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++ // Copyright 2009-2021 Intel Corporation
++ // SPDX-License-Identifier: Apache-2.0
++
++ #pragma once
++
++ #include "../common/default.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)/3, 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 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 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, 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 CurveGeometry>
++ __forceinline CatmullRomCurveT<Vec3ff> enlargeRadiusToMinWidth(const IntersectContext* 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;
++ }
++