// Copyright 2009-2020 Intel Corporation // SPDX-License-Identifier: Apache-2.0 #pragma once #include "catmullclark_patch.h" #include "bezier_curve.h" namespace embree { template 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 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 __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 __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 __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 __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 __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 __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 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& patch); __forceinline BezierPatchT(const CatmullClarkPatchT& patch, const BezierCurveT* border0, const BezierCurveT* border1, const BezierCurveT* border2, const BezierCurveT* border3); __forceinline BezierPatchT(const BSplinePatchT& 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 buttom 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 __forceinline vfloat eval(const size_t i, const vfloat& uu, const vfloat& vv, const Vec4& u_n, const Vec4& 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 __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 u_n = BezierBasis::eval(uu); const Vec4 v_n = BezierBasis::eval(vv); for (size_t i=0; i u_n = BezierBasis::derivative(uu); const Vec4 v_n = BezierBasis::eval(vv); for (size_t i=0; i u_n = BezierBasis::eval(uu); const Vec4 v_n = BezierBasis::derivative(vv); for (size_t i=0; i u_n = BezierBasis::derivative2(uu); const Vec4 v_n = BezierBasis::eval(vv); for (size_t i=0; i u_n = BezierBasis::eval(uu); const Vec4 v_n = BezierBasis::derivative2(vv); for (size_t i=0; i u_n = BezierBasis::derivative(uu); const Vec4 v_n = BezierBasis::derivative(vv); for (size_t i=0; i static __forceinline Vec3 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(x,y,z); } template __forceinline Vec3 eval(const vfloat& uu, const vfloat& vv) const { return eval(matrix,uu,vv); } template static __forceinline Vec3 normal(const Vertex matrix[4][4], const T& uu, const T& vv) { const Vec3 matrix_00 = Vec3(matrix[0][0].x,matrix[0][0].y,matrix[0][0].z); const Vec3 matrix_01 = Vec3(matrix[0][1].x,matrix[0][1].y,matrix[0][1].z); const Vec3 matrix_02 = Vec3(matrix[0][2].x,matrix[0][2].y,matrix[0][2].z); const Vec3 matrix_03 = Vec3(matrix[0][3].x,matrix[0][3].y,matrix[0][3].z); const Vec3 matrix_10 = Vec3(matrix[1][0].x,matrix[1][0].y,matrix[1][0].z); const Vec3 matrix_11 = Vec3(matrix[1][1].x,matrix[1][1].y,matrix[1][1].z); const Vec3 matrix_12 = Vec3(matrix[1][2].x,matrix[1][2].y,matrix[1][2].z); const Vec3 matrix_13 = Vec3(matrix[1][3].x,matrix[1][3].y,matrix[1][3].z); const Vec3 matrix_20 = Vec3(matrix[2][0].x,matrix[2][0].y,matrix[2][0].z); const Vec3 matrix_21 = Vec3(matrix[2][1].x,matrix[2][1].y,matrix[2][1].z); const Vec3 matrix_22 = Vec3(matrix[2][2].x,matrix[2][2].y,matrix[2][2].z); const Vec3 matrix_23 = Vec3(matrix[2][3].x,matrix[2][3].y,matrix[2][3].z); const Vec3 matrix_30 = Vec3(matrix[3][0].x,matrix[3][0].y,matrix[3][0].z); const Vec3 matrix_31 = Vec3(matrix[3][1].x,matrix[3][1].y,matrix[3][1].z); const Vec3 matrix_32 = Vec3(matrix[3][2].x,matrix[3][2].y,matrix[3][2].z); const Vec3 matrix_33 = Vec3(matrix[3][3].x,matrix[3][3].y,matrix[3][3].z); /* tangentU */ const Vec3 col0 = deCasteljau(vv, matrix_00, matrix_10, matrix_20, matrix_30); const Vec3 col1 = deCasteljau(vv, matrix_01, matrix_11, matrix_21, matrix_31); const Vec3 col2 = deCasteljau(vv, matrix_02, matrix_12, matrix_22, matrix_32); const Vec3 col3 = deCasteljau(vv, matrix_03, matrix_13, matrix_23, matrix_33); const Vec3 tangentU = deCasteljau_tangent(uu, col0, col1, col2, col3); /* tangentV */ const Vec3 row0 = deCasteljau(uu, matrix_00, matrix_01, matrix_02, matrix_03); const Vec3 row1 = deCasteljau(uu, matrix_10, matrix_11, matrix_12, matrix_13); const Vec3 row2 = deCasteljau(uu, matrix_20, matrix_21, matrix_22, matrix_23); const Vec3 row3 = deCasteljau(uu, matrix_30, matrix_31, matrix_32, matrix_33); const Vec3 tangentV = deCasteljau_tangent(vv, row0, row1, row2, row3); /* normal = tangentU x tangentV */ const Vec3 n = cross(tangentU,tangentV); return n; } template __forceinline Vec3 normal(const vfloat& uu, const vfloat& vv) const { return normal(matrix,uu,vv); } }; typedef BezierPatchT BezierPatch3fa; }