text: // Copyright 2009-2020 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;
  }
  