1 files changed, 671 insertions, 0 deletions
diff --git a/thirdparty/embree/kernels/subdiv/bezier_curve.h b/thirdparty/embree/kernels/subdiv/bezier_curve.h
new file mode 100644
index 0000000000..a5adad5cc9
--- /dev/null
+++ b/thirdparty/embree/kernels/subdiv/bezier_curve.h
@@ -0,0 +1,671 @@
+// 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.u.lower << ", " << a.u.upper << "), " << 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));
+      }
+      
+      __forceinline CubicBezierCurve<vfloatx> vxfm(const Vertex& dx) const {
+        return CubicBezierCurve<vfloatx>(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(step)*(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(step)*(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 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>
+      __forceinline void veval(const vfloat<M>& t, Vec4vf<M>& p, Vec4vf<M>& dp) const
+      {
+        const Vec4vf<M> p00 = v0;
+        const Vec4vf<M> p01 = v1;
+        const Vec4vf<M> p02 = v2;
+        const Vec4vf<M> p03 = v3;
+        
+        const Vec4vf<M> p10 = lerp(p00,p01,t);
+        const Vec4vf<M> p11 = lerp(p01,p02,t);
+        const Vec4vf<M> p12 = lerp(p02,p03,t);
+        const Vec4vf<M> p20 = lerp(p10,p11,t);
+        const Vec4vf<M> p21 = lerp(p11,p12,t);
+        const Vec4vf<M> 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);
+        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))));
+      }
+      
+      template<int M, typename Vec = Vec4vf<M>>
+      __forceinline Vec eval1(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedBezierBasis::N);
+        assert(ofs <= size);
+        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))));
+      }
+      
+      template<int M, typename Vec = Vec4vf<M>>
+      __forceinline Vec derivative0(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedBezierBasis::N);
+        assert(ofs <= size);
+        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))));
+      }
+      
+      template<int M, typename Vec = Vec4vf<M>>
+      __forceinline Vec derivative1(const int ofs, const int size) const
+      {
+        assert(size <= PrecomputedBezierBasis::N);
+        assert(ofs <= size);
+        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))));
+      }
+
+      /* 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(step);
+          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(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)));
+          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(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(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;
+  
+  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);
+  }
+
+  template<typename CurveGeometry>
+  __forceinline CubicBezierCurve<Vec3ff> enlargeRadiusToMinWidth(const IntersectContext* 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));
+  }
+}