->v3.w);
+        return BezierCurveT<Vec3ff>(q0,q1,q2,q3);
+      }
+    };
+
+  template<typename Vertex>
+    __forceinline void convert(const HermiteCurveT<Vertex>& icurve, BezierCurveT<Vertex>& ocurve)
+  {
+    ocurve = BezierCurveT<Vertex>(icurve.v0,icurve.v1,icurve.v2,icurve.v3);
+  }
+  
+  template<typename CurveGeometry>
+  __forceinline HermiteCurveT<Vec3ff> enlargeRadiusToMinWidth(const RayQueryContext* context, const CurveGeometry* geom, const Vec3fa& ray_org, const HermiteCurveT<Vec3ff>& curve) {
+    return HermiteCurveT<Vec3ff>(enlargeRadiusToMinWidth(context,geom,ray_org,BezierCurveT<Vec3ff>(curve)));
+  }
+  
+  typedef HermiteCurveT<Vec3fa> HermiteCurve3fa;
+}
+

thirdparty/embree/kernels/subdiv/linear_bezier_patch.h

@@ -0,0 +1,443 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "bezier_curve.h"
+
+namespace embree
+{
+  namespace isa
+  {   
+    template<typename V>
+      struct TensorLinearQuadraticBezierSurface
+      {
+        QuadraticBezierCurve<V> L;
+        QuadraticBezierCurve<V> R;
+        
+        __forceinline TensorLinearQuadraticBezierSurface() {}
+        
+        __forceinline TensorLinearQuadraticBezierSurface(const TensorLinearQuadraticBezierSurface<V>& curve)
+          : L(curve.L), R(curve.R) {}
+        
+        __forceinline TensorLinearQuadraticBezierSurface& operator= (const TensorLinearQuadraticBezierSurface& other) {
+          L = other.L; R = other.R; return *this;
+        }
+          
+          __forceinline TensorLinearQuadraticBezierSurface(const QuadraticBezierCurve<V>& L, const QuadraticBezierCurve<V>& R)
+            : L(L), R(R) {}
+        
+        __forceinline BBox<V> bounds() const {
+          return merge(L.bounds(),R.bounds());
+        }
+      };
+
+#if !defined(__SYCL_DEVICE_ONLY__)   
+    template<>
+      struct TensorLinearQuadraticBezierSurface<Vec2fa>
+    {
+      QuadraticBezierCurve<vfloat4> LR;
+      
+      __forceinline TensorLinearQuadraticBezierSurface() {}
+      
+      __forceinline TensorLinearQuadraticBezierSurface(const TensorLinearQuadraticBezierSurface<Vec2fa>& curve)
+        : LR(curve.LR) {}
+      
+      __forceinline TensorLinearQuadraticBezierSurface& operator= (const TensorLinearQuadraticBezierSurface& other) {
+        LR = other.LR; return *this;
+      }
+      
+      __forceinline TensorLinearQuadraticBezierSurface(const QuadraticBezierCurve<vfloat4>& LR)
+        : LR(LR) {}
+      
+      __forceinline BBox<Vec2fa> bounds() const
+      {
+        const BBox<vfloat4> b = LR.bounds();
+        const BBox<Vec2fa> bl(Vec2fa(b.lower),Vec2fa(b.upper));
+        const BBox<Vec2fa> br(Vec2fa(shuffle<2,3,2,3>(b.lower)),Vec2fa(shuffle<2,3,2,3>(b.upper)));
+        return merge(bl,br);
+      }
+    };
+#endif
+    
+    template<typename V>
+      struct TensorLinearCubicBezierSurface
+      {
+        CubicBezierCurve<V> L;
+        CubicBezierCurve<V> R;
+        
+        __forceinline TensorLinearCubicBezierSurface() {}
+        
+        __forceinline TensorLinearCubicBezierSurface(const TensorLinearCubicBezierSurface& curve)
+          : L(curve.L), R(curve.R) {}
+        
+        __forceinline TensorLinearCubicBezierSurface& operator= (const TensorLinearCubicBezierSurface& other) {
+          L = other.L; R = other.R; return *this;
+        }
+          
+        __forceinline TensorLinearCubicBezierSurface(const CubicBezierCurve<V>& L, const CubicBezierCurve<V>& R)
+          : L(L), R(R) {}
+
+        template<template<typename T> class SourceCurve>
+        __forceinline static TensorLinearCubicBezierSurface fromCenterAndNormalCurve(const SourceCurve<Vec3ff>& center, const SourceCurve<Vec3fa>& normal)
+        {
+          SourceCurve<Vec3ff> vcurve = center;
+          SourceCurve<Vec3fa> ncurve = normal;
+
+          /* here we construct a patch which follows the curve l(t) =
+           * p(t) +/- r(t)*normalize(cross(n(t),dp(t))) */
+          
+          const Vec3ff p0   = vcurve.eval(0.0f);
+          const Vec3ff dp0  = vcurve.eval_du(0.0f);
+          //const Vec3ff ddp0 = vcurve.eval_dudu(0.0f); // ddp0 is assumed to be 0
+
+          const Vec3fa n0   = ncurve.eval(0.0f);
+          const Vec3fa dn0  = ncurve.eval_du(0.0f);
+
+          const Vec3ff p1   = vcurve.eval(1.0f);
+          const Vec3ff dp1  = vcurve.eval_du(1.0f);
+          //const Vec3ff ddp1 = vcurve.eval_dudu(1.0f);  // ddp1 is assumed to be 0
+
+          const Vec3fa n1   = ncurve.eval(1.0f);
+          const Vec3fa dn1  = ncurve.eval_du(1.0f);
+
+          const Vec3fa bt0  = cross(n0,dp0);
+          const Vec3fa dbt0 = cross(dn0,dp0);// + cross(n0,ddp0);
+
+          const Vec3fa bt1  = cross(n1,dp1);
+          const Vec3fa dbt1 = cross(dn1,dp1);// + cross(n1,ddp1);
+            
+          const Vec3fa k0  = normalize(bt0);
+          const Vec3fa dk0 = dnormalize(bt0,dbt0);
+          
+          const Vec3fa k1 = normalize(bt1);
+          const Vec3fa dk1 = dnormalize(bt1,dbt1);
+                    
+          const Vec3fa l0 = p0 - p0.w*k0;
+          const Vec3fa dl0 = dp0 - (dp0.w*k0 + p0.w*dk0);
+
+          const Vec3fa r0 = p0 + p0.w*k0;
+          const Vec3fa dr0 = dp0 + (dp0.w*k0 + p0.w*dk0);
+
+          const Vec3fa l1 = p1 - p1.w*k1;
+          const Vec3fa dl1 = dp1 - (dp1.w*k1 + p1.w*dk1);
+
+          const Vec3fa r1 = p1 + p1.w*k1;
+          const Vec3fa dr1 = dp1 + (dp1.w*k1 + p1.w*dk1);
+
+          const float scale = 1.0f/3.0f;
+          CubicBezierCurve<V> L(l0,l0+scale*dl0,l1-scale*dl1,l1);
+          CubicBezierCurve<V> R(r0,r0+scale*dr0,r1-scale*dr1,r1);
+          return TensorLinearCubicBezierSurface(L,R);
+        }
+
+        __forceinline BBox<V> bounds() const {
+          return merge(L.bounds(),R.bounds());
+        }
+
+        __forceinline BBox3fa accurateBounds() const {
+          return merge(L.accurateBounds(),R.accurateBounds());
+        }
+        
+        __forceinline CubicBezierCurve<Interval1f> reduce_v() const {
+          return merge(CubicBezierCurve<Interval<V>>(L),CubicBezierCurve<Interval<V>>(R));
+        }
+        
+        __forceinline LinearBezierCurve<Interval1f> reduce_u() const {
+          return LinearBezierCurve<Interval1f>(L.bounds(),R.bounds());
+        }
+        
+        __forceinline TensorLinearCubicBezierSurface<float> xfm(const V& dx) const {
+          return TensorLinearCubicBezierSurface<float>(L.xfm(dx),R.xfm(dx));
+        }
+
+        template<int W>
+        __forceinline TensorLinearCubicBezierSurface<vfloat<W>> vxfm(const V& dx) const {
+          return TensorLinearCubicBezierSurface<vfloat<W>>(L.template vxfm<W>(dx),R.template vxfm<W>(dx));
+        }
+        
+        __forceinline TensorLinearCubicBezierSurface<float> xfm(const V& dx, const V& p) const {
+          return TensorLinearCubicBezierSurface<float>(L.xfm(dx,p),R.xfm(dx,p));
+        }
+
+        __forceinline TensorLinearCubicBezierSurface<Vec3fa> xfm(const LinearSpace3fa& space) const {
+          return TensorLinearCubicBezierSurface(L.xfm(space),R.xfm(space));
+        }
+        
+        __forceinline TensorLinearCubicBezierSurface<Vec3fa> xfm(const LinearSpace3fa& space, const Vec3fa& p) const {
+          return TensorLinearCubicBezierSurface(L.xfm(space,p),R.xfm(space,p));
+        }
+
+        __forceinline TensorLinearCubicBezierSurface<Vec3fa> xfm(const LinearSpace3fa& space, const Vec3fa& p, const float s) const {
+          return TensorLinearCubicBezierSurface(L.xfm(space,p,s),R.xfm(space,p,s));
+        }
+
+        __forceinline TensorLinearCubicBezierSurface clip_u(const Interval1f& u) const {
+          return TensorLinearCubicBezierSurface(L.clip(u),R.clip(u));
+        }
+        
+        __forceinline TensorLinearCubicBezierSurface clip_v(const Interval1f& v) const {
+          return TensorLinearCubicBezierSurface(clerp(L,R,V(v.lower)),clerp(L,R,V(v.upper)));
+        }
+        
+        __forceinline TensorLinearCubicBezierSurface clip(const Interval1f& u, const Interval1f& v) const {
+          return clip_v(v).clip_u(u);
+        }
+        
+        __forceinline void split_u(TensorLinearCubicBezierSurface& left, TensorLinearCubicBezierSurface& right, const float u = 0.5f) const
+        {
+          CubicBezierCurve<V> L0,L1; L.split(L0,L1,u);
+          CubicBezierCurve<V> R0,R1; R.split(R0,R1,u);
+          new (&left ) TensorLinearCubicBezierSurface(L0,R0);
+          new (&right) TensorLinearCubicBezierSurface(L1,R1);
+        }
+
+        __forceinline TensorLinearCubicBezierSurface<Vec2vfx> vsplit_u(vboolx& valid, const BBox1f& u) const {
+          valid = true; clear(valid,VSIZEX-1);
+          return TensorLinearCubicBezierSurface<Vec2vfx>(L.split(u),R.split(u));
+        }
+
+        template<int W>
+        __forceinline TensorLinearCubicBezierSurface<Vec2vf<W>> vsplit_u(vbool<W>& valid, const BBox1f& u, int& i, int N) const
+        {
+          valid = true; clear(valid,W-1); 
+          auto r = TensorLinearCubicBezierSurface<Vec2vf<W>>(L.template split<W>(u,i,N),R.template split<W>(u,i,N));
+          i += W-1;
+          return r;
+        }
+        
+        __forceinline V eval(const float u, const float v) const {
+          return clerp(L,R,V(v)).eval(u);
+        }
+        
+        __forceinline V eval_du(const float u, const float v) const {
+          return clerp(L,R,V(v)).eval_dt(u);
+        }
+        
+        __forceinline V eval_dv(const float u, const float v) const {
+          return (R-L).eval(u);
+        }
+        
+        __forceinline void eval(const float u, const float v, V& p, V& dpdu, V& dpdv) const
+        {
+          V p0, dp0du; L.eval(u,p0,dp0du);
+          V p1, dp1du; R.eval(u,p1,dp1du);
+          p = lerp(p0,p1,v);
+          dpdu = lerp(dp0du,dp1du,v);
+          dpdv = p1-p0;
+        }
+        
+        __forceinline TensorLinearQuadraticBezierSurface<V> derivative_u() const {
+          return TensorLinearQuadraticBezierSurface<V>(L.derivative(),R.derivative());
+        }
+        
+        __forceinline CubicBezierCurve<V> derivative_v() const {
+          return R-L;
+        }
+        
+        __forceinline V axis_u() const {
+          return (L.end()-L.begin())+(R.end()-R.begin());
+        }
+        
+        __forceinline V axis_v() const {
+          return (R.begin()-L.begin())+(R.end()-L.end());
+        }
+        
+        friend embree_ostream operator<<(embree_ostream cout, const TensorLinearCubicBezierSurface& a)
+        {
+          return cout << "TensorLinearCubicBezierSurface" << embree_endl
+                      << "{" << embree_endl
+                      << "  L = " << a.L << ", " << embree_endl
+                      << "  R = " << a.R << embree_endl
+                      << "}";
+        }
+
+        friend __forceinline TensorLinearCubicBezierSurface clerp(const TensorLinearCubicBezierSurface& a, const TensorLinearCubicBezierSurface& b, const float t) {
+          return TensorLinearCubicBezierSurface(clerp(a.L,b.L,V(t)), clerp(a.R,b.R,V(t)));
+        }
+      };
+
+#if !defined(__SYCL_DEVICE_ONLY__)
+    
+    template<>
+      struct TensorLinearCubicBezierSurface<Vec2fa>
+    {
+      CubicBezierCurve<vfloat4> LR;
+      
+      __forceinline TensorLinearCubicBezierSurface() {}
+      
+      __forceinline TensorLinearCubicBezierSurface(const TensorLinearCubicBezierSurface& curve)
+        : LR(curve.LR) {}
+      
+      __forceinline TensorLinearCubicBezierSurface& operator= (const TensorLinearCubicBezierSurface& other) {
+        LR = other.LR; return *this;
+      }
+      
+      __forceinline TensorLinearCubicBezierSurface(const CubicBezierCurve<vfloat4>& LR)
+        : LR(LR) {}
+      
+      __forceinline TensorLinearCubicBezierSurface(const CubicBezierCurve<Vec2fa>& L, const CubicBezierCurve<Vec2fa>& R)
+        : LR(shuffle<0,1,0,1>(vfloat4(L.v0),vfloat4(R.v0)),shuffle<0,1,0,1>(vfloat4(L.v1),vfloat4(R.v1)),shuffle<0,1,0,1>(vfloat4(L.v2),vfloat4(R.v2)),shuffle<0,1,0,1>(vfloat4(L.v3),vfloat4(R.v3))) {}
+      
+      __forceinline CubicBezierCurve<Vec2fa> getL() const {
+        return CubicBezierCurve<Vec2fa>(Vec2fa(LR.v0),Vec2fa(LR.v1),Vec2fa(LR.v2),Vec2fa(LR.v3));
+      }
+      
+      __forceinline CubicBezierCurve<Vec2fa> getR() const {
+        return CubicBezierCurve<Vec2fa>(Vec2fa(shuffle<2,3,2,3>(LR.v0)),Vec2fa(shuffle<2,3,2,3>(LR.v1)),Vec2fa(shuffle<2,3,2,3>(LR.v2)),Vec2fa(shuffle<2,3,2,3>(LR.v3)));
+      }
+      
+      __forceinline BBox<Vec2fa> bounds() const
+      {
+        const BBox<vfloat4> b = LR.bounds();
+        const BBox<Vec2fa> bl(Vec2fa(b.lower),Vec2fa(b.upper));
+        const BBox<Vec2fa> br(Vec2fa(shuffle<2,3,2,3>(b.lower)),Vec2fa(shuffle<2,3,2,3>(b.upper)));
+        return merge(bl,br);
+      }
+      
+      __forceinline BBox1f bounds(const Vec2fa& axis) const
+      {
+        const CubicBezierCurve<vfloat4> LRx = LR;
+        const CubicBezierCurve<vfloat4> LRy(shuffle<1,0,3,2>(LR.v0),shuffle<1,0,3,2>(LR.v1),shuffle<1,0,3,2>(LR.v2),shuffle<1,0,3,2>(LR.v3));
+        const CubicBezierCurve<vfloat4> LRa = cmadd(shuffle<0>(vfloat4(axis)),LRx,shuffle<1>(vfloat4(axis))*LRy);
+        const BBox<vfloat4> Lb = LRa.bounds();
+        const BBox<vfloat4> Rb(shuffle<3>(Lb.lower),shuffle<3>(Lb.upper));
+        const BBox<vfloat4> b = merge(Lb,Rb);
+        return BBox1f(b.lower[0],b.upper[0]);
+      }
+
+      __forceinline TensorLinearCubicBezierSurface<float> xfm(const Vec2fa& dx) const
+      {
+        const CubicBezierCurve<vfloat4> LRx = LR;
+        const CubicBezierCurve<vfloat4> LRy(shuffle<1,0,3,2>(LR.v0),shuffle<1,0,3,2>(LR.v1),shuffle<1,0,3,2>(LR.v2),shuffle<1,0,3,2>(LR.v3));
+        const CubicBezierCurve<vfloat4> LRa = cmadd(shuffle<0>(vfloat4(dx)),LRx,shuffle<1>(vfloat4(dx))*LRy);
+        return TensorLinearCubicBezierSurface<float>(CubicBezierCurve<float>(LRa.v0[0],LRa.v1[0],LRa.v2[0],LRa.v3[0]),
+                                                     CubicBezierCurve<float>(LRa.v0[2],LRa.v1[2],LRa.v2[2],LRa.v3[2]));
+      }
+      
+      __forceinline TensorLinearCubicBezierSurface<float> xfm(const Vec2fa& dx, const Vec2fa& p) const
+      {
+        const vfloat4 pxyxy = shuffle<0,1,0,1>(vfloat4(p));
+        const CubicBezierCurve<vfloat4> LRx = LR-pxyxy;
+        const CubicBezierCurve<vfloat4> LRy(shuffle<1,0,3,2>(LR.v0),shuffle<1,0,3,2>(LR.v1),shuffle<1,0,3,2>(LR.v2),shuffle<1,0,3,2>(LR.v3));
+        const CubicBezierCurve<vfloat4> LRa = cmadd(shuffle<0>(vfloat4(dx)),LRx,shuffle<1>(vfloat4(dx))*LRy);
+        return TensorLinearCubicBezierSurface<float>(CubicBezierCurve<float>(LRa.v0[0],LRa.v1[0],LRa.v2[0],LRa.v3[0]),
+                                                     CubicBezierCurve<float>(LRa.v0[2],LRa.v1[2],LRa.v2[2],LRa.v3[2]));
+      }
+
+      __forceinline TensorLinearCubicBezierSurface clip_u(const Interval1f& u) const {
+        return TensorLinearCubicBezierSurface(LR.clip(u));
+      }
+      
+      __forceinline TensorLinearCubicBezierSurface clip_v(const Interval1f& v) const
+      {
+        const CubicBezierCurve<vfloat4> LL(shuffle<0,1,0,1>(LR.v0),shuffle<0,1,0,1>(LR.v1),shuffle<0,1,0,1>(LR.v2),shuffle<0,1,0,1>(LR.v3));
+        const CubicBezierCurve<vfloat4> RR(shuffle<2,3,2,3>(LR.v0),shuffle<2,3,2,3>(LR.v1),shuffle<2,3,2,3>(LR.v2),shuffle<2,3,2,3>(LR.v3));
+        return TensorLinearCubicBezierSurface(clerp(LL,RR,vfloat4(v.lower,v.lower,v.upper,v.upper)));
+      }
+      
+      __forceinline TensorLinearCubicBezierSurface clip(const Interval1f& u, const Interval1f& v) const {
+        return clip_v(v).clip_u(u);
+      }
+      
+      __forceinline void split_u(TensorLinearCubicBezierSurface& left, TensorLinearCubicBezierSurface& right, const float u = 0.5f) const
+      {
+        CubicBezierCurve<vfloat4> LR0,LR1; LR.split(LR0,LR1,u);
+        new (&left ) TensorLinearCubicBezierSurface(LR0);
+        new (&right) TensorLinearCubicBezierSurface(LR1);
+      }
+
+      __forceinline TensorLinearCubicBezierSurface<Vec2vfx> vsplit_u(vboolx& valid, const BBox1f& u) const {
+        valid = true; clear(valid,VSIZEX-1);
+        return TensorLinearCubicBezierSurface<Vec2vfx>(getL().split(u),getR().split(u));
+      }
+      
+      template<int W>
+      __forceinline TensorLinearCubicBezierSurface<Vec2vf<W>> vsplit_u(vbool<W>& valid, const BBox1f& u, int& i, int N) const {
+        valid = true; clear(valid,W-1); 
+        auto r = TensorLinearCubicBezierSurface<Vec2vf<W>>(getL().split<W>(u,i,N),getR().split<W>(u,i,N));
+        i += W-1;
+        return r;
+      }
+      
+      __forceinline Vec2fa eval(const float u, const float v) const
+      {
+        const vfloat4 p = LR.eval(u);
+        return Vec2fa(lerp(shuffle<0,1,0,1>(p),shuffle<2,3,2,3>(p),v));
+      }
+      
+      __forceinline Vec2fa eval_du(const float u, const float v) const
+      {
+        const vfloat4 dpdu = LR.eval_dt(u);
+        return Vec2fa(lerp(shuffle<0,1,0,1>(dpdu),shuffle<2,3,2,3>(dpdu),v));
+      }
+      
+      __forceinline Vec2fa eval_dv(const float u, const float v) const
+      {
+        const vfloat4 p = LR.eval(u);
+        return Vec2fa(shuffle<2,3,2,3>(p)-shuffle<0,1,0,1>(p));
+      }
+      
+      __forceinline void eval(const float u, const float v, Vec2fa& p, Vec2fa& dpdu, Vec2fa& dpdv) const
+      {
+        vfloat4 p0, dp0du; LR.eval(u,p0,dp0du);
+        p = Vec2fa(lerp(shuffle<0,1,0,1>(p0),shuffle<2,3,2,3>(p0),v));
+        dpdu = Vec2fa(lerp(shuffle<0,1,0,1>(dp0du),shuffle<2,3,2,3>(dp0du),v));
+        dpdv = Vec2fa(shuffle<2,3,2,3>(p0)-shuffle<0,1,0,1>(p0));
+      }
+      
+      __forceinline TensorLinearQuadraticBezierSurface<Vec2fa> derivative_u() const {
+        return TensorLinearQuadraticBezierSurface<Vec2fa>(LR.derivative());
+      }
+      
+      __forceinline CubicBezierCurve<Vec2fa> derivative_v() const {
+        return getR()-getL();
+      }
+      
+      __forceinline Vec2fa axis_u() const
+      {
+        const CubicBezierCurve<Vec2fa> L = getL();
+        const CubicBezierCurve<Vec2fa> R = getR();
+        return (L.end()-L.begin())+(R.end()-R.begin());
+      }
+      
+      __forceinline Vec2fa axis_v() const
+      {
+        const CubicBezierCurve<Vec2fa> L = getL();
+        const CubicBezierCurve<Vec2fa> R = getR();
+        return (R.begin()-L.begin())+(R.end()-L.end());
+      }
+      
+      friend embree_ostream operator<<(embree_ostream cout, const TensorLinearCubicBezierSurface& a)
+      {
+        return cout << "TensorLinearCubicBezierSurface" << embree_endl
+                    << "{" << embree_endl
+                    << "  L = " << a.getL() << ", " << embree_endl
+                    << "  R = " << a.getR() << embree_endl
+                    << "}";
+      }
+    };
+
+    template<>
+    __forceinline TensorLinearCubicBezierSurface<Vec2f> TensorLinearCubicBezierSurface<Vec2fa>::vsplit_u<1>(bool& valid, const BBox1f& u, int& i, int N) const {
+      auto r = TensorLinearCubicBezierSurface<Vec2f>(getL().split1(u,i,N),getR().split1(u,i,N));
+      valid = true; i += 1;
+      return r;
+    }
+    
+#else
+
+    template<> template<>
+    __forceinline TensorLinearCubicBezierSurface<Vec2f> TensorLinearCubicBezierSurface<Vec2fa>::vsplit_u<1>(bool& valid, const BBox1f& u, int& i, int N) const {
+      auto r = TensorLinearCubicBezierSurface<Vec2f>(L.split1(u,i,N),R.split1(u,i,N));
+      valid = true; i += 1;
+      return r;
+    }
+
+#endif
+
+    typedef TensorLinearCubicBezierSurface<float> TensorLinearCubicBezierSurface1f;
+    typedef TensorLinearCubicBezierSurface<Vec2fa> TensorLinearCubicBezierSurface2fa;
+    typedef TensorLinearCubicBezierSurface<Vec3fa> TensorLinearCubicBezierSurface3fa;
+  }
+}

thirdparty/embree/kernels/subdiv/patch.h

@@ -0,0 +1,371 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "catmullclark_patch.h"
+#include "bilinear_patch.h"
+#include "bspline_patch.h"
+#include "bezier_patch.h"
+#include "gregory_patch.h"
+#include "tessellation_cache.h"
+
+#if 1
+#define PATCH_DEBUG_SUBDIVISION(ptr,x,y,z)
+#else
+#define PATCH_DEBUG_SUBDIVISION(ptr,x,y,z)            \
+  {                                                   \
+    size_t hex = (size_t)ptr;                          \
+    for (size_t i=0; i<4; i++) hex = hex ^ (hex >> 8);  \
+    const float c = (float)(((hex >> 0) ^ (hex >> 4) ^ (hex >> 8) ^ (hex >> 12) ^ (hex >> 16))&0xf)/15.0f; \
+    if (P) *P = Vertex(0.5f+0.5f*x,0.5f+0.5f*y,0.5f+0.5f*z,0.0f);         \
+    }               
+#endif
+
+#define PATCH_MAX_CACHE_DEPTH 2
+//#define PATCH_MIN_RESOLUTION 1     // FIXME: not yet completely implemented
+#define PATCH_MAX_EVAL_DEPTH_IRREGULAR 10     // maximum evaluation depth at irregular vertices (has to be larger or equal than PATCH_MAX_CACHE_DEPTH)
+#define PATCH_MAX_EVAL_DEPTH_CREASE 10       // maximum evaluation depth at crease features (has to be larger or equal than PATCH_MAX_CACHE_DEPTH)
+#define PATCH_USE_GREGORY 1        // 0 = no gregory, 1 = fill, 2 = as early as possible
+
+#if PATCH_USE_GREGORY==2
+#define PATCH_USE_BEZIER_PATCH 1   // enable use of bezier instead of b-spline patches
+#else
+#define PATCH_USE_BEZIER_PATCH 0   // enable use of bezier instead of b-spline patches
+#endif
+
+#if PATCH_USE_BEZIER_PATCH
+#  define RegularPatch  BezierPatch
+#  define RegularPatchT BezierPatchT<Vertex,Vertex_t>
+#else
+#  define RegularPatch  BSplinePatch
+#  define RegularPatchT BSplinePatchT<Vertex,Vertex_t>
+#endif
+
+#if PATCH_USE_GREGORY
+#define IrregularFillPatch GregoryPatch
+#define IrregularFillPatchT GregoryPatchT<Vertex,Vertex_t>
+#else
+#define IrregularFillPatch BilinearPatch
+#define IrregularFillPatchT BilinearPatchT<Vertex,Vertex_t>
+#endif
+
+namespace embree
+{
+  template<typename Vertex, typename Vertex_t = Vertex>
+    struct __aligned(64) PatchT
+    {
+    public:
+    
+    typedef GeneralCatmullClarkPatchT<Vertex,Vertex_t> GeneralCatmullClarkPatch;
+    typedef CatmullClarkPatchT<Vertex,Vertex_t> CatmullClarkPatch;
+    typedef CatmullClark1RingT<Vertex,Vertex_t> CatmullClarkRing;
+    typedef BezierCurveT<Vertex> BezierCurve;
+    
+    enum Type {
+      INVALID_PATCH = 0,
+      BILINEAR_PATCH = 1,
+      BSPLINE_PATCH = 2,  
+      BEZIER_PATCH = 3,  
+      GREGORY_PATCH = 4,
+      SUBDIVIDED_GENERAL_PATCH = 7,
+      SUBDIVIDED_QUAD_PATCH = 8,
+      EVAL_PATCH = 9,
+    };
+    
+    struct Ref
+    {
+      __forceinline Ref(void* p = nullptr) 
+        : ptr((size_t)p) {}
+
+      __forceinline operator bool() const { return ptr != 0; }
+      __forceinline operator size_t() const { return ptr; }
+
+      __forceinline Ref (Type ty, void* in) 
+        : ptr(((size_t)in)+ty) { assert((((size_t)in) & 0xF) == 0); }
+
+      __forceinline Type  type  () const { return (Type)(ptr & 0xF); }
+      __forceinline void* object() const { return (void*) (ptr & ~0xF); }
+
+      size_t ptr;
+    };
+
+    struct EvalPatch 
+    {
+      /* creates EvalPatch from a CatmullClarkPatch */
+      template<typename Allocator>
+      __noinline static Ref create(const Allocator& alloc, const CatmullClarkPatch& patch) 
+      {
+        size_t ofs = 0, bytes = patch.bytes();
+        void* ptr = alloc(bytes);
+        patch.serialize(ptr,ofs);
+        assert(ofs == bytes);
+        return Ref(EVAL_PATCH, ptr);
+      }
+    };
+
+    struct BilinearPatch 
+    {
+      /* creates BilinearPatch from a CatmullClarkPatch */
+      template<typename Allocator>
+      __noinline static Ref create(const Allocator& alloc, const CatmullClarkPatch& patch,
+                                   const BezierCurve* border0, const BezierCurve* border1, const BezierCurve* border2, const BezierCurve* border3) {
+        return Ref(BILINEAR_PATCH, new (alloc(sizeof(BilinearPatch))) BilinearPatch(patch));
+      }
+
+      __forceinline BilinearPatch (const CatmullClarkPatch& patch) 
+        : patch(patch) {}
+
+      /* creates BilinearPatch from 4 vertices */
+      template<typename Allocator>
+      __noinline static Ref create(const Allocator& alloc, const HalfEdge* edge, const char* vertices, size_t stride) {
+        return Ref(BILINEAR_PATCH, new (alloc(sizeof(BilinearPatch))) BilinearPatch(edge,vertices,stride));
+      }
+      
+      __forceinline BilinearPatch (const HalfEdge* edge, const char* vertices, size_t stride) 
+        : patch(edge,vertices,stride) {}
+      
+    public:
+      BilinearPatchT<Vertex,Vertex_t> patch;
+    };
+    
+    struct BSplinePatch 
+    {
+      /* creates BSplinePatch from a half edge */
+      template<typename Allocator>
+      __noinline static Ref create(const Allocator& alloc, const HalfEdge* edge, const char* vertices, size_t stride) {
+        return Ref(BSPLINE_PATCH, new (alloc(sizeof(BSplinePatch))) BSplinePatch(edge,vertices,stride));
+      }
+      
+      __forceinline BSplinePatch (const HalfEdge* edge, const char* vertices, size_t stride) 
+        : patch(edge,vertices,stride) {}
+      
+      /* creates BSplinePatch from a CatmullClarkPatch */
+      template<typename Allocator>
+      __noinline static Ref create(const Allocator& alloc, const CatmullClarkPatch& patch,
+                                   const BezierCurve* border0, const BezierCurve* border1, const BezierCurve* border2, const BezierCurve* border3) {
+        return Ref(BSPLINE_PATCH, new (alloc(sizeof(BSplinePatch))) BSplinePatch(patch,border0,border1,border2,border3));
+      }
+      
+      __forceinline BSplinePatch (const CatmullClarkPatch& patch, const BezierCurve* border0, const BezierCurve* border1, const BezierCurve* border2, const BezierCurve* border3) 
+        : patch(patch,border0,border1,border2,border3) {}
+      
+    public:
+      BSplinePatchT<Vertex,Vertex_t> patch;
+    };
+
+    struct BezierPatch
+    {
+      /* creates BezierPatch from a half edge */
+      template<typename Allocator>
+        __noinline static Ref create(const Allocator& alloc, const HalfEdge* edge, const char* vertices, size_t stride) {
+        return Ref(BEZIER_PATCH, new (alloc(sizeof(BezierPatch))) BezierPatch(edge,vertices,stride));
+      }
+      
+      __forceinline BezierPatch (const HalfEdge* edge, const char* vertices, size_t stride) 
+        : patch(edge,vertices,stride) {}
+      
+      /* creates Bezier from a CatmullClarkPatch */
+      template<typename Allocator>
+      __noinline static Ref create(const Allocator& alloc, const CatmullClarkPatch& patch,
+                                   const BezierCurve* border0, const BezierCurve* border1, const BezierCurve* border2, const BezierCurve* border3) {
+        return Ref(BEZIER_PATCH, new (alloc(sizeof(BezierPatch))) BezierPatch(patch,border0,border1,border2,border3));
+      }
+      
+      __forceinline BezierPatch (const CatmullClarkPatch& patch, const BezierCurve* border0, const BezierCurve* border1, const BezierCurve* border2, const BezierCurve* border3) 
+        : patch(patch,border0,border1,border2,border3) {}
+      
+    public:
+      BezierPatchT<Vertex,Vertex_t> patch;
+    };
+    
+    struct GregoryPatch
+    {
+      /* creates GregoryPatch from half edge */
+      template<typename Allocator>
+      __noinline static Ref create(const Allocator& alloc, const HalfEdge* edge, const char* vertices, size_t stride) {
+        return Ref(GREGORY_PATCH, new (alloc(sizeof(GregoryPatch))) GregoryPatch(edge,vertices,stride));
+      }
+      
+      __forceinline GregoryPatch (const HalfEdge* edge, const char* vertices, size_t stride) 
+        : patch(CatmullClarkPatch(edge,vertices,stride)) {}
+       
+      /* creates GregoryPatch from CatmullClarkPatch */
+      template<typename Allocator>
+      __noinline static Ref create(const Allocator& alloc, const CatmullClarkPatch& patch,
+                                   const BezierCurve* border0, const BezierCurve* border1, const BezierCurve* border2, const BezierCurve* border3) {
+        return Ref(GREGORY_PATCH, new (alloc(sizeof(GregoryPatch))) GregoryPatch(patch,border0,border1,border2,border3));
+      }
+      
+      __forceinline GregoryPatch (const CatmullClarkPatch& patch, const BezierCurve* border0, const BezierCurve* border1, const BezierCurve* border2, const BezierCurve* border3) 
+        : patch(patch,border0,border1,border2,border3) {}
+      
+    public:
+      GregoryPatchT<Vertex,Vertex_t> patch;
+    };
+    
+    struct SubdividedQuadPatch
+    {
+      template<typename Allocator>
+      __noinline static Ref create(const Allocator& alloc, Ref children[4]) {
+        return Ref(SUBDIVIDED_QUAD_PATCH, new (alloc(sizeof(SubdividedQuadPatch))) SubdividedQuadPatch(children));
+      }
+      
+      __forceinline SubdividedQuadPatch(Ref children[4]) {
+        for (size_t i=0; i<4; i++) child[i] = children[i];
+      }
+      
+    public:
+      Ref child[4];
+    };
+    
+    struct SubdividedGeneralPatch
+    {
+      template<typename Allocator>
+      __noinline static Ref create(const Allocator& alloc, Ref* children, const unsigned N) {
+        return Ref(SUBDIVIDED_GENERAL_PATCH, new (alloc(sizeof(SubdividedGeneralPatch))) SubdividedGeneralPatch(children,N));
+      }
+      
+      __forceinline SubdividedGeneralPatch(Ref* children, const unsigned N) : N(N) {
+        for (unsigned i=0; i<N; i++) child[i] = children[i];
+      }
+      
+      unsigned N;
+      Ref child[MAX_PATCH_VALENCE];
+    };
+    
+    /*! Default constructor. */
+    __forceinline PatchT () {}
+    
+    template<typename Allocator>
+      __noinline static Ref create(const Allocator& alloc, const HalfEdge* edge, const char* vertices, size_t stride)
+    {
+      if (PATCH_MAX_CACHE_DEPTH == 0) 
+        return nullptr;
+
+      Ref child(0);
+      switch (edge->patch_type) {
+      case HalfEdge::BILINEAR_PATCH:       child = BilinearPatch::create(alloc,edge,vertices,stride); break; 
+      case HalfEdge::REGULAR_QUAD_PATCH:   child = RegularPatch::create(alloc,edge,vertices,stride); break;
+#if PATCH_USE_GREGORY == 2
+      case HalfEdge::IRREGULAR_QUAD_PATCH: child = GregoryPatch::create(alloc,edge,vertices,stride); break;
+#endif
+      default: {
+        GeneralCatmullClarkPatch patch(edge,vertices,stride);
+        child = PatchT::create(alloc,patch,edge,vertices,stride,0);
+      }
+      }
+      return child;
+    }
+
+    template<typename Allocator>
+    __noinline static Ref create(const Allocator& alloc, GeneralCatmullClarkPatch& patch, const HalfEdge* edge, const char* vertices, size_t stride, size_t depth)
+    {  
+      /* convert into standard quad patch if possible */
+      if (likely(patch.isQuadPatch())) 
+      {
+        CatmullClarkPatch qpatch; patch.init(qpatch);
+        return PatchT::create(alloc,qpatch,edge,vertices,stride,depth);
+      }
+   
+      /* do only cache up to some depth */
+      if (depth >= PATCH_MAX_CACHE_DEPTH)
+        return nullptr;
+         
+      /* subdivide patch */
+      unsigned N;
+      array_t<CatmullClarkPatch,GeneralCatmullClarkPatch::SIZE> patches; 
+      patch.subdivide(patches,N);
+      
+      if (N == 4) 
+      {
+        Ref child[4];
+#if PATCH_USE_GREGORY == 2
+        BezierCurve borders[GeneralCatmullClarkPatch::SIZE]; patch.getLimitBorder(borders);
+        BezierCurve border0l,border0r; borders[0].subdivide(border0l,border0r);
+        BezierCurve border1l,border1r; borders[1].subdivide(border1l,border1r);
+        BezierCurve border2l,border2r; borders[2].subdivide(border2l,border2r);
+        BezierCurve border3l,border3r; borders[3].subdivide(border3l,border3r);
+        GeneralCatmullClarkPatch::fix_quad_ring_order(patches);
+        child[0] = PatchT::create(alloc,patches[0],edge,vertices,stride,depth+1,&border0l,nullptr,nullptr,&border3r);
+        child[1] = PatchT::create(alloc,patches[1],edge,vertices,stride,depth+1,&border0r,&border1l,nullptr,nullptr);
+        child[2] = PatchT::create(alloc,patches[2],edge,vertices,stride,depth+1,nullptr,&border1r,&border2l,nullptr);
+        child[3] = PatchT::create(alloc,patches[3],edge,vertices,stride,depth+1,nullptr,nullptr,&border2r,&border3l);
+#else
+        GeneralCatmullClarkPatch::fix_quad_ring_order(patches);
+        for (size_t i=0; i<4; i++)
+          child[i] = PatchT::create(alloc,patches[i],edge,vertices,stride,depth+1);
+#endif
+        return SubdividedQuadPatch::create(alloc,child);
+      }
+      else 
+      {
+        assert(N<MAX_PATCH_VALENCE);
+        Ref child[MAX_PATCH_VALENCE];
+        
+#if PATCH_USE_GREGORY == 2
+        BezierCurve borders[GeneralCatmullClarkPatch::SIZE]; 
+        patch.getLimitBorder(borders);
+
+        for (size_t i0=0; i0<N; i0++) {
+          const size_t i2 = i0==0 ? N-1 : i0-1; 
+          BezierCurve border0l,border0r; borders[i0].subdivide(border0l,border0r);
+          BezierCurve border2l,border2r; borders[i2].subdivide(border2l,border2r);
+          child[i0] = PatchT::create(alloc,patches[i0],edge,vertices,stride,depth+1, &border0l, nullptr, nullptr, &border2r);
+        }
+#else
+        for (size_t i=0; i<N; i++)
+          child[i] = PatchT::create(alloc,patches[i],edge,vertices,stride,depth+1);
+#endif
+        return SubdividedGeneralPatch::create(alloc,child,N);
+      }
+      
+      return nullptr;
+    }
+
+    static __forceinline bool final(const CatmullClarkPatch& patch, const typename CatmullClarkRing::Type type, size_t depth) 
+    {
+      const size_t max_eval_depth = (type & CatmullClarkRing::TYPE_CREASES) ? PATCH_MAX_EVAL_DEPTH_CREASE : PATCH_MAX_EVAL_DEPTH_IRREGULAR;
+//#if PATCH_MIN_RESOLUTION
+//      return patch.isFinalResolution(PATCH_MIN_RESOLUTION) || depth>=max_eval_depth;
+//#else
+      return depth>=max_eval_depth;
+//#endif
+    }
+
+    template<typename Allocator>
+      __noinline static Ref create(const Allocator& alloc, CatmullClarkPatch& patch, const HalfEdge* edge, const char* vertices, size_t stride, size_t depth,
+                                   const BezierCurve* border0 = nullptr, const BezierCurve* border1 = nullptr, const BezierCurve* border2 = nullptr, const BezierCurve* border3 = nullptr)
+    {
+      const typename CatmullClarkPatch::Type ty = patch.type();
+      if (unlikely(final(patch,ty,depth))) {
+        if (ty & CatmullClarkRing::TYPE_REGULAR) return RegularPatch::create(alloc,patch,border0,border1,border2,border3); 
+        else                                     return IrregularFillPatch::create(alloc,patch,border0,border1,border2,border3); 
+      }
+      else if (ty & CatmullClarkRing::TYPE_REGULAR_CREASES) { 
+        assert(depth > 0); return RegularPatch::create(alloc,patch,border0,border1,border2,border3); 
+      }
+#if PATCH_USE_GREGORY == 2
+      else if (ty & CatmullClarkRing::TYPE_GREGORY_CREASES) { 
+        assert(depth > 0); return GregoryPatch::create(alloc,patch,border0,border1,border2,border3); 
+      }
+#endif
+      else if (depth >= PATCH_MAX_CACHE_DEPTH) {
+        return EvalPatch::create(alloc,patch); 
+      }
+      
+      else 
+      {
+        Ref child[4];
+        array_t<CatmullClarkPatch,4> patches; 
+        patch.subdivide(patches);
+        
+        for (size_t i=0; i<4; i++)
+          child[i] = PatchT::create(alloc,patches[i],edge,vertices,stride,depth+1);
+        return SubdividedQuadPatch::create(alloc,child);
+      }
+    }
+  };
+
+  typedef PatchT<Vec3fa,Vec3fa_t> Patch3fa;
+}

thirdparty/embree/kernels/subdiv/patch_eval.h

@@ -0,0 +1,129 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "patch.h"
+#include "feature_adaptive_eval.h"
+
+namespace embree
+{
+  namespace isa
+  {
+    template<typename Vertex, typename Vertex_t = Vertex>
+      struct PatchEval
+      {
+      public:
+        
+        typedef PatchT<Vertex,Vertex_t> Patch;
+        typedef typename Patch::Ref Ref;
+        typedef CatmullClarkPatchT<Vertex,Vertex_t> CatmullClarkPatch;
+        
+        PatchEval (SharedLazyTessellationCache::CacheEntry& entry, size_t commitCounter, 
+                   const HalfEdge* edge, const char* vertices, size_t stride, const float u, const float v, 
+                   Vertex* P, Vertex* dPdu, Vertex* dPdv, Vertex* ddPdudu, Vertex* ddPdvdv, Vertex* ddPdudv)
+        : P(P), dPdu(dPdu), dPdv(dPdv), ddPdudu(ddPdudu), ddPdvdv(ddPdvdv), ddPdudv(ddPdudv)
+        {
+          /* conservative time for the very first allocation */
+          auto time = SharedLazyTessellationCache::sharedLazyTessellationCache.getTime(commitCounter);
+
+          Ref patch = SharedLazyTessellationCache::lookup(entry,commitCounter,[&] () {
+              auto alloc = [&](size_t bytes) { return SharedLazyTessellationCache::malloc(bytes); };
+              return Patch::create(alloc,edge,vertices,stride);
+            },true);
+
+          auto curTime = SharedLazyTessellationCache::sharedLazyTessellationCache.getTime(commitCounter);
+          const bool allAllocationsValid = SharedLazyTessellationCache::validTime(time,curTime);
+
+          if (patch && allAllocationsValid &&  eval(patch,u,v,1.0f,0)) {
+            SharedLazyTessellationCache::unlock();
+            return;
+          }
+          SharedLazyTessellationCache::unlock();
+          FeatureAdaptiveEval<Vertex,Vertex_t>(edge,vertices,stride,u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv);
+          PATCH_DEBUG_SUBDIVISION(edge,c,-1,-1);
+        }
+        
+        __forceinline bool eval_quad(const typename Patch::SubdividedQuadPatch* This, const float u, const float v, const float dscale, const size_t depth)
+        {
+          if (v < 0.5f) {
+            if (u < 0.5f) return eval(This->child[0],2.0f*u,2.0f*v,2.0f*dscale,depth+1);
+            else          return eval(This->child[1],2.0f*u-1.0f,2.0f*v,2.0f*dscale,depth+1);
+          } else {
+            if (u > 0.5f) return eval(This->child[2],2.0f*u-1.0f,2.0f*v-1.0f,2.0f*dscale,depth+1);
+            else          return eval(This->child[3],2.0f*u,2.0f*v-1.0f,2.0f*dscale,depth+1);
+          }
+        }
+        
+        bool eval_general(const typename Patch::SubdividedGeneralPatch* This, const float U, const float V, const size_t depth)
+        {
+          const unsigned l = (unsigned) floor(0.5f*U); const float u = 2.0f*frac(0.5f*U)-0.5f; 
+          const unsigned h = (unsigned) floor(0.5f*V); const float v = 2.0f*frac(0.5f*V)-0.5f; 
+          const unsigned i = 4*h+l; assert(i<This->N);
+          return eval(This->child[i],u,v,1.0f,depth+1);
+        }
+        
+        bool eval(Ref This, const float& u, const float& v, const float dscale, const size_t depth) 
+        {
+          if (!This) return false;
+          //PRINT(depth);
+          //PRINT2(u,v);
+          
+          switch (This.type()) 
+          {
+          case Patch::BILINEAR_PATCH: {
+            //PRINT("bilinear");
+            ((typename Patch::BilinearPatch*)This.object())->patch.eval(u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale); 
+            PATCH_DEBUG_SUBDIVISION(This,-1,c,c);
+            return true;
+          }
+          case Patch::BSPLINE_PATCH: {
+            //PRINT("bspline");
+            ((typename Patch::BSplinePatch*)This.object())->patch.eval(u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale);
+            PATCH_DEBUG_SUBDIVISION(This,-1,c,-1);
+            return true;
+          }
+          case Patch::BEZIER_PATCH: {
+            //PRINT("bezier");
+            ((typename Patch::BezierPatch*)This.object())->patch.eval(u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale);
+            PATCH_DEBUG_SUBDIVISION(This,-1,c,-1);
+            return true;
+          }
+          case Patch::GREGORY_PATCH: {
+            //PRINT("gregory");
+            ((typename Patch::GregoryPatch*)This.object())->patch.eval(u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale); 
+            PATCH_DEBUG_SUBDIVISION(This,-1,-1,c);
+            return true;
+          }
+          case Patch::SUBDIVIDED_QUAD_PATCH: {
+            //PRINT("subdivided quad");
+            return eval_quad(((typename Patch::SubdividedQuadPatch*)This.object()),u,v,dscale,depth);
+          }
+          case Patch::SUBDIVIDED_GENERAL_PATCH: { 
+            //PRINT("general_patch");
+            assert(dscale == 1.0f); 
+            return eval_general(((typename Patch::SubdividedGeneralPatch*)This.object()),u,v,depth); 
+          }
+          case Patch::EVAL_PATCH: { 
+            //PRINT("eval_patch");
+            CatmullClarkPatch patch; patch.deserialize(This.object());
+            FeatureAdaptiveEval<Vertex,Vertex_t>(patch,u,v,dscale,depth,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv);
+            return true;
+          }
+          default: 
+            assert(false); 
+            return false;
+          }
+        }
+        
+      private:
+        Vertex* const P;
+        Vertex* const dPdu;
+        Vertex* const dPdv;
+        Vertex* const ddPdudu;
+        Vertex* const ddPdvdv;
+        Vertex* const ddPdudv;
+      };
+  }
+}
+  

thirdparty/embree/kernels/subdiv/patch_eval_grid.h

@@ -0,0 +1,245 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "patch.h"
+#include "feature_adaptive_eval_grid.h"
+
+namespace embree
+{
+  namespace isa 
+  {
+    struct PatchEvalGrid
+    {
+      typedef Patch3fa Patch;
+      typedef Patch::Ref Ref;
+      typedef GeneralCatmullClarkPatch3fa GeneralCatmullClarkPatch;
+      typedef CatmullClarkPatch3fa CatmullClarkPatch;
+      typedef BSplinePatch3fa BSplinePatch;
+      typedef BezierPatch3fa BezierPatch;
+      typedef GregoryPatch3fa GregoryPatch;
+      typedef BilinearPatch3fa BilinearPatch;
+
+    private:
+      const unsigned x0,x1;
+      const unsigned y0,y1;
+      const unsigned swidth,sheight;
+      const float rcp_swidth, rcp_sheight;
+      float* const Px;
+      float* const Py;
+      float* const Pz;
+      float* const U;
+      float* const V;
+      float* const Nx;
+      float* const Ny;
+      float* const Nz;
+      const unsigned dwidth,dheight;
+      unsigned count;
+
+    public:      
+
+      PatchEvalGrid (Ref patch, unsigned subPatch,
+                     const unsigned x0, const unsigned x1, const unsigned y0, const unsigned y1, const unsigned swidth, const unsigned sheight, 
+                     float* Px, float* Py, float* Pz, float* U, float* V, 
+                     float* Nx, float* Ny, float* Nz,
+                     const unsigned dwidth, const unsigned dheight)
+      : x0(x0), x1(x1), y0(y0), y1(y1), swidth(swidth), sheight(sheight), rcp_swidth(1.0f/(swidth-1.0f)), rcp_sheight(1.0f/(sheight-1.0f)), 
+        Px(Px), Py(Py), Pz(Pz), U(U), V(V), Nx(Nx), Ny(Ny), Nz(Nz), dwidth(dwidth), dheight(dheight), count(0)
+      {
+        assert(swidth < (2<<20) && sheight < (2<<20));
+        const BBox2f srange(Vec2f(0.0f,0.0f),Vec2f(float(swidth-1),float(sheight-1)));
+        const BBox2f erange(Vec2f(float(x0),float(y0)),Vec2f((float)x1,(float)y1));
+        bool done MAYBE_UNUSED = eval(patch,subPatch,srange,erange);
+        assert(done);
+        assert(count == (x1-x0+1)*(y1-y0+1));
+      }
+
+      template<typename Patch>
+      __forceinline void evalLocalGrid(const Patch* patch, const BBox2f& srange, const int lx0, const int lx1, const int ly0, const int ly1)
+      {
+        const float scale_x = rcp(srange.upper.x-srange.lower.x);
+        const float scale_y = rcp(srange.upper.y-srange.lower.y);
+        count += (lx1-lx0)*(ly1-ly0);
+        
+#if 0
+        for (unsigned iy=ly0; iy<ly1; iy++) {
+          for (unsigned ix=lx0; ix<lx1; ix++) {
+            const float lu = select(ix == swidth -1, float(1.0f), (float(ix)-srange.lower.x)*scale_x);
+            const float lv = select(iy == sheight-1, float(1.0f), (float(iy)-srange.lower.y)*scale_y);
+            const Vec3fa p = patch->patch.eval(lu,lv);
+            const float u = float(ix)*rcp_swidth;
+            const float v = float(iy)*rcp_sheight;
+            const int ofs = (iy-y0)*dwidth+(ix-x0);
+            Px[ofs] = p.x;
+            Py[ofs] = p.y;
+            Pz[ofs] = p.z;
+            U[ofs] = u;
+            V[ofs] = v;
+          }
+        }
+#else
+        foreach2(lx0,lx1,ly0,ly1,[&](const vboolx& valid, const vintx& ix, const vintx& iy) {
+            const vfloatx lu = select(ix == swidth -1, vfloatx(1.0f), (vfloatx(ix)-srange.lower.x)*scale_x);
+            const vfloatx lv = select(iy == sheight-1, vfloatx(1.0f), (vfloatx(iy)-srange.lower.y)*scale_y);
+            const Vec3vfx p = patch->patch.eval(lu,lv);
+            Vec3vfx n = zero;
+            if (unlikely(Nx != nullptr)) n = normalize_safe(patch->patch.normal(lu,lv));
+            const vfloatx u = vfloatx(ix)*rcp_swidth;
+            const vfloatx v = vfloatx(iy)*rcp_sheight;
+            const vintx ofs = (iy-y0)*dwidth+(ix-x0);
+            if (likely(all(valid)) && all(iy==iy[0])) {
+              const unsigned ofs2 = ofs[0];
+              vfloatx::storeu(Px+ofs2,p.x);
+              vfloatx::storeu(Py+ofs2,p.y);
+              vfloatx::storeu(Pz+ofs2,p.z);
+              vfloatx::storeu(U+ofs2,u);
+              vfloatx::storeu(V+ofs2,v);
+              if (unlikely(Nx != nullptr)) {
+                vfloatx::storeu(Nx+ofs2,n.x);
+                vfloatx::storeu(Ny+ofs2,n.y);
+                vfloatx::storeu(Nz+ofs2,n.z);
+              }
+            } else {
+              foreach_unique_index(valid,iy,[&](const vboolx& valid, const int iy0, const int j) {
+                  const unsigned ofs2 = ofs[j]-j;
+                  vfloatx::storeu(valid,Px+ofs2,p.x);
+                  vfloatx::storeu(valid,Py+ofs2,p.y);
+                  vfloatx::storeu(valid,Pz+ofs2,p.z);
+                  vfloatx::storeu(valid,U+ofs2,u);
+                  vfloatx::storeu(valid,V+ofs2,v);
+                  if (unlikely(Nx != nullptr)) {
+                    vfloatx::storeu(valid,Nx+ofs2,n.x);
+                    vfloatx::storeu(valid,Ny+ofs2,n.y);
+                    vfloatx::storeu(valid,Nz+ofs2,n.z);
+                  }
+                });
+            }
+          });
+#endif
+      }
+
+      bool eval(Ref This, const BBox2f& srange, const BBox2f& erange, const unsigned depth) 
+      {
+        if (erange.empty())
+          return true;
+        
+        const int lx0 = (int) ceilf(erange.lower.x);
+        const int lx1 = (int) ceilf(erange.upper.x) + (erange.upper.x == x1 && (srange.lower.x < erange.upper.x || erange.upper.x == 0));
+        const int ly0 = (int) ceilf(erange.lower.y);
+        const int ly1 = (int) ceilf(erange.upper.y) + (erange.upper.y == y1 && (srange.lower.y < erange.upper.y || erange.upper.y == 0));
+        if (lx0 >= lx1 || ly0 >= ly1) 
+          return true;
+
+        if (!This) 
+          return false;
+        
+        switch (This.type()) 
+        {
+        case Patch::BILINEAR_PATCH: {
+          evalLocalGrid((Patch::BilinearPatch*)This.object(),srange,lx0,lx1,ly0,ly1);
+          return true;
+        }
+        case Patch::BSPLINE_PATCH: {
+          evalLocalGrid((Patch::BSplinePatch*)This.object(),srange,lx0,lx1,ly0,ly1);
+          return true;
+        }
+        case Patch::BEZIER_PATCH: {
+          evalLocalGrid((Patch::BezierPatch*)This.object(),srange,lx0,lx1,ly0,ly1);
+          return true;
+        }
+        case Patch::GREGORY_PATCH: {
+          evalLocalGrid((Patch::GregoryPatch*)This.object(),srange,lx0,lx1,ly0,ly1);
+          return true;
+        }
+        case Patch::SUBDIVIDED_QUAD_PATCH: 
+        {
+          const Vec2f c = srange.center();
+          const BBox2f srange0(srange.lower,c);
+          const BBox2f srange1(Vec2f(c.x,srange.lower.y),Vec2f(srange.upper.x,c.y));
+          const BBox2f srange2(c,srange.upper);
+          const BBox2f srange3(Vec2f(srange.lower.x,c.y),Vec2f(c.x,srange.upper.y));
+          
+          Patch::SubdividedQuadPatch* patch = (Patch::SubdividedQuadPatch*)This.object();
+          eval(patch->child[0],srange0,intersect(srange0,erange),depth+1);
+          eval(patch->child[1],srange1,intersect(srange1,erange),depth+1);
+          eval(patch->child[2],srange2,intersect(srange2,erange),depth+1);
+          eval(patch->child[3],srange3,intersect(srange3,erange),depth+1);
+          return true;
+        }
+        case Patch::EVAL_PATCH: { 
+          CatmullClarkPatch patch; patch.deserialize(This.object());
+          FeatureAdaptiveEvalGrid(patch,srange,erange,depth,x0,x1,y0,y1,swidth,sheight,Px,Py,Pz,U,V,Nx,Ny,Nz,dwidth,dheight);
+          count += (lx1-lx0)*(ly1-ly0);
+          return true;
+        }
+        default: 
+          assert(false); 
+          return false;
+        }
+      }
+
+      bool eval(Ref This, unsigned subPatch, const BBox2f& srange, const BBox2f& erange) 
+      {
+        if (!This) 
+          return false;
+
+        switch (This.type()) 
+        {
+        case Patch::SUBDIVIDED_GENERAL_PATCH: { 
+          Patch::SubdividedGeneralPatch* patch = (Patch::SubdividedGeneralPatch*)This.object();
+          assert(subPatch < patch->N);
+          return eval(patch->child[subPatch],srange,erange,1);
+        }
+        default: 
+          assert(subPatch == 0);
+          return eval(This,srange,erange,0);
+        }
+      }
+    };
+
+    __forceinline unsigned patch_eval_subdivision_count (const HalfEdge* h)
+    {
+      const unsigned N = h->numEdges();
+      if (N == 4) return 1;
+      else return N;
+    }
+    
+    template<typename Tessellator>
+      inline void patch_eval_subdivision (const HalfEdge* h, Tessellator tessellator)
+    {
+      const unsigned N = h->numEdges();
+      int neighborSubdiv[GeneralCatmullClarkPatch3fa::SIZE]; // FIXME: use array_t
+      float levels[GeneralCatmullClarkPatch3fa::SIZE];
+      for (unsigned i=0; i<N; i++) {
+        assert(i<GeneralCatmullClarkPatch3fa::SIZE);
+        neighborSubdiv[i] = h->hasOpposite() ? h->opposite()->numEdges() != 4 : 0; 
+        levels[i] = h->edge_level;
+        h = h->next();
+      }      
+      if (N == 4)
+      {
+        const Vec2f uv[4] = { Vec2f(0.0f,0.0f), Vec2f(1.0f,0.0f), Vec2f(1.0f,1.0f), Vec2f(0.0f,1.0f) };
+        tessellator(uv,neighborSubdiv,levels,0);
+      }
+      else
+      {
+        for (unsigned i=0; i<N; i++) 
+        {
+          assert(i<MAX_PATCH_VALENCE);
+          static_assert(MAX_PATCH_VALENCE <= 16, "MAX_PATCH_VALENCE > 16");
+          const int h = (i >> 2) & 3, l = i & 3;
+          const Vec2f subPatchID((float)l,(float)h);
+          const Vec2f uv[4] = { 2.0f*subPatchID + (0.5f+Vec2f(0.0f,0.0f)),
+                                2.0f*subPatchID + (0.5f+Vec2f(1.0f,0.0f)),
+                                2.0f*subPatchID + (0.5f+Vec2f(1.0f,1.0f)),
+                                2.0f*subPatchID + (0.5f+Vec2f(0.0f,1.0f)) };
+          const int neighborSubdiv1[4] = { 0,0,0,0 }; 
+          const float levels1[4] = { 0.5f*levels[(i+0)%N], 0.5f*levels[(i+0)%N], 0.5f*levels[(i+N-1)%N], 0.5f*levels[(i+N-1)%N] };
+          tessellator(uv,neighborSubdiv1,levels1,i);
+        }
+      }
+    }
+  }
+}
+

thirdparty/embree/kernels/subdiv/patch_eval_simd.h

@@ -0,0 +1,127 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "patch.h"
+#include "feature_adaptive_eval_simd.h"
+
+namespace embree
+{
+  namespace isa
+  {
+    template<typename vbool, typename vint, typename vfloat, typename Vertex, typename Vertex_t = Vertex>
+      struct PatchEvalSimd
+      {
+      public:
+        
+        typedef PatchT<Vertex,Vertex_t> Patch;
+        typedef typename Patch::Ref Ref;
+        typedef CatmullClarkPatchT<Vertex,Vertex_t> CatmullClarkPatch;
+
+        PatchEvalSimd (SharedLazyTessellationCache::CacheEntry& entry, size_t commitCounter, 
+                       const HalfEdge* edge, const char* vertices, size_t stride, const vbool& valid0, const vfloat& u, const vfloat& v, 
+                       float* P, float* dPdu, float* dPdv, float* ddPdudu, float* ddPdvdv, float* ddPdudv, const size_t dstride, const size_t N)
+        : P(P), dPdu(dPdu), dPdv(dPdv), ddPdudu(ddPdudu), ddPdvdv(ddPdvdv), ddPdudv(ddPdudv), dstride(dstride), N(N)
+        {
+          /* conservative time for the very first allocation */
+          auto time = SharedLazyTessellationCache::sharedLazyTessellationCache.getTime(commitCounter);
+
+          Ref patch = SharedLazyTessellationCache::lookup(entry,commitCounter,[&] () {
+              auto alloc = [](size_t bytes) { return SharedLazyTessellationCache::malloc(bytes); };
+              return Patch::create(alloc,edge,vertices,stride);
+            }, true);
+
+          auto curTime = SharedLazyTessellationCache::sharedLazyTessellationCache.getTime(commitCounter);
+          const bool allAllocationsValid = SharedLazyTessellationCache::validTime(time,curTime);
+          
+          patch = allAllocationsValid ? patch : nullptr;
+
+          /* use cached data structure for calculations */
+          const vbool valid1 = patch ? eval(valid0,patch,u,v,1.0f,0) : vbool(false);
+          SharedLazyTessellationCache::unlock();
+          const vbool valid2 = valid0 & !valid1;
+          if (any(valid2)) {
+            FeatureAdaptiveEvalSimd<vbool,vint,vfloat,Vertex,Vertex_t>(edge,vertices,stride,valid2,u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dstride,N);
+          }
+        }
+        
+        vbool eval_quad(const vbool& valid, const typename Patch::SubdividedQuadPatch* This, const vfloat& u, const vfloat& v, const float dscale, const size_t depth)
+        {
+          vbool ret = false;
+          const vbool u0_mask = u < 0.5f, u1_mask = u >= 0.5f;
+          const vbool v0_mask = v < 0.5f, v1_mask = v >= 0.5f;
+          const vbool u0v0_mask = valid & u0_mask & v0_mask;
+          const vbool u0v1_mask = valid & u0_mask & v1_mask;
+          const vbool u1v0_mask = valid & u1_mask & v0_mask;
+          const vbool u1v1_mask = valid & u1_mask & v1_mask;
+          if (any(u0v0_mask)) ret |= eval(u0v0_mask,This->child[0],2.0f*u,2.0f*v,2.0f*dscale,depth+1);
+          if (any(u1v0_mask)) ret |= eval(u1v0_mask,This->child[1],2.0f*u-1.0f,2.0f*v,2.0f*dscale,depth+1);
+          if (any(u1v1_mask)) ret |= eval(u1v1_mask,This->child[2],2.0f*u-1.0f,2.0f*v-1.0f,2.0f*dscale,depth+1);
+          if (any(u0v1_mask)) ret |= eval(u0v1_mask,This->child[3],2.0f*u,2.0f*v-1.0f,2.0f*dscale,depth+1);
+          return ret;
+        }
+        
+        vbool eval_general(const vbool& valid, const typename Patch::SubdividedGeneralPatch* patch, const vfloat& U, const vfloat& V, const size_t depth)
+        {
+          vbool ret = false;
+          const vint l = (vint)floor(0.5f*U); const vfloat u = 2.0f*frac(0.5f*U)-0.5f; 
+          const vint h = (vint)floor(0.5f*V); const vfloat v = 2.0f*frac(0.5f*V)-0.5f; 
+          const vint i = (h<<2)+l; assert(all(valid,i<patch->N));
+          foreach_unique(valid,i,[&](const vbool& valid, const int i) {
+              ret |= eval(valid,patch->child[i],u,v,1.0f,depth+1);
+            });
+          return ret;
+        }
+        
+        vbool eval(const vbool& valid, Ref This, const vfloat& u, const vfloat& v, const float dscale, const size_t depth) 
+        {
+          if (!This) return false;
+          switch (This.type()) 
+          {
+          case Patch::BILINEAR_PATCH: {
+            ((typename Patch::BilinearPatch*)This.object())->patch.eval(valid,u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale,dstride,N); 
+            return valid;
+          }
+          case Patch::BSPLINE_PATCH: {
+            ((typename Patch::BSplinePatch*)This.object())->patch.eval(valid,u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale,dstride,N);
+            return valid;
+          }
+          case Patch::BEZIER_PATCH: {
+            ((typename Patch::BezierPatch*)This.object())->patch.eval(valid,u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale,dstride,N);
+            return valid;
+          }
+          case Patch::GREGORY_PATCH: {
+            ((typename Patch::GregoryPatch*)This.object())->patch.eval(valid,u,v,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale,dstride,N); 
+            return valid;
+          }
+          case Patch::SUBDIVIDED_QUAD_PATCH: {
+            return eval_quad(valid,((typename Patch::SubdividedQuadPatch*)This.object()),u,v,dscale,depth);
+          }
+          case Patch::SUBDIVIDED_GENERAL_PATCH: { 
+            assert(dscale == 1.0f); 
+            return eval_general(valid,((typename Patch::SubdividedGeneralPatch*)This.object()),u,v,depth); 
+          }
+          case Patch::EVAL_PATCH: { 
+            CatmullClarkPatch patch; patch.deserialize(This.object());
+            FeatureAdaptiveEvalSimd<vbool,vint,vfloat,Vertex,Vertex_t>(patch,valid,u,v,dscale,depth,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dstride,N);
+            return valid;
+          }
+          default: 
+            assert(false); 
+            return false;
+          }
+        }
+
+      private:
+        float* const P;
+        float* const dPdu;
+        float* const dPdv;
+        float* const ddPdudu;
+        float* const ddPdvdv;
+        float* const ddPdudv;
+        const size_t dstride;
+        const size_t N;
+      };
+  }
+}

thirdparty/embree/kernels/subdiv/subdivpatch1base.h

@@ -0,0 +1,156 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "../geometry/primitive.h"
+#include "bspline_patch.h"
+#include "bezier_patch.h"
+#include "gregory_patch.h"
+#include "gregory_patch_dense.h"
+#include "tessellation.h"
+#include "tessellation_cache.h"
+#include "gridrange.h"
+#include "patch_eval_grid.h"
+#include "feature_adaptive_eval_grid.h"
+#include "../common/scene_subdiv_mesh.h"
+
+namespace embree
+{
+  struct __aligned(64) SubdivPatch1Base
+  {
+  public:
+
+    enum Type {
+      INVALID_PATCH          = 0,
+      BSPLINE_PATCH          = 1,  
+      BEZIER_PATCH           = 2,  
+      GREGORY_PATCH          = 3,
+      EVAL_PATCH             = 5,
+      BILINEAR_PATCH         = 6,
+    };
+
+    enum Flags {
+      TRANSITION_PATCH       = 16, 
+    };
+
+    /*! Default constructor. */
+    __forceinline SubdivPatch1Base () {}
+
+    SubdivPatch1Base (const unsigned int gID,
+                      const unsigned int pID,
+                      const unsigned int subPatch,
+                      const SubdivMesh *const mesh,
+                      const size_t time,
+                      const Vec2f uv[4],
+                      const float edge_level[4],
+                      const int subdiv[4],
+                      const int simd_width);
+
+    __forceinline bool needsStitching() const {
+      return flags & TRANSITION_PATCH;      
+    }
+
+    __forceinline Vec2f getUV(const size_t i) const {
+      return Vec2f((float)u[i],(float)v[i]) * (8.0f/0x10000);
+    }
+
+    static void computeEdgeLevels(const float edge_level[4], const int subdiv[4], float level[4]);
+    static Vec2i computeGridSize(const float level[4]);
+    bool updateEdgeLevels(const float edge_level[4], const int subdiv[4], const SubdivMesh *const mesh, const int simd_width);
+
+  public:
+
+    __forceinline size_t getGridBytes() const {
+      const size_t grid_size_xyzuv = (grid_size_simd_blocks * VSIZEX) * 4;
+      return 64*((grid_size_xyzuv+15) / 16);
+    }
+
+    __forceinline void write_lock()     { mtx.lock();   }
+    __forceinline void write_unlock()   { mtx.unlock(); }
+    __forceinline bool try_write_lock() { return mtx.try_lock(); }
+    //__forceinline bool try_read_lock()  { return mtx.try_read_lock(); }
+
+    __forceinline void resetRootRef() {
+      //assert( mtx.hasInitialState() );
+      root_ref = SharedLazyTessellationCache::Tag();
+    }
+
+    __forceinline SharedLazyTessellationCache::CacheEntry& entry() {
+      return (SharedLazyTessellationCache::CacheEntry&) root_ref;
+    }
+
+  public:    
+    __forceinline unsigned int geomID() const  {
+      return geom;
+    } 
+
+    __forceinline unsigned int primID() const  {
+      return prim;
+    } 
+
+  public:
+    SharedLazyTessellationCache::Tag root_ref;
+    SpinLock mtx;
+
+    unsigned short u[4];                        //!< 16bit discretized u,v coordinates
+    unsigned short v[4];
+    float level[4];
+
+    unsigned char flags;
+    unsigned char type;
+    unsigned short grid_u_res;
+    unsigned int geom;                          //!< geometry ID of the subdivision mesh this patch belongs to
+    unsigned int prim;                          //!< primitive ID of this subdivision patch
+    unsigned short grid_v_res;
+
+    unsigned short grid_size_simd_blocks;
+    unsigned int time_;
+
+    struct PatchHalfEdge {
+      const HalfEdge* edge;
+      unsigned subPatch;
+    };
+
+    Vec3fa patch_v[4][4];
+
+    const HalfEdge *edge() const { return ((PatchHalfEdge*)patch_v)->edge; }
+    unsigned time() const { return time_; }
+    unsigned subPatch() const { return ((PatchHalfEdge*)patch_v)->subPatch; }
+
+    void set_edge(const HalfEdge *h) const { ((PatchHalfEdge*)patch_v)->edge = h; }
+    void set_subPatch(const unsigned s) const { ((PatchHalfEdge*)patch_v)->subPatch = s; }
+  };
+
+  namespace isa
+  {
+    Vec3fa patchEval(const SubdivPatch1Base& patch, const float uu, const float vv);
+    Vec3fa patchNormal(const SubdivPatch1Base& patch, const float uu, const float vv);
+    
+    template<typename simdf>
+      Vec3<simdf> patchEval(const SubdivPatch1Base& patch, const simdf& uu, const simdf& vv); 
+
+    template<typename simdf>
+      Vec3<simdf> patchNormal(const SubdivPatch1Base& patch, const simdf& uu, const simdf& vv); 
+   
+
+    /* eval grid over patch and stich edges when required */      
+    void evalGrid(const SubdivPatch1Base& patch,
+                  const unsigned x0, const unsigned x1,
+                  const unsigned y0, const unsigned y1,
+                  const unsigned swidth, const unsigned sheight,
+                  float *__restrict__ const grid_x,
+                  float *__restrict__ const grid_y,
+                  float *__restrict__ const grid_z,
+                  float *__restrict__ const grid_u,
+                  float *__restrict__ const grid_v,
+                  const SubdivMesh* const geom);
+
+    /* eval grid over patch and stich edges when required */      
+    BBox3fa evalGridBounds(const SubdivPatch1Base& patch,
+                           const unsigned x0, const unsigned x1,
+                           const unsigned y0, const unsigned y1,
+                           const unsigned swidth, const unsigned sheight,
+                           const SubdivMesh* const geom);
+  }
+}

thirdparty/embree/kernels/subdiv/tessellation.h

@@ -0,0 +1,161 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+namespace embree
+{
+  /* adjust discret tessellation level for feature-adaptive pre-subdivision */
+  __forceinline float adjustTessellationLevel(float l, const size_t sublevel)
+  {
+    for (size_t i=0; i<sublevel; i++) l *= 0.5f;
+    float r = ceilf(l);      
+    for (size_t i=0; i<sublevel; i++) r *= 2.0f;
+    return r;
+  }
+  
+  __forceinline int stitch(const int x, const int fine, const int coarse) {
+    return (2*x+1)*coarse/(2*fine);
+  }
+
+  __forceinline void stitchGridEdges(const unsigned int low_rate,
+                                     const unsigned int high_rate,
+                                     const unsigned int x0,
+                                     const unsigned int x1,
+				    float * __restrict__ const uv_array,
+				    const unsigned int uv_array_step)
+  {
+#if 1
+    const float inv_low_rate = rcp((float)(low_rate-1));
+    for (unsigned x=x0; x<=x1; x++) {
+      uv_array[(x-x0)*uv_array_step] = float(stitch(x,high_rate-1,low_rate-1))*inv_low_rate;
+    }
+    if (unlikely(x1 == high_rate-1))
+      uv_array[(x1-x0)*uv_array_step] = 1.0f;
+#else
+    assert(low_rate < high_rate);
+    assert(high_rate >= 2);
+    
+    const float inv_low_rate = rcp((float)(low_rate-1));
+    const unsigned int dy = low_rate  - 1; 
+    const unsigned int dx = high_rate - 1;
+    
+    int p = 2*dy-dx;  
+    
+    unsigned int offset = 0;
+    unsigned int y = 0;
+    float value = 0.0f;
+    for(unsigned int x=0;x<high_rate-1; x++) // '<=' would be correct but we will leave the 1.0f at the end
+    {
+      uv_array[offset] = value;
+      
+      offset += uv_array_step;      
+      if (unlikely(p > 0))
+      {
+	y++;
+	value = (float)y * inv_low_rate;
+	p -= 2*dx;
+      }
+      p += 2*dy;
+    }
+#endif
+  }
+  
+  __forceinline void stitchUVGrid(const float edge_levels[4],
+                                  const unsigned int swidth,
+                                  const unsigned int sheight,
+                                  const unsigned int x0,
+                                  const unsigned int y0,
+				  const unsigned int grid_u_res,
+				  const unsigned int grid_v_res,
+				  float * __restrict__ const u_array,
+				  float * __restrict__ const v_array)
+  {
+    const unsigned int x1 = x0+grid_u_res-1;
+    const unsigned int y1 = y0+grid_v_res-1;
+    const unsigned int int_edge_points0 = (unsigned int)edge_levels[0] + 1;
+    const unsigned int int_edge_points1 = (unsigned int)edge_levels[1] + 1;
+    const unsigned int int_edge_points2 = (unsigned int)edge_levels[2] + 1;
+    const unsigned int int_edge_points3 = (unsigned int)edge_levels[3] + 1;
+    
+    if (unlikely(y0 == 0 && int_edge_points0 < swidth))
+      stitchGridEdges(int_edge_points0,swidth,x0,x1,u_array,1);
+    
+    if (unlikely(y1 == sheight-1 && int_edge_points2 < swidth))
+      stitchGridEdges(int_edge_points2,swidth,x0,x1,&u_array[(grid_v_res-1)*grid_u_res],1);
+    
+    if (unlikely(x0 == 0 && int_edge_points1 < sheight))
+      stitchGridEdges(int_edge_points1,sheight,y0,y1,&v_array[grid_u_res-1],grid_u_res);
+    
+    if (unlikely(x1 == swidth-1 && int_edge_points3 < sheight))
+      stitchGridEdges(int_edge_points3,sheight,y0,y1,v_array,grid_u_res);  
+  }
+  
+  __forceinline void gridUVTessellator(const float edge_levels[4],  
+                                       const unsigned int swidth,
+                                       const unsigned int sheight,
+                                       const unsigned int x0,
+                                       const unsigned int y0,
+				       const unsigned int grid_u_res,
+				       const unsigned int grid_v_res,
+				       float * __restrict__ const u_array,
+				       float * __restrict__ const v_array)
+  {
+    assert( grid_u_res >= 1);
+    assert( grid_v_res >= 1);
+    assert( edge_levels[0] >= 1.0f );
+    assert( edge_levels[1] >= 1.0f );
+    assert( edge_levels[2] >= 1.0f );
+    assert( edge_levels[3] >= 1.0f );
+    
+#if defined(__AVX__)
+    const vint8 grid_u_segments = vint8(swidth)-1;
+    const vint8 grid_v_segments = vint8(sheight)-1;
+    
+    const vfloat8 inv_grid_u_segments = rcp(vfloat8(grid_u_segments));
+    const vfloat8 inv_grid_v_segments = rcp(vfloat8(grid_v_segments));
+    
+    unsigned int index = 0;
+    vint8 v_i( zero );
+    for (unsigned int y=0;y<grid_v_res;y++,index+=grid_u_res,v_i += 1)
+    {
+      vint8 u_i ( step );
+      
+      const vbool8 m_v = v_i < grid_v_segments;
+      
+      for (unsigned int x=0;x<grid_u_res;x+=8, u_i += 8)
+      {
+        const vbool8 m_u = u_i < grid_u_segments;
+	const vfloat8 u = select(m_u, vfloat8(x0+u_i) * inv_grid_u_segments, 1.0f);
+	const vfloat8 v = select(m_v, vfloat8(y0+v_i) * inv_grid_v_segments, 1.0f);
+	vfloat8::storeu(&u_array[index + x],u);
+	vfloat8::storeu(&v_array[index + x],v);	   
+      }
+    }       
+ #else   
+    const vint4 grid_u_segments = vint4(swidth)-1;
+    const vint4 grid_v_segments = vint4(sheight)-1;
+    
+    const vfloat4 inv_grid_u_segments = rcp(vfloat4(grid_u_segments));
+    const vfloat4 inv_grid_v_segments = rcp(vfloat4(grid_v_segments));
+    
+    unsigned int index = 0;
+    vint4 v_i( zero );
+    for (unsigned int y=0;y<grid_v_res;y++,index+=grid_u_res,v_i += 1)
+    {
+      vint4 u_i ( step );
+      
+      const vbool4 m_v = v_i < grid_v_segments;
+      
+      for (unsigned int x=0;x<grid_u_res;x+=4, u_i += 4)
+      {
+        const vbool4 m_u = u_i < grid_u_segments;
+	const vfloat4 u = select(m_u, vfloat4(x0+u_i) * inv_grid_u_segments, 1.0f);
+	const vfloat4 v = select(m_v, vfloat4(y0+v_i) * inv_grid_v_segments, 1.0f);
+        vfloat4::storeu(&u_array[index + x],u);
+	vfloat4::storeu(&v_array[index + x],v);	   
+      }
+    }       
+#endif
+  } 
+}

thirdparty/embree/kernels/subdiv/tessellation_cache.h

@@ -0,0 +1,325 @@
+// Copyright 2009-2021 Intel Corporation
+// SPDX-License-Identifier: Apache-2.0
+
+#pragma once
+
+#include "../common/default.h"
+
+/* force a complete cache invalidation when running out of allocation space */
+#define FORCE_SIMPLE_FLUSH 0
+
+#define THREAD_BLOCK_ATOMIC_ADD 4
+
+#if defined(DEBUG)
+#define CACHE_STATS(x) 
+#else
+#define CACHE_STATS(x) 
+#endif
+
+namespace embree
+{
+  class SharedTessellationCacheStats
+  {
+  public:
+    /* stats */
+    static std::atomic<size_t> cache_accesses;
+    static std::atomic<size_t> cache_hits;
+    static std::atomic<size_t> cache_misses;
+    static std::atomic<size_t> cache_flushes;                
+    static size_t        cache_num_patches;
+    __aligned(64) static SpinLock mtx;
+    
+    /* print stats for debugging */                 
+    static void printStats();
+    static void clearStats();
+  };
+  
+  void resizeTessellationCache(size_t new_size);
+  void resetTessellationCache();
+  
+ ////////////////////////////////////////////////////////////////////////////////
+ ////////////////////////////////////////////////////////////////////////////////
+ ////////////////////////////////////////////////////////////////////////////////
+
+ struct __aligned(64) ThreadWorkState 
+ {
+   ALIGNED_STRUCT_(64);
+
+   std::atomic<size_t> counter;
+   ThreadWorkState* next;
+   bool allocated;
+
+   __forceinline ThreadWorkState(bool allocated = false) 
+     : counter(0), next(nullptr), allocated(allocated) 
+   {
+     assert( ((size_t)this % 64) == 0 ); 
+   }   
+ };
+
+ class __aligned(64) SharedLazyTessellationCache 
+ {
+ public:
+   
+   static const size_t NUM_CACHE_SEGMENTS              = 8;
+   static const size_t NUM_PREALLOC_THREAD_WORK_STATES = 512;
+   static const size_t COMMIT_INDEX_SHIFT              = 32+8;
+#if defined(__64BIT__)
+   static const size_t REF_TAG_MASK                    = 0xffffffffff;
+#else
+   static const size_t REF_TAG_MASK                    = 0x7FFFFFFF;
+#endif
+   static const size_t MAX_TESSELLATION_CACHE_SIZE     = REF_TAG_MASK+1;
+   static const size_t BLOCK_SIZE                      = 64;
+   
+
+    /*! Per thread tessellation ref cache */
+   static __thread ThreadWorkState* init_t_state;
+   static ThreadWorkState* current_t_state;
+   
+   static __forceinline ThreadWorkState *threadState() 
+   {
+     if (unlikely(!init_t_state))
+       /* sets init_t_state, can't return pointer due to macosx icc bug*/
+       SharedLazyTessellationCache::sharedLazyTessellationCache.getNextRenderThreadWorkState();
+     return init_t_state;
+   }
+
+   struct Tag
+   {
+     __forceinline Tag() : data(0) {}
+
+     __forceinline Tag(void* ptr, size_t combinedTime) { 
+       init(ptr,combinedTime);
+     }
+
+     __forceinline Tag(size_t ptr, size_t combinedTime) {
+       init((void*)ptr,combinedTime); 
+     }
+
+     __forceinline void init(void* ptr, size_t combinedTime)
+     {
+       if (ptr == nullptr) {
+         data = 0;
+         return;
+       }
+       int64_t new_root_ref = (int64_t) ptr;
+       new_root_ref -= (int64_t)SharedLazyTessellationCache::sharedLazyTessellationCache.getDataPtr();                                
+       assert( new_root_ref <= (int64_t)REF_TAG_MASK );
+       new_root_ref |= (int64_t)combinedTime << COMMIT_INDEX_SHIFT; 
+       data = new_root_ref;
+     }
+
+     __forceinline int64_t get() const { return data.load(); }
+     __forceinline void set( int64_t v ) { data.store(v); }
+     __forceinline void reset() { data.store(0); }
+
+   private:
+     atomic<int64_t> data;
+   };
+
+   static __forceinline size_t extractCommitIndex(const int64_t v) { return v >> SharedLazyTessellationCache::COMMIT_INDEX_SHIFT; }
+
+   struct CacheEntry
+   {
+     Tag tag;
+     SpinLock mutex;
+   };
+
+ private:
+
+   float *data;
+   bool hugepages;
+   size_t size;
+   size_t maxBlocks;
+   ThreadWorkState *threadWorkState;
+      
+   __aligned(64) std::atomic<size_t> localTime;
+   __aligned(64) std::atomic<size_t> next_block;
+   __aligned(64) SpinLock   reset_state;
+   __aligned(64) SpinLock   linkedlist_mtx;
+   __aligned(64) std::atomic<size_t> switch_block_threshold;
+   __aligned(64) std::atomic<size_t> numRenderThreads;
+
+
+ public:
+
+      
+   SharedLazyTessellationCache();
+   ~SharedLazyTessellationCache();
+
+   void getNextRenderThreadWorkState();
+
+   __forceinline size_t maxAllocSize() const {
+     return switch_block_threshold;
+   }
+
+   __forceinline size_t getCurrentIndex() { return localTime.load(); }
+   __forceinline void   addCurrentIndex(const size_t i=1) { localTime.fetch_add(i); }
+
+   __forceinline size_t getTime(const size_t globalTime) {
+     return localTime.load()+NUM_CACHE_SEGMENTS*globalTime;
+   }
+
+
+   __forceinline size_t lockThread  (ThreadWorkState *const t_state, const ssize_t plus=1) { return t_state->counter.fetch_add(plus);  }
+   __forceinline size_t unlockThread(ThreadWorkState *const t_state, const ssize_t plus=-1) { assert(isLocked(t_state)); return t_state->counter.fetch_add(plus); }
+
+   __forceinline bool isLocked(ThreadWorkState *const t_state) { return t_state->counter.load() != 0; }
+
+   static __forceinline void lock  () { sharedLazyTessellationCache.lockThread(threadState()); }
+   static __forceinline void unlock() { sharedLazyTessellationCache.unlockThread(threadState()); }
+   static __forceinline bool isLocked() { return sharedLazyTessellationCache.isLocked(threadState()); }
+   static __forceinline size_t getState() { return threadState()->counter.load(); }
+   static __forceinline void lockThreadLoop() { sharedLazyTessellationCache.lockThreadLoop(threadState()); }
+
+   static __forceinline size_t getTCacheTime(const size_t globalTime) {
+     return sharedLazyTessellationCache.getTime(globalTime);
+   }
+
+   /* per thread lock */
+   __forceinline void lockThreadLoop (ThreadWorkState *const t_state) 
+   { 
+     while(1)
+     {
+       size_t lock = SharedLazyTessellationCache::sharedLazyTessellationCache.lockThread(t_state,1);
+       if (unlikely(lock >= THREAD_BLOCK_ATOMIC_ADD))
+       {
+         /* lock failed wait until sync phase is over */
+         sharedLazyTessellationCache.unlockThread(t_state,-1);	       
+         sharedLazyTessellationCache.waitForUsersLessEqual(t_state,0);
+       }
+       else
+         break;
+     }
+   }
+
+   static __forceinline void* lookup(CacheEntry& entry, size_t globalTime)
+   {   
+     const int64_t subdiv_patch_root_ref = entry.tag.get(); 
+     CACHE_STATS(SharedTessellationCacheStats::cache_accesses++);
+     
+     if (likely(subdiv_patch_root_ref != 0)) 
+     {
+       const size_t subdiv_patch_root = (subdiv_patch_root_ref & REF_TAG_MASK) + (size_t)sharedLazyTessellationCache.getDataPtr();
+       const size_t subdiv_patch_cache_index = extractCommitIndex(subdiv_patch_root_ref);
+       
+       if (likely( sharedLazyTessellationCache.validCacheIndex(subdiv_patch_cache_index,globalTime) ))
+       {
+         CACHE_STATS(SharedTessellationCacheStats::cache_hits++);
+         return (void*) subdiv_patch_root;
+       }
+     }
+     CACHE_STATS(SharedTessellationCacheStats::cache_misses++);
+     return nullptr;
+   }
+
+   template<typename Constructor>
+     static __forceinline auto lookup (CacheEntry& entry, size_t globalTime, const Constructor constructor, const bool before=false) -> decltype(constructor())
+   {
+     ThreadWorkState *t_state = SharedLazyTessellationCache::threadState();
+
+     while (true)
+     {
+       sharedLazyTessellationCache.lockThreadLoop(t_state);
+       void* patch = SharedLazyTessellationCache::lookup(entry,globalTime);
+       if (patch) return (decltype(constructor())) patch;
+       
+       if (entry.mutex.try_lock())
+       {
+         if (!validTag(entry.tag,globalTime)) 
+         {
+           auto timeBefore = sharedLazyTessellationCache.getTime(globalTime);
+           auto ret = constructor(); // thread is locked here!
+           assert(ret);
+           /* this should never return nullptr */
+           auto timeAfter = sharedLazyTessellationCache.getTime(globalTime);
+           auto time = before ? timeBefore : timeAfter;
+           __memory_barrier();
+           entry.tag = SharedLazyTessellationCache::Tag(ret,time);
+           __memory_barrier();
+           entry.mutex.unlock();
+           return ret;
+         }
+         entry.mutex.unlock();
+       }
+       SharedLazyTessellationCache::sharedLazyTessellationCache.unlockThread(t_state);
+     }
+   }
+   
+   __forceinline bool validCacheIndex(const size_t i, const size_t globalTime)
+   {
+#if FORCE_SIMPLE_FLUSH == 1
+     return i == getTime(globalTime);
+#else
+     return i+(NUM_CACHE_SEGMENTS-1) >= getTime(globalTime);
+#endif
+   }
+
+   static __forceinline bool validTime(const size_t oldtime, const size_t newTime)
+   {
+     return oldtime+(NUM_CACHE_SEGMENTS-1) >= newTime;
+   }
+
+
+    static __forceinline bool validTag(const Tag& tag, size_t globalTime)
+    {
+      const int64_t subdiv_patch_root_ref = tag.get(); 
+      if (subdiv_patch_root_ref == 0) return false;
+      const size_t subdiv_patch_cache_index = extractCommitIndex(subdiv_patch_root_ref);
+      return sharedLazyTessellationCache.validCacheIndex(subdiv_patch_cache_index,globalTime);
+    }
+
+   void waitForUsersLessEqual(ThreadWorkState *const t_state,
+			      const unsigned int users);
+    
+   __forceinline size_t alloc(const size_t blocks)
+   {
+     if (unlikely(blocks >= switch_block_threshold))
+       throw_RTCError(RTC_ERROR_INVALID_OPERATION,"allocation exceeds size of tessellation cache segment");
+
+     assert(blocks < switch_block_threshold);
+     size_t index = next_block.fetch_add(blocks);
+     if (unlikely(index + blocks >= switch_block_threshold)) return (size_t)-1;
+     return index;
+   }
+
+   static __forceinline void* malloc(const size_t bytes)
+   {
+     size_t block_index = -1;
+     ThreadWorkState *const t_state = threadState();
+     while (true)
+     {
+       block_index = sharedLazyTessellationCache.alloc((bytes+BLOCK_SIZE-1)/BLOCK_SIZE);
+       if (block_index == (size_t)-1)
+       {
+         sharedLazyTessellationCache.unlockThread(t_state);		  
+         sharedLazyTessellationCache.allocNextSegment();
+         sharedLazyTessellationCache.lockThread(t_state);
+         continue; 
+       }
+       break;
+     }
+     return sharedLazyTessellationCache.getBlockPtr(block_index);
+   }
+
+   __forceinline void *getBlockPtr(const size_t block_index)
+   {
+     assert(block_index < maxBlocks);
+     assert(data);
+     assert(block_index*16 <= size);
+     return (void*)&data[block_index*16];
+   }
+
+   __forceinline void*  getDataPtr()      { return data; }
+   __forceinline size_t getNumUsedBytes() { return next_block * BLOCK_SIZE; }
+   __forceinline size_t getMaxBlocks()    { return maxBlocks; }
+   __forceinline size_t getSize()         { return size; }
+
+   void allocNextSegment();
+   void realloc(const size_t newSize);
+
+   void reset();
+
+   static SharedLazyTessellationCache sharedLazyTessellationCache;
+ };
+}