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// 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;
}
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