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++ // Copyright 2009-2021 Intel Corporation
++ // SPDX-License-Identifier: Apache-2.0
++
++ #pragma once
++
++ #include "bezier_curve.h"
++
++ namespace embree
++ {
++ namespace isa
++ {
++ template<typename V>
++ struct TensorLinearQuadraticBezierSurface
++ {
++ QuadraticBezierCurve<V> L;
++ QuadraticBezierCurve<V> R;
++
++ __forceinline TensorLinearQuadraticBezierSurface() {}
++
++ __forceinline TensorLinearQuadraticBezierSurface(const TensorLinearQuadraticBezierSurface<V>& curve)
++ : L(curve.L), R(curve.R) {}
++
++ __forceinline TensorLinearQuadraticBezierSurface& operator= (const TensorLinearQuadraticBezierSurface& other) {
++ L = other.L; R = other.R; return *this;
++ }
++
++ __forceinline TensorLinearQuadraticBezierSurface(const QuadraticBezierCurve<V>& L, const QuadraticBezierCurve<V>& R)
++ : L(L), R(R) {}
++
++ __forceinline BBox<V> bounds() const {
++ return merge(L.bounds(),R.bounds());
++ }
++ };
++
++ template<>
++ struct TensorLinearQuadraticBezierSurface<Vec2fa>
++ {
++ QuadraticBezierCurve<vfloat4> LR;
++
++ __forceinline TensorLinearQuadraticBezierSurface() {}
++
++ __forceinline TensorLinearQuadraticBezierSurface(const TensorLinearQuadraticBezierSurface<Vec2fa>& curve)
++ : LR(curve.LR) {}
++
++ __forceinline TensorLinearQuadraticBezierSurface& operator= (const TensorLinearQuadraticBezierSurface& other) {
++ LR = other.LR; return *this;
++ }
++
++ __forceinline TensorLinearQuadraticBezierSurface(const QuadraticBezierCurve<vfloat4>& LR)
++ : LR(LR) {}
++
++ __forceinline BBox<Vec2fa> bounds() const
++ {
++ const BBox<vfloat4> b = LR.bounds();
++ const BBox<Vec2fa> bl(Vec2fa(b.lower),Vec2fa(b.upper));
++ const BBox<Vec2fa> br(Vec2fa(shuffle<2,3,2,3>(b.lower)),Vec2fa(shuffle<2,3,2,3>(b.upper)));
++ return merge(bl,br);
++ }
++ };
++
++ template<typename V>
++ struct TensorLinearCubicBezierSurface
++ {
++ CubicBezierCurve<V> L;
++ CubicBezierCurve<V> R;
++
++ __forceinline TensorLinearCubicBezierSurface() {}
++
++ __forceinline TensorLinearCubicBezierSurface(const TensorLinearCubicBezierSurface& curve)
++ : L(curve.L), R(curve.R) {}
++
++ __forceinline TensorLinearCubicBezierSurface& operator= (const TensorLinearCubicBezierSurface& other) {
++ L = other.L; R = other.R; return *this;
++ }
++
++ __forceinline TensorLinearCubicBezierSurface(const CubicBezierCurve<V>& L, const CubicBezierCurve<V>& R)
++ : L(L), R(R) {}
++
++ template<template<typename T> class SourceCurve>
++ __forceinline static TensorLinearCubicBezierSurface fromCenterAndNormalCurve(const SourceCurve<Vec3ff>& center, const SourceCurve<Vec3fa>& normal)
++ {
++ SourceCurve<Vec3ff> vcurve = center;
++ SourceCurve<Vec3fa> ncurve = normal;
++
++ /* here we construct a patch which follows the curve l(t) =
++ * p(t) +/- r(t)*normalize(cross(n(t),dp(t))) */
++
++ const Vec3ff p0 = vcurve.eval(0.0f);
++ const Vec3ff dp0 = vcurve.eval_du(0.0f);
++ //const Vec3ff ddp0 = vcurve.eval_dudu(0.0f); // ddp0 is assumed to be 0
++
++ const Vec3fa n0 = ncurve.eval(0.0f);
++ const Vec3fa dn0 = ncurve.eval_du(0.0f);
++
++ const Vec3ff p1 = vcurve.eval(1.0f);
++ const Vec3ff dp1 = vcurve.eval_du(1.0f);
++ //const Vec3ff ddp1 = vcurve.eval_dudu(1.0f); // ddp1 is assumed to be 0
++
++ const Vec3fa n1 = ncurve.eval(1.0f);
++ const Vec3fa dn1 = ncurve.eval_du(1.0f);
++
++ const Vec3fa bt0 = cross(n0,dp0);
++ const Vec3fa dbt0 = cross(dn0,dp0);// + cross(n0,ddp0);
++
++ const Vec3fa bt1 = cross(n1,dp1);
++ const Vec3fa dbt1 = cross(dn1,dp1);// + cross(n1,ddp1);
++
++ const Vec3fa k0 = normalize(bt0);
++ const Vec3fa dk0 = dnormalize(bt0,dbt0);
++
++ const Vec3fa k1 = normalize(bt1);
++ const Vec3fa dk1 = dnormalize(bt1,dbt1);
++
++ const Vec3fa l0 = p0 - p0.w*k0;
++ const Vec3fa dl0 = dp0 - (dp0.w*k0 + p0.w*dk0);
++
++ const Vec3fa r0 = p0 + p0.w*k0;
++ const Vec3fa dr0 = dp0 + (dp0.w*k0 + p0.w*dk0);
++
++ const Vec3fa l1 = p1 - p1.w*k1;
++ const Vec3fa dl1 = dp1 - (dp1.w*k1 + p1.w*dk1);
++
++ const Vec3fa r1 = p1 + p1.w*k1;
++ const Vec3fa dr1 = dp1 + (dp1.w*k1 + p1.w*dk1);
++
++ const float scale = 1.0f/3.0f;
++ CubicBezierCurve<V> L(l0,l0+scale*dl0,l1-scale*dl1,l1);
++ CubicBezierCurve<V> R(r0,r0+scale*dr0,r1-scale*dr1,r1);
++ return TensorLinearCubicBezierSurface(L,R);
++ }
++
++ __forceinline BBox<V> bounds() const {
++ return merge(L.bounds(),R.bounds());
++ }
++
++ __forceinline BBox3fa accurateBounds() const {
++ return merge(L.accurateBounds(),R.accurateBounds());
++ }
++
++ __forceinline CubicBezierCurve<Interval1f> reduce_v() const {
++ return merge(CubicBezierCurve<Interval<V>>(L),CubicBezierCurve<Interval<V>>(R));
++ }
++
++ __forceinline LinearBezierCurve<Interval1f> reduce_u() const {
++ return LinearBezierCurve<Interval1f>(L.bounds(),R.bounds());
++ }
++
++ __forceinline TensorLinearCubicBezierSurface<float> xfm(const V& dx) const {
++ return TensorLinearCubicBezierSurface<float>(L.xfm(dx),R.xfm(dx));
++ }
++
++ __forceinline TensorLinearCubicBezierSurface<vfloatx> vxfm(const V& dx) const {
++ return TensorLinearCubicBezierSurface<vfloatx>(L.vxfm(dx),R.vxfm(dx));
++ }
++
++ __forceinline TensorLinearCubicBezierSurface<float> xfm(const V& dx, const V& p) const {
++ return TensorLinearCubicBezierSurface<float>(L.xfm(dx,p),R.xfm(dx,p));
++ }
++
++ __forceinline TensorLinearCubicBezierSurface<Vec3fa> xfm(const LinearSpace3fa& space) const {
++ return TensorLinearCubicBezierSurface(L.xfm(space),R.xfm(space));
++ }
++
++ __forceinline TensorLinearCubicBezierSurface<Vec3fa> xfm(const LinearSpace3fa& space, const Vec3fa& p) const {
++ return TensorLinearCubicBezierSurface(L.xfm(space,p),R.xfm(space,p));
++ }
++
++ __forceinline TensorLinearCubicBezierSurface<Vec3fa> xfm(const LinearSpace3fa& space, const Vec3fa& p, const float s) const {
++ return TensorLinearCubicBezierSurface(L.xfm(space,p,s),R.xfm(space,p,s));
++ }
++
++ __forceinline TensorLinearCubicBezierSurface clip_u(const Interval1f& u) const {
++ return TensorLinearCubicBezierSurface(L.clip(u),R.clip(u));
++ }
++
++ __forceinline TensorLinearCubicBezierSurface clip_v(const Interval1f& v) const {
++ return TensorLinearCubicBezierSurface(clerp(L,R,V(v.lower)),clerp(L,R,V(v.upper)));
++ }
++
++ __forceinline TensorLinearCubicBezierSurface clip(const Interval1f& u, const Interval1f& v) const {
++ return clip_v(v).clip_u(u);
++ }
++
++ __forceinline void split_u(TensorLinearCubicBezierSurface& left, TensorLinearCubicBezierSurface& right, const float u = 0.5f) const
++ {
++ CubicBezierCurve<V> L0,L1; L.split(L0,L1,u);
++ CubicBezierCurve<V> R0,R1; R.split(R0,R1,u);
++ new (&left ) TensorLinearCubicBezierSurface(L0,R0);
++ new (&right) TensorLinearCubicBezierSurface(L1,R1);
++ }
++
++ __forceinline TensorLinearCubicBezierSurface<Vec2vfx> vsplit_u(vboolx& valid, const BBox1f& u) const {
++ valid = true; clear(valid,VSIZEX-1);
++ return TensorLinearCubicBezierSurface<Vec2vfx>(L.split(u),R.split(u));
++ }
++
++ __forceinline V eval(const float u, const float v) const {
++ return clerp(L,R,V(v)).eval(u);
++ }
++
++ __forceinline V eval_du(const float u, const float v) const {
++ return clerp(L,R,V(v)).eval_dt(u);
++ }
++
++ __forceinline V eval_dv(const float u, const float v) const {
++ return (R-L).eval(u);
++ }
++
++ __forceinline void eval(const float u, const float v, V& p, V& dpdu, V& dpdv) const
++ {
++ V p0, dp0du; L.eval(u,p0,dp0du);
++ V p1, dp1du; R.eval(u,p1,dp1du);
++ p = lerp(p0,p1,v);
++ dpdu = lerp(dp0du,dp1du,v);
++ dpdv = p1-p0;
++ }
++
++ __forceinline TensorLinearQuadraticBezierSurface<V> derivative_u() const {
++ return TensorLinearQuadraticBezierSurface<V>(L.derivative(),R.derivative());
++ }
++
++ __forceinline CubicBezierCurve<V> derivative_v() const {
++ return R-L;
++ }
++
++ __forceinline V axis_u() const {
++ return (L.end()-L.begin())+(R.end()-R.begin());
++ }
++
++ __forceinline V axis_v() const {
++ return (R.begin()-L.begin())+(R.end()-L.end());
++ }
++
++ friend embree_ostream operator<<(embree_ostream cout, const TensorLinearCubicBezierSurface& a)
++ {
++ return cout << "TensorLinearCubicBezierSurface" << embree_endl
++ << "{" << embree_endl
++ << " L = " << a.L << ", " << embree_endl
++ << " R = " << a.R << embree_endl
++ << "}";
++ }
++
++ friend __forceinline TensorLinearCubicBezierSurface clerp(const TensorLinearCubicBezierSurface& a, const TensorLinearCubicBezierSurface& b, const float t) {
++ return TensorLinearCubicBezierSurface(clerp(a.L,b.L,V(t)), clerp(a.R,b.R,V(t)));
++ }
++ };
++
++ template<>
++ struct TensorLinearCubicBezierSurface<Vec2fa>
++ {
++ CubicBezierCurve<vfloat4> LR;
++
++ __forceinline TensorLinearCubicBezierSurface() {}
++
++ __forceinline TensorLinearCubicBezierSurface(const TensorLinearCubicBezierSurface& curve)
++ : LR(curve.LR) {}
++
++ __forceinline TensorLinearCubicBezierSurface& operator= (const TensorLinearCubicBezierSurface& other) {
++ LR = other.LR; return *this;
++ }
++
++ __forceinline TensorLinearCubicBezierSurface(const CubicBezierCurve<vfloat4>& LR)
++ : LR(LR) {}
++
++ __forceinline TensorLinearCubicBezierSurface(const CubicBezierCurve<Vec2fa>& L, const CubicBezierCurve<Vec2fa>& R)
++ : LR(shuffle<0,1,0,1>(vfloat4(L.v0),vfloat4(R.v0)),shuffle<0,1,0,1>(vfloat4(L.v1),vfloat4(R.v1)),shuffle<0,1,0,1>(vfloat4(L.v2),vfloat4(R.v2)),shuffle<0,1,0,1>(vfloat4(L.v3),vfloat4(R.v3))) {}
++
++ __forceinline CubicBezierCurve<Vec2fa> getL() const {
++ return CubicBezierCurve<Vec2fa>(Vec2fa(LR.v0),Vec2fa(LR.v1),Vec2fa(LR.v2),Vec2fa(LR.v3));
++ }
++
++ __forceinline CubicBezierCurve<Vec2fa> getR() const {
++ return CubicBezierCurve<Vec2fa>(Vec2fa(shuffle<2,3,2,3>(LR.v0)),Vec2fa(shuffle<2,3,2,3>(LR.v1)),Vec2fa(shuffle<2,3,2,3>(LR.v2)),Vec2fa(shuffle<2,3,2,3>(LR.v3)));
++ }
++
++ __forceinline BBox<Vec2fa> bounds() const
++ {
++ const BBox<vfloat4> b = LR.bounds();
++ const BBox<Vec2fa> bl(Vec2fa(b.lower),Vec2fa(b.upper));
++ const BBox<Vec2fa> br(Vec2fa(shuffle<2,3,2,3>(b.lower)),Vec2fa(shuffle<2,3,2,3>(b.upper)));
++ return merge(bl,br);
++ }
++
++ __forceinline BBox1f bounds(const Vec2fa& axis) const
++ {
++ const CubicBezierCurve<vfloat4> LRx = LR;
++ const CubicBezierCurve<vfloat4> LRy(shuffle<1,0,3,2>(LR.v0),shuffle<1,0,3,2>(LR.v1),shuffle<1,0,3,2>(LR.v2),shuffle<1,0,3,2>(LR.v3));
++ const CubicBezierCurve<vfloat4> LRa = cmadd(shuffle<0>(vfloat4(axis)),LRx,shuffle<1>(vfloat4(axis))*LRy);
++ const BBox<vfloat4> Lb = LRa.bounds();
++ const BBox<vfloat4> Rb(shuffle<3>(Lb.lower),shuffle<3>(Lb.upper));
++ const BBox<vfloat4> b = merge(Lb,Rb);
++ return BBox1f(b.lower[0],b.upper[0]);
++ }
++
++ __forceinline TensorLinearCubicBezierSurface<float> xfm(const Vec2fa& dx) const
++ {
++ const CubicBezierCurve<vfloat4> LRx = LR;
++ const CubicBezierCurve<vfloat4> LRy(shuffle<1,0,3,2>(LR.v0),shuffle<1,0,3,2>(LR.v1),shuffle<1,0,3,2>(LR.v2),shuffle<1,0,3,2>(LR.v3));
++ const CubicBezierCurve<vfloat4> LRa = cmadd(shuffle<0>(vfloat4(dx)),LRx,shuffle<1>(vfloat4(dx))*LRy);
++ return TensorLinearCubicBezierSurface<float>(CubicBezierCurve<float>(LRa.v0[0],LRa.v1[0],LRa.v2[0],LRa.v3[0]),
++ CubicBezierCurve<float>(LRa.v0[2],LRa.v1[2],LRa.v2[2],LRa.v3[2]));
++ }
++
++ __forceinline TensorLinearCubicBezierSurface<float> xfm(const Vec2fa& dx, const Vec2fa& p) const
++ {
++ const vfloat4 pxyxy = shuffle<0,1,0,1>(vfloat4(p));
++ const CubicBezierCurve<vfloat4> LRx = LR-pxyxy;
++ const CubicBezierCurve<vfloat4> LRy(shuffle<1,0,3,2>(LR.v0),shuffle<1,0,3,2>(LR.v1),shuffle<1,0,3,2>(LR.v2),shuffle<1,0,3,2>(LR.v3));
++ const CubicBezierCurve<vfloat4> LRa = cmadd(shuffle<0>(vfloat4(dx)),LRx,shuffle<1>(vfloat4(dx))*LRy);
++ return TensorLinearCubicBezierSurface<float>(CubicBezierCurve<float>(LRa.v0[0],LRa.v1[0],LRa.v2[0],LRa.v3[0]),
++ CubicBezierCurve<float>(LRa.v0[2],LRa.v1[2],LRa.v2[2],LRa.v3[2]));
++ }
++
++ __forceinline TensorLinearCubicBezierSurface clip_u(const Interval1f& u) const {
++ return TensorLinearCubicBezierSurface(LR.clip(u));
++ }
++
++ __forceinline TensorLinearCubicBezierSurface clip_v(const Interval1f& v) const
++ {
++ const CubicBezierCurve<vfloat4> LL(shuffle<0,1,0,1>(LR.v0),shuffle<0,1,0,1>(LR.v1),shuffle<0,1,0,1>(LR.v2),shuffle<0,1,0,1>(LR.v3));
++ const CubicBezierCurve<vfloat4> RR(shuffle<2,3,2,3>(LR.v0),shuffle<2,3,2,3>(LR.v1),shuffle<2,3,2,3>(LR.v2),shuffle<2,3,2,3>(LR.v3));
++ return TensorLinearCubicBezierSurface(clerp(LL,RR,vfloat4(v.lower,v.lower,v.upper,v.upper)));
++ }
++
++ __forceinline TensorLinearCubicBezierSurface clip(const Interval1f& u, const Interval1f& v) const {
++ return clip_v(v).clip_u(u);
++ }
++
++ __forceinline void split_u(TensorLinearCubicBezierSurface& left, TensorLinearCubicBezierSurface& right, const float u = 0.5f) const
++ {
++ CubicBezierCurve<vfloat4> LR0,LR1; LR.split(LR0,LR1,u);
++ new (&left ) TensorLinearCubicBezierSurface(LR0);
++ new (&right) TensorLinearCubicBezierSurface(LR1);
++ }
++
++ __forceinline TensorLinearCubicBezierSurface<Vec2vfx> vsplit_u(vboolx& valid, const BBox1f& u) const {
++ valid = true; clear(valid,VSIZEX-1);
++ return TensorLinearCubicBezierSurface<Vec2vfx>(getL().split(u),getR().split(u));
++ }
++
++ __forceinline Vec2fa eval(const float u, const float v) const
++ {
++ const vfloat4 p = LR.eval(u);
++ return Vec2fa(lerp(shuffle<0,1,0,1>(p),shuffle<2,3,2,3>(p),v));
++ }
++
++ __forceinline Vec2fa eval_du(const float u, const float v) const
++ {
++ const vfloat4 dpdu = LR.eval_dt(u);
++ return Vec2fa(lerp(shuffle<0,1,0,1>(dpdu),shuffle<2,3,2,3>(dpdu),v));
++ }
++
++ __forceinline Vec2fa eval_dv(const float u, const float v) const
++ {
++ const vfloat4 p = LR.eval(u);
++ return Vec2fa(shuffle<2,3,2,3>(p)-shuffle<0,1,0,1>(p));
++ }
++
++ __forceinline void eval(const float u, const float v, Vec2fa& p, Vec2fa& dpdu, Vec2fa& dpdv) const
++ {
++ vfloat4 p0, dp0du; LR.eval(u,p0,dp0du);
++ p = Vec2fa(lerp(shuffle<0,1,0,1>(p0),shuffle<2,3,2,3>(p0),v));
++ dpdu = Vec2fa(lerp(shuffle<0,1,0,1>(dp0du),shuffle<2,3,2,3>(dp0du),v));
++ dpdv = Vec2fa(shuffle<2,3,2,3>(p0)-shuffle<0,1,0,1>(p0));
++ }
++
++ __forceinline TensorLinearQuadraticBezierSurface<Vec2fa> derivative_u() const {
++ return TensorLinearQuadraticBezierSurface<Vec2fa>(LR.derivative());
++ }
++
++ __forceinline CubicBezierCurve<Vec2fa> derivative_v() const {
++ return getR()-getL();
++ }
++
++ __forceinline Vec2fa axis_u() const
++ {
++ const CubicBezierCurve<Vec2fa> L = getL();
++ const CubicBezierCurve<Vec2fa> R = getR();
++ return (L.end()-L.begin())+(R.end()-R.begin());
++ }
++
++ __forceinline Vec2fa axis_v() const
++ {
++ const CubicBezierCurve<Vec2fa> L = getL();
++ const CubicBezierCurve<Vec2fa> R = getR();
++ return (R.begin()-L.begin())+(R.end()-L.end());
++ }
++
++ friend embree_ostream operator<<(embree_ostream cout, const TensorLinearCubicBezierSurface& a)
++ {
++ return cout << "TensorLinearCubicBezierSurface" << embree_endl
++ << "{" << embree_endl
++ << " L = " << a.getL() << ", " << embree_endl
++ << " R = " << a.getR() << embree_endl
++ << "}";
++ }
++ };
++
++ typedef TensorLinearCubicBezierSurface<float> TensorLinearCubicBezierSurface1f;
++ typedef TensorLinearCubicBezierSurface<Vec2fa> TensorLinearCubicBezierSurface2fa;
++ typedef TensorLinearCubicBezierSurface<Vec3fa> TensorLinearCubicBezierSurface3fa;
++ }
++ }