1// Copyright 2009-2021 Intel Corporation
2// SPDX-License-Identifier: Apache-2.0
3
4#pragma once
5
6#include "vec3.h"
7#include "quaternion.h"
8
9namespace embree
10{
11 ////////////////////////////////////////////////////////////////////////////////
12 /// 3D Linear Transform (3x3 Matrix)
13 ////////////////////////////////////////////////////////////////////////////////
14
15 template<typename T> struct LinearSpace3
16 {
17 typedef T Vector;
18 typedef typename T::Scalar Scalar;
19
20 /*! default matrix constructor */
21 __forceinline LinearSpace3 ( ) {}
22 __forceinline LinearSpace3 ( const LinearSpace3& other ) { vx = other.vx; vy = other.vy; vz = other.vz; }
23 __forceinline LinearSpace3& operator=( const LinearSpace3& other ) { vx = other.vx; vy = other.vy; vz = other.vz; return *this; }
24
25 template<typename L1> __forceinline LinearSpace3( const LinearSpace3<L1>& s ) : vx(s.vx), vy(s.vy), vz(s.vz) {}
26
27 /*! matrix construction from column vectors */
28 __forceinline LinearSpace3(const Vector& vx, const Vector& vy, const Vector& vz)
29 : vx(vx), vy(vy), vz(vz) {}
30
31 /*! construction from quaternion */
32 __forceinline LinearSpace3( const QuaternionT<Scalar>& q )
33 : vx((q.r*q.r + q.i*q.i - q.j*q.j - q.k*q.k), 2.0f*(q.i*q.j + q.r*q.k), 2.0f*(q.i*q.k - q.r*q.j))
34 , vy(2.0f*(q.i*q.j - q.r*q.k), (q.r*q.r - q.i*q.i + q.j*q.j - q.k*q.k), 2.0f*(q.j*q.k + q.r*q.i))
35 , vz(2.0f*(q.i*q.k + q.r*q.j), 2.0f*(q.j*q.k - q.r*q.i), (q.r*q.r - q.i*q.i - q.j*q.j + q.k*q.k)) {}
36
37 /*! matrix construction from row mayor data */
38 __forceinline LinearSpace3(const Scalar& m00, const Scalar& m01, const Scalar& m02,
39 const Scalar& m10, const Scalar& m11, const Scalar& m12,
40 const Scalar& m20, const Scalar& m21, const Scalar& m22)
41 : vx(m00,m10,m20), vy(m01,m11,m21), vz(m02,m12,m22) {}
42
43 /*! compute the determinant of the matrix */
44 __forceinline const Scalar det() const { return dot(vx,cross(vy,vz)); }
45
46 /*! compute adjoint matrix */
47 __forceinline const LinearSpace3 adjoint() const { return LinearSpace3(cross(vy,vz),cross(vz,vx),cross(vx,vy)).transposed(); }
48
49 /*! compute inverse matrix */
50 __forceinline const LinearSpace3 inverse() const { return adjoint()/det(); }
51
52 /*! compute transposed matrix */
53 __forceinline const LinearSpace3 transposed() const { return LinearSpace3(vx.x,vx.y,vx.z,vy.x,vy.y,vy.z,vz.x,vz.y,vz.z); }
54
55 /*! returns first row of matrix */
56 __forceinline Vector row0() const { return Vector(vx.x,vy.x,vz.x); }
57
58 /*! returns second row of matrix */
59 __forceinline Vector row1() const { return Vector(vx.y,vy.y,vz.y); }
60
61 /*! returns third row of matrix */
62 __forceinline Vector row2() const { return Vector(vx.z,vy.z,vz.z); }
63
64 ////////////////////////////////////////////////////////////////////////////////
65 /// Constants
66 ////////////////////////////////////////////////////////////////////////////////
67
68 __forceinline LinearSpace3( ZeroTy ) : vx(zero), vy(zero), vz(zero) {}
69 __forceinline LinearSpace3( OneTy ) : vx(one, zero, zero), vy(zero, one, zero), vz(zero, zero, one) {}
70
71 /*! return matrix for scaling */
72 static __forceinline LinearSpace3 scale(const Vector& s) {
73 return LinearSpace3(s.x, 0, 0,
74 0 , s.y, 0,
75 0 , 0, s.z);
76 }
77
78 /*! return matrix for rotation around arbitrary axis */
79 static __forceinline LinearSpace3 rotate(const Vector& _u, const Scalar& r) {
80 Vector u = normalize(_u);
81 Scalar s = sin(r), c = cos(r);
82 return LinearSpace3(u.x*u.x+(1-u.x*u.x)*c, u.x*u.y*(1-c)-u.z*s, u.x*u.z*(1-c)+u.y*s,
83 u.x*u.y*(1-c)+u.z*s, u.y*u.y+(1-u.y*u.y)*c, u.y*u.z*(1-c)-u.x*s,
84 u.x*u.z*(1-c)-u.y*s, u.y*u.z*(1-c)+u.x*s, u.z*u.z+(1-u.z*u.z)*c);
85 }
86
87 public:
88
89 /*! the column vectors of the matrix */
90 Vector vx,vy,vz;
91 };
92
93 /*! compute transposed matrix */
94 template<> __forceinline const LinearSpace3<Vec3fa> LinearSpace3<Vec3fa>::transposed() const {
95 vfloat4 rx,ry,rz; transpose(r0: (vfloat4&)vx,r1: (vfloat4&)vy,r2: (vfloat4&)vz,r3: vfloat4(zero),c0&: rx,c1&: ry,c2&: rz);
96 return LinearSpace3<Vec3fa>(Vec3fa(rx),Vec3fa(ry),Vec3fa(rz));
97 }
98
99 template<typename T>
100 __forceinline const LinearSpace3<T> transposed(const LinearSpace3<T>& xfm) {
101 return xfm.transposed();
102 }
103
104 ////////////////////////////////////////////////////////////////////////////////
105 // Unary Operators
106 ////////////////////////////////////////////////////////////////////////////////
107
108 template<typename T> __forceinline LinearSpace3<T> operator -( const LinearSpace3<T>& a ) { return LinearSpace3<T>(-a.vx,-a.vy,-a.vz); }
109 template<typename T> __forceinline LinearSpace3<T> operator +( const LinearSpace3<T>& a ) { return LinearSpace3<T>(+a.vx,+a.vy,+a.vz); }
110 template<typename T> __forceinline LinearSpace3<T> rcp ( const LinearSpace3<T>& a ) { return a.inverse(); }
111
112 /* constructs a coordinate frame form a normalized normal */
113 template<typename T> __forceinline LinearSpace3<T> frame(const T& N)
114 {
115 const T dx0(0,N.z,-N.y);
116 const T dx1(-N.z,0,N.x);
117 const T dx = normalize(select(dot(dx0,dx0) > dot(dx1,dx1),dx0,dx1));
118 const T dy = normalize(cross(N,dx));
119 return LinearSpace3<T>(dx,dy,N);
120 }
121
122 /* constructs a coordinate frame from a normal and approximate x-direction */
123 template<typename T> __forceinline LinearSpace3<T> frame(const T& N, const T& dxi)
124 {
125 if (abs(dot(dxi,N)) > 0.99f) return frame(N); // fallback in case N and dxi are very parallel
126 const T dx = normalize(cross(dxi,N));
127 const T dy = normalize(cross(N,dx));
128 return LinearSpace3<T>(dx,dy,N);
129 }
130
131 /* clamps linear space to range -1 to +1 */
132 template<typename T> __forceinline LinearSpace3<T> clamp(const LinearSpace3<T>& space) {
133 return LinearSpace3<T>(clamp(space.vx,T(-1.0f),T(1.0f)),
134 clamp(space.vy,T(-1.0f),T(1.0f)),
135 clamp(space.vz,T(-1.0f),T(1.0f)));
136 }
137
138 ////////////////////////////////////////////////////////////////////////////////
139 // Binary Operators
140 ////////////////////////////////////////////////////////////////////////////////
141
142 template<typename T> __forceinline LinearSpace3<T> operator +( const LinearSpace3<T>& a, const LinearSpace3<T>& b ) { return LinearSpace3<T>(a.vx+b.vx,a.vy+b.vy,a.vz+b.vz); }
143 template<typename T> __forceinline LinearSpace3<T> operator -( const LinearSpace3<T>& a, const LinearSpace3<T>& b ) { return LinearSpace3<T>(a.vx-b.vx,a.vy-b.vy,a.vz-b.vz); }
144
145 template<typename T> __forceinline LinearSpace3<T> operator*(const typename T::Scalar & a, const LinearSpace3<T>& b) { return LinearSpace3<T>(a*b.vx, a*b.vy, a*b.vz); }
146 template<typename T> __forceinline T operator*(const LinearSpace3<T>& a, const T & b) { return madd(T(b.x),a.vx,madd(T(b.y),a.vy,T(b.z)*a.vz)); }
147 template<typename T> __forceinline LinearSpace3<T> operator*(const LinearSpace3<T>& a, const LinearSpace3<T>& b) { return LinearSpace3<T>(a*b.vx, a*b.vy, a*b.vz); }
148
149 template<typename T> __forceinline LinearSpace3<T> operator/(const LinearSpace3<T>& a, const typename T::Scalar & b) { return LinearSpace3<T>(a.vx/b, a.vy/b, a.vz/b); }
150 template<typename T> __forceinline LinearSpace3<T> operator/(const LinearSpace3<T>& a, const LinearSpace3<T>& b) { return a * rcp(b); }
151
152 template<typename T> __forceinline LinearSpace3<T>& operator *=( LinearSpace3<T>& a, const LinearSpace3<T>& b ) { return a = a * b; }
153 template<typename T> __forceinline LinearSpace3<T>& operator /=( LinearSpace3<T>& a, const LinearSpace3<T>& b ) { return a = a / b; }
154
155 template<typename T> __forceinline T xfmPoint (const LinearSpace3<T>& s, const T & a) { return madd(T(a.x),s.vx,madd(T(a.y),s.vy,T(a.z)*s.vz)); }
156 template<typename T> __forceinline T xfmVector(const LinearSpace3<T>& s, const T & a) { return madd(T(a.x),s.vx,madd(T(a.y),s.vy,T(a.z)*s.vz)); }
157 template<typename T> __forceinline T xfmNormal(const LinearSpace3<T>& s, const T & a) { return xfmVector(s.inverse().transposed(),a); }
158
159 ////////////////////////////////////////////////////////////////////////////////
160 /// Comparison Operators
161 ////////////////////////////////////////////////////////////////////////////////
162
163 template<typename T> __forceinline bool operator ==( const LinearSpace3<T>& a, const LinearSpace3<T>& b ) { return a.vx == b.vx && a.vy == b.vy && a.vz == b.vz; }
164 template<typename T> __forceinline bool operator !=( const LinearSpace3<T>& a, const LinearSpace3<T>& b ) { return a.vx != b.vx || a.vy != b.vy || a.vz != b.vz; }
165
166 ////////////////////////////////////////////////////////////////////////////////
167 /// Select
168 ////////////////////////////////////////////////////////////////////////////////
169
170 template<typename T> __forceinline LinearSpace3<T> select ( const typename T::Scalar::Bool& s, const LinearSpace3<T>& t, const LinearSpace3<T>& f ) {
171 return LinearSpace3<T>(select(s,t.vx,f.vx),select(s,t.vy,f.vy),select(s,t.vz,f.vz));
172 }
173
174 /*! blending */
175 template<typename T>
176 __forceinline LinearSpace3<T> lerp(const LinearSpace3<T>& l0, const LinearSpace3<T>& l1, const float t)
177 {
178 return LinearSpace3<T>(lerp(l0.vx,l1.vx,t),
179 lerp(l0.vy,l1.vy,t),
180 lerp(l0.vz,l1.vz,t));
181 }
182
183 ////////////////////////////////////////////////////////////////////////////////
184 /// Output Operators
185 ////////////////////////////////////////////////////////////////////////////////
186
187 template<typename T> static embree_ostream operator<<(embree_ostream cout, const LinearSpace3<T>& m) {
188 return cout << "{ vx = " << m.vx << ", vy = " << m.vy << ", vz = " << m.vz << "}";
189 }
190
191 /*! Shortcuts for common linear spaces. */
192 typedef LinearSpace3<Vec3f> LinearSpace3f;
193 typedef LinearSpace3<Vec3fa> LinearSpace3fa;
194 typedef LinearSpace3<Vec3fx> LinearSpace3fx;
195 typedef LinearSpace3<Vec3ff> LinearSpace3ff;
196
197 template<int N> using LinearSpace3vf = LinearSpace3<Vec3<vfloat<N>>>;
198 typedef LinearSpace3<Vec3<vfloat<4>>> LinearSpace3vf4;
199 typedef LinearSpace3<Vec3<vfloat<8>>> LinearSpace3vf8;
200 typedef LinearSpace3<Vec3<vfloat<16>>> LinearSpace3vf16;
201
202 /*! blending */
203 template<typename T, typename S>
204 __forceinline LinearSpace3<T> lerp(const LinearSpace3<T>& l0,
205 const LinearSpace3<T>& l1,
206 const S& t)
207 {
208 return LinearSpace3<T>(lerp(l0.vx,l1.vx,t),
209 lerp(l0.vy,l1.vy,t),
210 lerp(l0.vz,l1.vz,t));
211 }
212
213}
214

source code of qtquick3d/src/3rdparty/embree/common/math/linearspace3.h