1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
|
// Copyright 2013 The Chromium Authors
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.
#ifdef UNSAFE_BUFFERS_BUILD
// TODO(crbug.com/354829279): Remove this and convert code to safer constructs.
#pragma allow_unsafe_buffers
#endif
#include "ui/gfx/geometry/matrix3_f.h"
#include <string.h>
#include <algorithm>
#include <cmath>
#include <limits>
#include "base/strings/stringprintf.h"
namespace {
// This is only to make accessing indices self-explanatory.
enum MatrixCoordinates {
M00,
M01,
M02,
M10,
M11,
M12,
M20,
M21,
M22,
M_END
};
template<typename T>
double Determinant3x3(T data[M_END]) {
// This routine is separated from the Matrix3F::Determinant because in
// computing inverse we do want higher precision afforded by the explicit
// use of 'double'.
return
static_cast<double>(data[M00]) * (
static_cast<double>(data[M11]) * data[M22] -
static_cast<double>(data[M12]) * data[M21]) +
static_cast<double>(data[M01]) * (
static_cast<double>(data[M12]) * data[M20] -
static_cast<double>(data[M10]) * data[M22]) +
static_cast<double>(data[M02]) * (
static_cast<double>(data[M10]) * data[M21] -
static_cast<double>(data[M11]) * data[M20]);
}
} // namespace
namespace gfx {
Matrix3F::Matrix3F() {
}
Matrix3F::~Matrix3F() {
}
// static
Matrix3F Matrix3F::Zeros() {
Matrix3F matrix;
matrix.set(0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f);
return matrix;
}
// static
Matrix3F Matrix3F::Ones() {
Matrix3F matrix;
matrix.set(1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f, 1.0f);
return matrix;
}
// static
Matrix3F Matrix3F::Identity() {
Matrix3F matrix;
matrix.set(1.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 1.0f);
return matrix;
}
// static
Matrix3F Matrix3F::FromOuterProduct(const Vector3dF& a, const Vector3dF& bt) {
Matrix3F matrix;
matrix.set(a.x() * bt.x(), a.x() * bt.y(), a.x() * bt.z(),
a.y() * bt.x(), a.y() * bt.y(), a.y() * bt.z(),
a.z() * bt.x(), a.z() * bt.y(), a.z() * bt.z());
return matrix;
}
bool Matrix3F::IsEqual(const Matrix3F& rhs) const {
return 0 == memcmp(data_.data(), rhs.data_.data(),
(data_.size() * sizeof(decltype(data_)::value_type)));
}
bool Matrix3F::IsNear(const Matrix3F& rhs, float precision) const {
DCHECK(precision >= 0);
for (int i = 0; i < M_END; ++i) {
if (std::abs(data_[i] - rhs.data_[i]) > precision)
return false;
}
return true;
}
Matrix3F Matrix3F::Add(const Matrix3F& rhs) const {
Matrix3F result;
for (int i = 0; i < M_END; ++i)
result.data_[i] = data_[i] + rhs.data_[i];
return result;
}
Matrix3F Matrix3F::Subtract(const Matrix3F& rhs) const {
Matrix3F result;
for (int i = 0; i < M_END; ++i)
result.data_[i] = data_[i] - rhs.data_[i];
return result;
}
Matrix3F Matrix3F::Inverse() const {
Matrix3F inverse = Matrix3F::Zeros();
double determinant = Determinant3x3(data_.data());
if (std::numeric_limits<float>::epsilon() > std::abs(determinant))
return inverse; // Singular matrix. Return Zeros().
inverse.set(
static_cast<float>((data_[M11] * data_[M22] - data_[M12] * data_[M21]) /
determinant),
static_cast<float>((data_[M02] * data_[M21] - data_[M01] * data_[M22]) /
determinant),
static_cast<float>((data_[M01] * data_[M12] - data_[M02] * data_[M11]) /
determinant),
static_cast<float>((data_[M12] * data_[M20] - data_[M10] * data_[M22]) /
determinant),
static_cast<float>((data_[M00] * data_[M22] - data_[M02] * data_[M20]) /
determinant),
static_cast<float>((data_[M02] * data_[M10] - data_[M00] * data_[M12]) /
determinant),
static_cast<float>((data_[M10] * data_[M21] - data_[M11] * data_[M20]) /
determinant),
static_cast<float>((data_[M01] * data_[M20] - data_[M00] * data_[M21]) /
determinant),
static_cast<float>((data_[M00] * data_[M11] - data_[M01] * data_[M10]) /
determinant));
return inverse;
}
Matrix3F Matrix3F::Transpose() const {
Matrix3F transpose;
transpose.set(data_[M00], data_[M10], data_[M20], data_[M01], data_[M11],
data_[M21], data_[M02], data_[M12], data_[M22]);
return transpose;
}
float Matrix3F::Determinant() const {
return static_cast<float>(Determinant3x3(data_.data()));
}
Matrix3F MatrixProduct(const Matrix3F& lhs, const Matrix3F& rhs) {
Matrix3F result = Matrix3F::Zeros();
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
result.set(i, j, DotProduct(lhs.get_row(i), rhs.get_column(j)));
}
}
return result;
}
Vector3dF MatrixProduct(const Matrix3F& lhs, const Vector3dF& rhs) {
return Vector3dF(DotProduct(lhs.get_row(0), rhs),
DotProduct(lhs.get_row(1), rhs),
DotProduct(lhs.get_row(2), rhs));
}
std::string Matrix3F::ToString() const {
return base::StringPrintf(
"[[%+0.4f, %+0.4f, %+0.4f],"
" [%+0.4f, %+0.4f, %+0.4f],"
" [%+0.4f, %+0.4f, %+0.4f]]",
data_[M00], data_[M01], data_[M02], data_[M10], data_[M11], data_[M12],
data_[M20], data_[M21], data_[M22]);
}
} // namespace gfx
|
