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SkMatrixInvert.cpp
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1/*
2 * Copyright 2021 Google LLC
3 *
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
6 */
7
8#include "src/core/SkMatrixInvert.h"
9
10#include "include/private/base/SkFloatingPoint.h"
11
12SkScalar SkInvert2x2Matrix(const SkScalar inMatrix[4], SkScalar outMatrix[4]) {
13 double a00 = inMatrix[0];
14 double a01 = inMatrix[1];
15 double a10 = inMatrix[2];
16 double a11 = inMatrix[3];
17
18 // Calculate the determinant
19 double determinant = a00 * a11 - a01 * a10;
20 if (outMatrix) {
21 double invdet = sk_ieee_double_divide(1.0, determinant);
22 outMatrix[0] = a11 * invdet;
23 outMatrix[1] = -a01 * invdet;
24 outMatrix[2] = -a10 * invdet;
25 outMatrix[3] = a00 * invdet;
26 // If 1/det overflows to infinity (i.e. det is denormalized) or any of the inverted matrix
27 // values is non-finite, return zero to indicate a non-invertible matrix.
28 if (!SkIsFinite(outMatrix, 4)) {
29 determinant = 0.0f;
30 }
31 }
32 return determinant;
33}
34
35SkScalar SkInvert3x3Matrix(const SkScalar inMatrix[9], SkScalar outMatrix[9]) {
36 double a00 = inMatrix[0];
37 double a01 = inMatrix[1];
38 double a02 = inMatrix[2];
39 double a10 = inMatrix[3];
40 double a11 = inMatrix[4];
41 double a12 = inMatrix[5];
42 double a20 = inMatrix[6];
43 double a21 = inMatrix[7];
44 double a22 = inMatrix[8];
45
46 double b01 = a22 * a11 - a12 * a21;
47 double b11 = -a22 * a10 + a12 * a20;
48 double b21 = a21 * a10 - a11 * a20;
49
50 // Calculate the determinant
51 double determinant = a00 * b01 + a01 * b11 + a02 * b21;
52 if (outMatrix) {
53 double invdet = sk_ieee_double_divide(1.0, determinant);
54 outMatrix[0] = b01 * invdet;
55 outMatrix[1] = (-a22 * a01 + a02 * a21) * invdet;
56 outMatrix[2] = ( a12 * a01 - a02 * a11) * invdet;
57 outMatrix[3] = b11 * invdet;
58 outMatrix[4] = ( a22 * a00 - a02 * a20) * invdet;
59 outMatrix[5] = (-a12 * a00 + a02 * a10) * invdet;
60 outMatrix[6] = b21 * invdet;
61 outMatrix[7] = (-a21 * a00 + a01 * a20) * invdet;
62 outMatrix[8] = ( a11 * a00 - a01 * a10) * invdet;
63 // If 1/det overflows to infinity (i.e. det is denormalized) or any of the inverted matrix
64 // values is non-finite, return zero to indicate a non-invertible matrix.
65 if (!SkIsFinite(outMatrix, 9)) {
66 determinant = 0.0f;
67 }
68 }
69 return determinant;
70}
71
72SkScalar SkInvert4x4Matrix(const SkScalar inMatrix[16], SkScalar outMatrix[16]) {
73 double a00 = inMatrix[0];
74 double a01 = inMatrix[1];
75 double a02 = inMatrix[2];
76 double a03 = inMatrix[3];
77 double a10 = inMatrix[4];
78 double a11 = inMatrix[5];
79 double a12 = inMatrix[6];
80 double a13 = inMatrix[7];
81 double a20 = inMatrix[8];
82 double a21 = inMatrix[9];
83 double a22 = inMatrix[10];
84 double a23 = inMatrix[11];
85 double a30 = inMatrix[12];
86 double a31 = inMatrix[13];
87 double a32 = inMatrix[14];
88 double a33 = inMatrix[15];
89
90 double b00 = a00 * a11 - a01 * a10;
91 double b01 = a00 * a12 - a02 * a10;
92 double b02 = a00 * a13 - a03 * a10;
93 double b03 = a01 * a12 - a02 * a11;
94 double b04 = a01 * a13 - a03 * a11;
95 double b05 = a02 * a13 - a03 * a12;
96 double b06 = a20 * a31 - a21 * a30;
97 double b07 = a20 * a32 - a22 * a30;
98 double b08 = a20 * a33 - a23 * a30;
99 double b09 = a21 * a32 - a22 * a31;
100 double b10 = a21 * a33 - a23 * a31;
101 double b11 = a22 * a33 - a23 * a32;
102
103 // Calculate the determinant
104 double determinant = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
105 if (outMatrix) {
106 double invdet = sk_ieee_double_divide(1.0, determinant);
107 b00 *= invdet;
108 b01 *= invdet;
109 b02 *= invdet;
110 b03 *= invdet;
111 b04 *= invdet;
112 b05 *= invdet;
113 b06 *= invdet;
114 b07 *= invdet;
115 b08 *= invdet;
116 b09 *= invdet;
117 b10 *= invdet;
118 b11 *= invdet;
119
120 outMatrix[0] = a11 * b11 - a12 * b10 + a13 * b09;
121 outMatrix[1] = a02 * b10 - a01 * b11 - a03 * b09;
122 outMatrix[2] = a31 * b05 - a32 * b04 + a33 * b03;
123 outMatrix[3] = a22 * b04 - a21 * b05 - a23 * b03;
124 outMatrix[4] = a12 * b08 - a10 * b11 - a13 * b07;
125 outMatrix[5] = a00 * b11 - a02 * b08 + a03 * b07;
126 outMatrix[6] = a32 * b02 - a30 * b05 - a33 * b01;
127 outMatrix[7] = a20 * b05 - a22 * b02 + a23 * b01;
128 outMatrix[8] = a10 * b10 - a11 * b08 + a13 * b06;
129 outMatrix[9] = a01 * b08 - a00 * b10 - a03 * b06;
130 outMatrix[10] = a30 * b04 - a31 * b02 + a33 * b00;
131 outMatrix[11] = a21 * b02 - a20 * b04 - a23 * b00;
132 outMatrix[12] = a11 * b07 - a10 * b09 - a12 * b06;
133 outMatrix[13] = a00 * b09 - a01 * b07 + a02 * b06;
134 outMatrix[14] = a31 * b01 - a30 * b03 - a32 * b00;
135 outMatrix[15] = a20 * b03 - a21 * b01 + a22 * b00;
136
137 // If 1/det overflows to infinity (i.e. det is denormalized) or any of the inverted matrix
138 // values is non-finite, return zero to indicate a non-invertible matrix.
139 if (!SkIsFinite(outMatrix, 16)) {
140 determinant = 0.0f;
141 }
142 }
143 return determinant;
144}
SkIsFinite
static bool SkIsFinite(T x, Pack... values)
Definition SkFloatingPoint.h:50
sk_ieee_double_divide
static constexpr double sk_ieee_double_divide(double numer, double denom)
Definition SkFloatingPoint.h:150
SkInvert2x2Matrix
SkScalar SkInvert2x2Matrix(const SkScalar inMatrix[4], SkScalar outMatrix[4])
Definition SkMatrixInvert.cpp:12
SkInvert3x3Matrix
SkScalar SkInvert3x3Matrix(const SkScalar inMatrix[9], SkScalar outMatrix[9])
Definition SkMatrixInvert.cpp:35
SkInvert4x4Matrix
SkScalar SkInvert4x4Matrix(const SkScalar inMatrix[16], SkScalar outMatrix[16])
Definition SkMatrixInvert.cpp:72
SkScalar
float SkScalar
Definition extension.cpp:12
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