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
|
#pragma once
#include <initializer_list>
template<typename num, int h, int w>
struct Mat
{
num data[h][w];
Mat<num, h, w> operator+(const Mat<num, h, w>& other) const
{
Mat<num, h, w> ret;
for (int j = 0; j < h; j++)
for (int i = 0; i < w; i++)
ret(j, i) = this->operator ()(j, i) + other(j, i);
return ret;
}
Mat<num, h, w> operator-(const Mat<num, h, w>& other) const
{
Mat<num, h, w> ret;
for (int j = 0; j < h; j++)
for (int i = 0; i < w; i++)
ret(j, i) = this->operator ()(j, i) - other(j, i);
return ret;
}
template<int p>
Mat<num, w, p> operator*(const Mat<num, w, p>& other) const
{
Mat<num, w, p> ret;
for (int j = 0; j < w; j++)
for (int i = 0; i < p; i++)
{
num sum = num(0);
for (int k = 0; k < h; k++)
sum += data[j][k]*other.data[k][i];
ret.data[j][i] = sum;
}
return ret;
}
num operator()(int j, int i) const { return data[j][i]; }
num& operator()(int j, int i) { return data[j][i]; }
Mat(std::initializer_list<num>&& list)
{
auto iter = list.begin();
for (int i = 0; i < h; i++)
for (int j = 0; j < w; j++)
data[i][j] = *iter++;
}
Mat()
{
for (int j = 0; j < h; j++)
for (int i = 0; i < w; i++)
data[j][i] = 0;
}
Mat(const num* mem)
{
for (int j = 0; j < h; j++)
for (int i = 0; i < w; i++)
data[j][i] = mem[i*h+j];
}
// XXX add more operators as needed, third-party dependencies mostly
// not needed merely for matrix algebra -sh 20141030
static Mat<num, h, h> eye()
{
Mat<num, h, h> ret;
for (int j = 0; j < h; j++)
for (int i = 0; i < w; i++)
ret.data[j][i] = 0;
for (int i = 0; i < h; i++)
ret.data[i][i] = 1;
return ret;
}
Mat<num, w, h> t() const
{
Mat<num, w, h> ret;
for (int j = 0; j < h; j++)
for (int i = 0; i < w; i++)
ret.data[i][j] = data[j][i];
return ret;
}
template<int h_, int w_> using dmat = Mat<double, h_, w_>;
// http://stackoverflow.com/a/18436193
static dmat<3, 1> rmat_to_euler(const dmat<3, 3>& R)
{
static constexpr double pi = 3.141592653;
const double up = 90 * pi / 180.;
static constexpr double bound = 1. - 2e-4;
if (R(0, 2) > bound)
{
double roll = atan(R(1, 0) / R(2, 0));
return dmat<3, 1>({0., up, roll});
}
if (R(0, 2) < -bound)
{
double roll = atan(R(1, 0) / R(2, 0));
return dmat<3, 1>({0., -up, roll});
}
double pitch = asin(-R(0, 2));
double roll = atan2(R(1, 2), R(2, 2));
double yaw = atan2(R(0, 1), R(0, 0));
return dmat<3, 1>({yaw, pitch, roll});
}
// tait-bryan angles, not euler
static dmat<3, 3> euler_to_rmat(const double* input)
{
static constexpr double pi = 3.141592653;
auto H = input[0] * pi / 180;
auto P = input[1] * pi / 180;
auto B = input[2] * pi / 180;
const auto c1 = cos(H);
const auto s1 = sin(H);
const auto c2 = cos(P);
const auto s2 = sin(P);
const auto c3 = cos(B);
const auto s3 = sin(B);
double foo[] = {
// z
c1 * c2,
c1 * s2 * s3 - c3 * s1,
s1 * s3 + c1 * c3 * s2,
// y
c2 * s1,
c1 * c3 + s1 * s2 * s3,
c3 * s1 * s2 - c1 * s3,
// x
-s2,
c2 * s3,
c2 * c3
};
return dmat<3, 3>(foo);
}
};
template<int h, int w> using dmat = Mat<double, h, w>;
|
