362 lines
15 KiB
C++
362 lines
15 KiB
C++
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// Copyright 2009-2020 Intel Corporation
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// SPDX-License-Identifier: Apache-2.0
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#pragma once
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#include "linearspace2.h"
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#include "linearspace3.h"
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#include "quaternion.h"
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#include "bbox.h"
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#include "vec4.h"
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namespace embree
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{
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#define VectorT typename L::Vector
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#define ScalarT typename L::Vector::Scalar
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////////////////////////////////////////////////////////////////////////////////
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// Affine Space
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////////////////////////////////////////////////////////////////////////////////
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template<typename L>
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struct AffineSpaceT
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{
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L l; /*< linear part of affine space */
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VectorT p; /*< affine part of affine space */
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////////////////////////////////////////////////////////////////////////////////
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// Constructors, Assignment, Cast, Copy Operations
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////////////////////////////////////////////////////////////////////////////////
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__forceinline AffineSpaceT ( ) { }
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__forceinline AffineSpaceT ( const AffineSpaceT& other ) { l = other.l; p = other.p; }
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__forceinline AffineSpaceT ( const L & other ) { l = other ; p = VectorT(zero); }
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__forceinline AffineSpaceT& operator=( const AffineSpaceT& other ) { l = other.l; p = other.p; return *this; }
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__forceinline AffineSpaceT( const VectorT& vx, const VectorT& vy, const VectorT& vz, const VectorT& p ) : l(vx,vy,vz), p(p) {}
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__forceinline AffineSpaceT( const L& l, const VectorT& p ) : l(l), p(p) {}
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template<typename L1> __forceinline AffineSpaceT( const AffineSpaceT<L1>& s ) : l(s.l), p(s.p) {}
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////////////////////////////////////////////////////////////////////////////////
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// Constants
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////////////////////////////////////////////////////////////////////////////////
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__forceinline AffineSpaceT( ZeroTy ) : l(zero), p(zero) {}
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__forceinline AffineSpaceT( OneTy ) : l(one), p(zero) {}
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/*! return matrix for scaling */
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static __forceinline AffineSpaceT scale(const VectorT& s) { return L::scale(s); }
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/*! return matrix for translation */
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static __forceinline AffineSpaceT translate(const VectorT& p) { return AffineSpaceT(one,p); }
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/*! return matrix for rotation, only in 2D */
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static __forceinline AffineSpaceT rotate(const ScalarT& r) { return L::rotate(r); }
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/*! return matrix for rotation around arbitrary point (2D) or axis (3D) */
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static __forceinline AffineSpaceT rotate(const VectorT& u, const ScalarT& r) { return L::rotate(u,r); }
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/*! return matrix for rotation around arbitrary axis and point, only in 3D */
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static __forceinline AffineSpaceT rotate(const VectorT& p, const VectorT& u, const ScalarT& r) { return translate(+p) * rotate(u,r) * translate(-p); }
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/*! return matrix for looking at given point, only in 3D */
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static __forceinline AffineSpaceT lookat(const VectorT& eye, const VectorT& point, const VectorT& up) {
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VectorT Z = normalize(point-eye);
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VectorT U = normalize(cross(up,Z));
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VectorT V = normalize(cross(Z,U));
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return AffineSpaceT(L(U,V,Z),eye);
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}
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};
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// template specialization to get correct identity matrix for type AffineSpace3fa
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template<>
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__forceinline AffineSpaceT<LinearSpace3ff>::AffineSpaceT( OneTy ) : l(one), p(0.f, 0.f, 0.f, 1.f) {}
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////////////////////////////////////////////////////////////////////////////////
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// Unary Operators
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////////////////////////////////////////////////////////////////////////////////
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template<typename L> __forceinline AffineSpaceT<L> operator -( const AffineSpaceT<L>& a ) { return AffineSpaceT<L>(-a.l,-a.p); }
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template<typename L> __forceinline AffineSpaceT<L> operator +( const AffineSpaceT<L>& a ) { return AffineSpaceT<L>(+a.l,+a.p); }
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template<typename L> __forceinline AffineSpaceT<L> rcp( const AffineSpaceT<L>& a ) { L il = rcp(a.l); return AffineSpaceT<L>(il,-(il*a.p)); }
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////////////////////////////////////////////////////////////////////////////////
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// Binary Operators
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////////////////////////////////////////////////////////////////////////////////
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template<typename L> __forceinline const AffineSpaceT<L> operator +( const AffineSpaceT<L>& a, const AffineSpaceT<L>& b ) { return AffineSpaceT<L>(a.l+b.l,a.p+b.p); }
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template<typename L> __forceinline const AffineSpaceT<L> operator -( const AffineSpaceT<L>& a, const AffineSpaceT<L>& b ) { return AffineSpaceT<L>(a.l-b.l,a.p-b.p); }
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template<typename L> __forceinline const AffineSpaceT<L> operator *( const ScalarT & a, const AffineSpaceT<L>& b ) { return AffineSpaceT<L>(a*b.l,a*b.p); }
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template<typename L> __forceinline const AffineSpaceT<L> operator *( const AffineSpaceT<L>& a, const AffineSpaceT<L>& b ) { return AffineSpaceT<L>(a.l*b.l,a.l*b.p+a.p); }
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template<typename L> __forceinline const AffineSpaceT<L> operator /( const AffineSpaceT<L>& a, const AffineSpaceT<L>& b ) { return a * rcp(b); }
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template<typename L> __forceinline const AffineSpaceT<L> operator /( const AffineSpaceT<L>& a, const ScalarT & b ) { return a * rcp(b); }
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template<typename L> __forceinline AffineSpaceT<L>& operator *=( AffineSpaceT<L>& a, const AffineSpaceT<L>& b ) { return a = a * b; }
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template<typename L> __forceinline AffineSpaceT<L>& operator *=( AffineSpaceT<L>& a, const ScalarT & b ) { return a = a * b; }
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template<typename L> __forceinline AffineSpaceT<L>& operator /=( AffineSpaceT<L>& a, const AffineSpaceT<L>& b ) { return a = a / b; }
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template<typename L> __forceinline AffineSpaceT<L>& operator /=( AffineSpaceT<L>& a, const ScalarT & b ) { return a = a / b; }
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template<typename L> __forceinline VectorT xfmPoint (const AffineSpaceT<L>& m, const VectorT& p) { return madd(VectorT(p.x),m.l.vx,madd(VectorT(p.y),m.l.vy,madd(VectorT(p.z),m.l.vz,m.p))); }
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template<typename L> __forceinline VectorT xfmVector(const AffineSpaceT<L>& m, const VectorT& v) { return xfmVector(m.l,v); }
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template<typename L> __forceinline VectorT xfmNormal(const AffineSpaceT<L>& m, const VectorT& n) { return xfmNormal(m.l,n); }
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__forceinline const BBox<Vec3fa> xfmBounds(const AffineSpaceT<LinearSpace3<Vec3fa> >& m, const BBox<Vec3fa>& b)
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{
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BBox3fa dst = empty;
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const Vec3fa p0(b.lower.x,b.lower.y,b.lower.z); dst.extend(xfmPoint(m,p0));
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const Vec3fa p1(b.lower.x,b.lower.y,b.upper.z); dst.extend(xfmPoint(m,p1));
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const Vec3fa p2(b.lower.x,b.upper.y,b.lower.z); dst.extend(xfmPoint(m,p2));
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const Vec3fa p3(b.lower.x,b.upper.y,b.upper.z); dst.extend(xfmPoint(m,p3));
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const Vec3fa p4(b.upper.x,b.lower.y,b.lower.z); dst.extend(xfmPoint(m,p4));
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const Vec3fa p5(b.upper.x,b.lower.y,b.upper.z); dst.extend(xfmPoint(m,p5));
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const Vec3fa p6(b.upper.x,b.upper.y,b.lower.z); dst.extend(xfmPoint(m,p6));
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const Vec3fa p7(b.upper.x,b.upper.y,b.upper.z); dst.extend(xfmPoint(m,p7));
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return dst;
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}
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////////////////////////////////////////////////////////////////////////////////
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/// Comparison Operators
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////////////////////////////////////////////////////////////////////////////////
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template<typename L> __forceinline bool operator ==( const AffineSpaceT<L>& a, const AffineSpaceT<L>& b ) { return a.l == b.l && a.p == b.p; }
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template<typename L> __forceinline bool operator !=( const AffineSpaceT<L>& a, const AffineSpaceT<L>& b ) { return a.l != b.l || a.p != b.p; }
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////////////////////////////////////////////////////////////////////////////////
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/// Select
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////////////////////////////////////////////////////////////////////////////////
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template<typename L> __forceinline AffineSpaceT<L> select ( const typename L::Vector::Scalar::Bool& s, const AffineSpaceT<L>& t, const AffineSpaceT<L>& f ) {
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return AffineSpaceT<L>(select(s,t.l,f.l),select(s,t.p,f.p));
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}
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////////////////////////////////////////////////////////////////////////////////
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// Output Operators
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////////////////////////////////////////////////////////////////////////////////
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template<typename L> static embree_ostream operator<<(embree_ostream cout, const AffineSpaceT<L>& m) {
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return cout << "{ l = " << m.l << ", p = " << m.p << " }";
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}
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////////////////////////////////////////////////////////////////////////////////
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// Template Instantiations
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////////////////////////////////////////////////////////////////////////////////
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typedef AffineSpaceT<LinearSpace2f> AffineSpace2f;
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typedef AffineSpaceT<LinearSpace3f> AffineSpace3f;
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typedef AffineSpaceT<LinearSpace3fa> AffineSpace3fa;
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typedef AffineSpaceT<LinearSpace3fx> AffineSpace3fx;
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typedef AffineSpaceT<LinearSpace3ff> AffineSpace3ff;
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typedef AffineSpaceT<Quaternion3f > OrthonormalSpace3f;
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template<int N> using AffineSpace3vf = AffineSpaceT<LinearSpace3<Vec3<vfloat<N>>>>;
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typedef AffineSpaceT<LinearSpace3<Vec3<vfloat<4>>>> AffineSpace3vf4;
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typedef AffineSpaceT<LinearSpace3<Vec3<vfloat<8>>>> AffineSpace3vf8;
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typedef AffineSpaceT<LinearSpace3<Vec3<vfloat<16>>>> AffineSpace3vf16;
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template<int N> using AffineSpace3vff = AffineSpaceT<LinearSpace3<Vec4<vfloat<N>>>>;
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typedef AffineSpaceT<LinearSpace3<Vec4<vfloat<4>>>> AffineSpace3vfa4;
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typedef AffineSpaceT<LinearSpace3<Vec4<vfloat<8>>>> AffineSpace3vfa8;
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typedef AffineSpaceT<LinearSpace3<Vec4<vfloat<16>>>> AffineSpace3vfa16;
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//////////////////////////////////////////////////////////////////////////////
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/// Interpolation
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//////////////////////////////////////////////////////////////////////////////
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template<typename T, typename R>
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__forceinline AffineSpaceT<T> lerp(const AffineSpaceT<T>& M0,
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const AffineSpaceT<T>& M1,
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const R& t)
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{
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return AffineSpaceT<T>(lerp(M0.l,M1.l,t),lerp(M0.p,M1.p,t));
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}
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// slerp interprets the 16 floats of the matrix M = D * R * S as components of
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// three matrizes (D, R, S) that are interpolated individually.
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template<typename T> __forceinline AffineSpaceT<LinearSpace3<Vec3<T>>>
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slerp(const AffineSpaceT<LinearSpace3<Vec4<T>>>& M0,
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const AffineSpaceT<LinearSpace3<Vec4<T>>>& M1,
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const T& t)
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{
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QuaternionT<T> q0(M0.p.w, M0.l.vx.w, M0.l.vy.w, M0.l.vz.w);
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QuaternionT<T> q1(M1.p.w, M1.l.vx.w, M1.l.vy.w, M1.l.vz.w);
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QuaternionT<T> q = slerp(q0, q1, t);
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AffineSpaceT<LinearSpace3<Vec3<T>>> S = lerp(M0, M1, t);
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AffineSpaceT<LinearSpace3<Vec3<T>>> D(one);
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D.p.x = S.l.vx.y;
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D.p.y = S.l.vx.z;
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D.p.z = S.l.vy.z;
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S.l.vx.y = 0;
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S.l.vx.z = 0;
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S.l.vy.z = 0;
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AffineSpaceT<LinearSpace3<Vec3<T>>> R = LinearSpace3<Vec3<T>>(q);
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return D * R * S;
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}
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// this is a specialized version for Vec3fa because that does
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// not play along nicely with the other templated Vec3/Vec4 types
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__forceinline AffineSpace3fa slerp(const AffineSpace3ff& M0,
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const AffineSpace3ff& M1,
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const float& t)
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{
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Quaternion3f q0(M0.p.w, M0.l.vx.w, M0.l.vy.w, M0.l.vz.w);
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Quaternion3f q1(M1.p.w, M1.l.vx.w, M1.l.vy.w, M1.l.vz.w);
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Quaternion3f q = slerp(q0, q1, t);
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AffineSpace3fa S = lerp(M0, M1, t);
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AffineSpace3fa D(one);
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D.p.x = S.l.vx.y;
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D.p.y = S.l.vx.z;
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D.p.z = S.l.vy.z;
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S.l.vx.y = 0;
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S.l.vx.z = 0;
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S.l.vy.z = 0;
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AffineSpace3fa R = LinearSpace3fa(q);
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return D * R * S;
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}
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__forceinline AffineSpace3fa quaternionDecompositionToAffineSpace(const AffineSpace3ff& qd)
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{
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// compute affine transform from quaternion decomposition
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Quaternion3f q(qd.p.w, qd.l.vx.w, qd.l.vy.w, qd.l.vz.w);
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AffineSpace3fa M = qd;
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AffineSpace3fa D(one);
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D.p.x = M.l.vx.y;
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D.p.y = M.l.vx.z;
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D.p.z = M.l.vy.z;
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M.l.vx.y = 0;
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M.l.vx.z = 0;
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M.l.vy.z = 0;
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AffineSpace3fa R = LinearSpace3fa(q);
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return D * R * M;
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}
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__forceinline void quaternionDecomposition(const AffineSpace3ff& qd, Vec3fa& T, Quaternion3f& q, AffineSpace3fa& S)
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{
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q = Quaternion3f(qd.p.w, qd.l.vx.w, qd.l.vy.w, qd.l.vz.w);
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S = qd;
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T.x = qd.l.vx.y;
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T.y = qd.l.vx.z;
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T.z = qd.l.vy.z;
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S.l.vx.y = 0;
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S.l.vx.z = 0;
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S.l.vy.z = 0;
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}
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__forceinline AffineSpace3fx quaternionDecomposition(Vec3fa const& T, Quaternion3f const& q, AffineSpace3fa const& S)
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{
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AffineSpace3ff M = S;
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M.l.vx.w = q.i;
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M.l.vy.w = q.j;
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M.l.vz.w = q.k;
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M.p.w = q.r;
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M.l.vx.y = T.x;
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M.l.vx.z = T.y;
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M.l.vy.z = T.z;
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return M;
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}
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struct __aligned(16) QuaternionDecomposition
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{
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float scale_x = 1.f;
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float scale_y = 1.f;
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float scale_z = 1.f;
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float skew_xy = 0.f;
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float skew_xz = 0.f;
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float skew_yz = 0.f;
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float shift_x = 0.f;
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float shift_y = 0.f;
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float shift_z = 0.f;
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float quaternion_r = 1.f;
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float quaternion_i = 0.f;
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float quaternion_j = 0.f;
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float quaternion_k = 0.f;
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float translation_x = 0.f;
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float translation_y = 0.f;
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float translation_z = 0.f;
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};
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__forceinline QuaternionDecomposition quaternionDecomposition(AffineSpace3ff const& M)
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{
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QuaternionDecomposition qd;
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qd.scale_x = M.l.vx.x;
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qd.scale_y = M.l.vy.y;
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qd.scale_z = M.l.vz.z;
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qd.shift_x = M.p.x;
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qd.shift_y = M.p.y;
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qd.shift_z = M.p.z;
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qd.translation_x = M.l.vx.y;
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qd.translation_y = M.l.vx.z;
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||
|
|
qd.translation_z = M.l.vy.z;
|
||
|
|
qd.skew_xy = M.l.vy.x;
|
||
|
|
qd.skew_xz = M.l.vz.x;
|
||
|
|
qd.skew_yz = M.l.vz.y;
|
||
|
|
qd.quaternion_r = M.p.w;
|
||
|
|
qd.quaternion_i = M.l.vx.w;
|
||
|
|
qd.quaternion_j = M.l.vy.w;
|
||
|
|
qd.quaternion_k = M.l.vz.w;
|
||
|
|
return qd;
|
||
|
|
}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////
|
||
|
|
/*
|
||
|
|
* ! Template Specialization for 2D: return matrix for rotation around point
|
||
|
|
* (rotation around arbitrarty vector is not meaningful in 2D)
|
||
|
|
*/
|
||
|
|
template<> __forceinline
|
||
|
|
AffineSpace2f AffineSpace2f::rotate(const Vec2f& p, const float& r) {
|
||
|
|
return translate(+p)*AffineSpace2f(LinearSpace2f::rotate(r))*translate(-p);
|
||
|
|
}
|
||
|
|
|
||
|
|
////////////////////////////////////////////////////////////////////////////////
|
||
|
|
// Similarity Transform
|
||
|
|
//
|
||
|
|
// checks, if M is a similarity transformation, i.e if there exists a factor D
|
||
|
|
// such that for all x,y: distance(Mx, My) = D * distance(x, y)
|
||
|
|
////////////////////////////////////////////////////////////////////////////////
|
||
|
|
__forceinline bool similarityTransform(const AffineSpace3fa& M, float* D)
|
||
|
|
{
|
||
|
|
if (D) *D = 0.f;
|
||
|
|
if (abs(dot(M.l.vx, M.l.vy)) > 1e-5f) return false;
|
||
|
|
if (abs(dot(M.l.vx, M.l.vz)) > 1e-5f) return false;
|
||
|
|
if (abs(dot(M.l.vy, M.l.vz)) > 1e-5f) return false;
|
||
|
|
|
||
|
|
const float D_x = dot(M.l.vx, M.l.vx);
|
||
|
|
const float D_y = dot(M.l.vy, M.l.vy);
|
||
|
|
const float D_z = dot(M.l.vz, M.l.vz);
|
||
|
|
|
||
|
|
if (abs(D_x - D_y) > 1e-5f ||
|
||
|
|
abs(D_x - D_z) > 1e-5f ||
|
||
|
|
abs(D_y - D_z) > 1e-5f)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
if (D) *D = sqrtf(D_x);
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
__forceinline void AffineSpace3fa_store_unaligned(const AffineSpace3fa &source, AffineSpace3fa* ptr)
|
||
|
|
{
|
||
|
|
Vec3fa::storeu(&ptr->l.vx, source.l.vx);
|
||
|
|
Vec3fa::storeu(&ptr->l.vy, source.l.vy);
|
||
|
|
Vec3fa::storeu(&ptr->l.vz, source.l.vz);
|
||
|
|
Vec3fa::storeu(&ptr->p, source.p);
|
||
|
|
}
|
||
|
|
|
||
|
|
__forceinline AffineSpace3fa AffineSpace3fa_load_unaligned(AffineSpace3fa* ptr)
|
||
|
|
{
|
||
|
|
AffineSpace3fa space;
|
||
|
|
space.l.vx = Vec3fa::loadu(&ptr->l.vx);
|
||
|
|
space.l.vy = Vec3fa::loadu(&ptr->l.vy);
|
||
|
|
space.l.vz = Vec3fa::loadu(&ptr->l.vz);
|
||
|
|
space.p = Vec3fa::loadu(&ptr->p);
|
||
|
|
return space;
|
||
|
|
}
|
||
|
|
|
||
|
|
#undef VectorT
|
||
|
|
#undef ScalarT
|
||
|
|
}
|