1// Copyright 2009-2021 Intel Corporation
2// SPDX-License-Identifier: Apache-2.0
3
4#pragma once
5
6#include "vec2.h"
7
8namespace embree
9{
10 ////////////////////////////////////////////////////////////////////////////////
11 /// 2D Linear Transform (2x2 Matrix)
12 ////////////////////////////////////////////////////////////////////////////////
13
14 template<typename T> struct LinearSpace2
15 {
16 typedef T Vector;
17 typedef typename T::Scalar Scalar;
18
19 /*! default matrix constructor */
20 __forceinline LinearSpace2 ( ) {}
21 __forceinline LinearSpace2 ( const LinearSpace2& other ) { vx = other.vx; vy = other.vy; }
22 __forceinline LinearSpace2& operator=( const LinearSpace2& other ) { vx = other.vx; vy = other.vy; return *this; }
23
24 template<typename L1> __forceinline LinearSpace2( const LinearSpace2<L1>& s ) : vx(s.vx), vy(s.vy) {}
25
26 /*! matrix construction from column vectors */
27 __forceinline LinearSpace2(const Vector& vx, const Vector& vy)
28 : vx(vx), vy(vy) {}
29
30 /*! matrix construction from row mayor data */
31 __forceinline LinearSpace2(const Scalar& m00, const Scalar& m01,
32 const Scalar& m10, const Scalar& m11)
33 : vx(m00,m10), vy(m01,m11) {}
34
35 /*! compute the determinant of the matrix */
36 __forceinline const Scalar det() const { return vx.x*vy.y - vx.y*vy.x; }
37
38 /*! compute adjoint matrix */
39 __forceinline const LinearSpace2 adjoint() const { return LinearSpace2(vy.y,-vy.x,-vx.y,vx.x); }
40
41 /*! compute inverse matrix */
42 __forceinline const LinearSpace2 inverse() const { return adjoint()/det(); }
43
44 /*! compute transposed matrix */
45 __forceinline const LinearSpace2 transposed() const { return LinearSpace2(vx.x,vx.y,vy.x,vy.y); }
46
47 /*! returns first row of matrix */
48 __forceinline Vector row0() const { return Vector(vx.x,vy.x); }
49
50 /*! returns second row of matrix */
51 __forceinline Vector row1() const { return Vector(vx.y,vy.y); }
52
53 ////////////////////////////////////////////////////////////////////////////////
54 /// Constants
55 ////////////////////////////////////////////////////////////////////////////////
56
57 __forceinline LinearSpace2( ZeroTy ) : vx(zero), vy(zero) {}
58 __forceinline LinearSpace2( OneTy ) : vx(one, zero), vy(zero, one) {}
59
60 /*! return matrix for scaling */
61 static __forceinline LinearSpace2 scale(const Vector& s) {
62 return LinearSpace2(s.x, 0,
63 0 , s.y);
64 }
65
66 /*! return matrix for rotation */
67 static __forceinline LinearSpace2 rotate(const Scalar& r) {
68 Scalar s = sin(r), c = cos(r);
69 return LinearSpace2(c, -s,
70 s, c);
71 }
72
73 /*! return closest orthogonal matrix (i.e. a general rotation including reflection) */
74 LinearSpace2 orthogonal() const
75 {
76 LinearSpace2 m = *this;
77
78 // mirrored?
79 Scalar mirror(one);
80 if (m.det() < Scalar(zero)) {
81 m.vx = -m.vx;
82 mirror = -mirror;
83 }
84
85 // rotation
86 for (int i = 0; i < 99; i++) {
87 const LinearSpace2 m_next = 0.5 * (m + m.transposed().inverse());
88 const LinearSpace2 d = m_next - m;
89 m = m_next;
90 // norm^2 of difference small enough?
91 if (max(dot(d.vx, d.vx), dot(d.vy, d.vy)) < 1e-8)
92 break;
93 }
94
95 // rotation * mirror_x
96 return LinearSpace2(mirror*m.vx, m.vy);
97 }
98
99 public:
100
101 /*! the column vectors of the matrix */
102 Vector vx,vy;
103 };
104
105 ////////////////////////////////////////////////////////////////////////////////
106 // Unary Operators
107 ////////////////////////////////////////////////////////////////////////////////
108
109 template<typename T> __forceinline LinearSpace2<T> operator -( const LinearSpace2<T>& a ) { return LinearSpace2<T>(-a.vx,-a.vy); }
110 template<typename T> __forceinline LinearSpace2<T> operator +( const LinearSpace2<T>& a ) { return LinearSpace2<T>(+a.vx,+a.vy); }
111 template<typename T> __forceinline LinearSpace2<T> rcp ( const LinearSpace2<T>& a ) { return a.inverse(); }
112
113 ////////////////////////////////////////////////////////////////////////////////
114 // Binary Operators
115 ////////////////////////////////////////////////////////////////////////////////
116
117 template<typename T> __forceinline LinearSpace2<T> operator +( const LinearSpace2<T>& a, const LinearSpace2<T>& b ) { return LinearSpace2<T>(a.vx+b.vx,a.vy+b.vy); }
118 template<typename T> __forceinline LinearSpace2<T> operator -( const LinearSpace2<T>& a, const LinearSpace2<T>& b ) { return LinearSpace2<T>(a.vx-b.vx,a.vy-b.vy); }
119
120 template<typename T> __forceinline LinearSpace2<T> operator*(const typename T::Scalar & a, const LinearSpace2<T>& b) { return LinearSpace2<T>(a*b.vx, a*b.vy); }
121 template<typename T> __forceinline T operator*(const LinearSpace2<T>& a, const T & b) { return b.x*a.vx + b.y*a.vy; }
122 template<typename T> __forceinline LinearSpace2<T> operator*(const LinearSpace2<T>& a, const LinearSpace2<T>& b) { return LinearSpace2<T>(a*b.vx, a*b.vy); }
123
124 template<typename T> __forceinline LinearSpace2<T> operator/(const LinearSpace2<T>& a, const typename T::Scalar & b) { return LinearSpace2<T>(a.vx/b, a.vy/b); }
125 template<typename T> __forceinline LinearSpace2<T> operator/(const LinearSpace2<T>& a, const LinearSpace2<T>& b) { return a * rcp(b); }
126
127 template<typename T> __forceinline LinearSpace2<T>& operator *=( LinearSpace2<T>& a, const LinearSpace2<T>& b ) { return a = a * b; }
128 template<typename T> __forceinline LinearSpace2<T>& operator /=( LinearSpace2<T>& a, const LinearSpace2<T>& b ) { return a = a / b; }
129
130 ////////////////////////////////////////////////////////////////////////////////
131 /// Comparison Operators
132 ////////////////////////////////////////////////////////////////////////////////
133
134 template<typename T> __forceinline bool operator ==( const LinearSpace2<T>& a, const LinearSpace2<T>& b ) { return a.vx == b.vx && a.vy == b.vy; }
135 template<typename T> __forceinline bool operator !=( const LinearSpace2<T>& a, const LinearSpace2<T>& b ) { return a.vx != b.vx || a.vy != b.vy; }
136
137 ////////////////////////////////////////////////////////////////////////////////
138 /// Output Operators
139 ////////////////////////////////////////////////////////////////////////////////
140
141 template<typename T> static embree_ostream operator<<(embree_ostream cout, const LinearSpace2<T>& m) {
142 return cout << "{ vx = " << m.vx << ", vy = " << m.vy << "}";
143 }
144
145 /*! Shortcuts for common linear spaces. */
146 typedef LinearSpace2<Vec2f> LinearSpace2f;
147 typedef LinearSpace2<Vec2fa> LinearSpace2fa;
148}
149

source code of qtquick3d/src/3rdparty/embree/common/math/linearspace2.h