// 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; }