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
|
/* Copyright (c) 2008-2022 the MRtrix3 contributors.
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*
* Covered Software is provided under this License on an "as is"
* basis, without warranty of any kind, either expressed, implied, or
* statutory, including, without limitation, warranties that the
* Covered Software is free of defects, merchantable, fit for a
* particular purpose or non-infringing.
* See the Mozilla Public License v. 2.0 for more details.
*
* For more details, see http://www.mrtrix.org/.
*/
#ifndef __math_sphere_h__
#define __math_sphere_h__
#include <cmath>
#include <sys/types.h>
#include <type_traits>
#include <Eigen/Core>
#include "math/math.h"
namespace MR
{
namespace Math
{
namespace Sphere
{
//! convert spherical coordinates to Cartesian coordinates
template <class VectorType1, class VectorType2>
inline typename std::enable_if<VectorType1::IsVectorAtCompileTime, void>::type
spherical2cartesian (const VectorType1& az_el_r, VectorType2&& xyz)
{
if (az_el_r.size() == 3) {
xyz[0] = az_el_r[2] * std::sin (az_el_r[1]) * std::cos (az_el_r[0]);
xyz[1] = az_el_r[2] * std::sin (az_el_r[1]) * std::sin (az_el_r[0]);
xyz[2] = az_el_r[2] * cos (az_el_r[1]);
} else {
xyz[0] = std::sin (az_el_r[1]) * std::cos (az_el_r[0]);
xyz[1] = std::sin (az_el_r[1]) * std::sin (az_el_r[0]);
xyz[2] = cos (az_el_r[1]);
}
}
//! convert matrix of spherical coordinates to Cartesian coordinates
template <class MatrixType1, class MatrixType2>
inline typename std::enable_if<!MatrixType1::IsVectorAtCompileTime, void>::type
spherical2cartesian (const MatrixType1& az_el, MatrixType2&& cartesian)
{
cartesian.resize (az_el.rows(), 3);
for (ssize_t dir = 0; dir < az_el.rows(); ++dir)
spherical2cartesian (az_el.row (dir), cartesian.row (dir));
}
//! convert matrix of spherical coordinates to Cartesian coordinates
template <class MatrixType>
inline typename std::enable_if<!MatrixType::IsVectorAtCompileTime, Eigen::MatrixXd>::type
spherical2cartesian (const MatrixType& az_el)
{
Eigen::MatrixXd cartesian (az_el.rows(), 3);
for (ssize_t dir = 0; dir < az_el.rows(); ++dir)
spherical2cartesian (az_el.row (dir), cartesian.row (dir));
return cartesian;
}
//! convert Cartesian coordinates to spherical coordinates
template <class VectorType1, class VectorType2>
inline typename std::enable_if<VectorType1::IsVectorAtCompileTime, void>::type
cartesian2spherical (const VectorType1& xyz, VectorType2&& az_el_r)
{
auto r = std::sqrt (Math::pow2(xyz[0]) + Math::pow2(xyz[1]) + Math::pow2(xyz[2]));
az_el_r[0] = std::atan2 (xyz[1], xyz[0]);
az_el_r[1] = std::acos (xyz[2] / r);
if (az_el_r.size() == 3)
az_el_r[2] = r;
}
//! convert matrix of Cartesian coordinates to spherical coordinates
template <class MatrixType1, class MatrixType2>
inline typename std::enable_if<!MatrixType1::IsVectorAtCompileTime, void>::type
cartesian2spherical (const MatrixType1& cartesian, MatrixType2&& az_el, bool include_r = false)
{
az_el.allocate (cartesian.rows(), include_r ? 3 : 2);
for (ssize_t dir = 0; dir < cartesian.rows(); ++dir)
cartesian2spherical (cartesian.row (dir), az_el.row (dir));
}
//! convert matrix of Cartesian coordinates to spherical coordinates
template <class MatrixType>
inline typename std::enable_if<!MatrixType::IsVectorAtCompileTime, Eigen::MatrixXd>::type
cartesian2spherical (const MatrixType& cartesian, bool include_r = false)
{
Eigen::MatrixXd az_el (cartesian.rows(), include_r ? 3 : 2);
for (ssize_t dir = 0; dir < cartesian.rows(); ++dir)
cartesian2spherical (cartesian.row (dir), az_el.row (dir));
return az_el;
}
//! normalise a set of Cartesian coordinates
template <class MatrixType>
inline void normalise_cartesian (MatrixType& cartesian)
{
assert (cartesian.cols() == 3);
for (ssize_t i = 0; i < cartesian.rows(); i++) {
auto norm = cartesian.row(i).norm();
if (norm)
cartesian.row(i).array() /= norm;
}
}
}
}
}
#endif
|
