This repository has been archived by the owner on Apr 16, 2024. It is now read-only.
-
Notifications
You must be signed in to change notification settings - Fork 0
/
EulerAngles_8h_source.html
319 lines (317 loc) · 37.2 KB
/
EulerAngles_8h_source.html
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
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.9.7"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Eigen: EulerAngles.h Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="resize.js"></script>
<script type="text/javascript" src="navtreedata.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
$(document).ready(function() { init_search(); });
/* @license-end */
</script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
jax: ["input/TeX","output/HTML-CSS"],
});
</script>
<script type="text/javascript" async="async" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js"></script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
<link href="eigendoxy.css" rel="stylesheet" type="text/css">
<!-- -->
<script type="text/javascript" src="eigen_navtree_hacks.js"></script>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr style="height: 56px;">
<td id="projectlogo"><img alt="Logo" src="Eigen_Silly_Professor_64x64.png"/></td>
<td id="projectalign" style="padding-left: 0.5em;">
<div id="projectname"><a href="http://eigen.tuxfamily.org">Eigen</a>
 <span id="projectnumber">3.4.90 (git rev 21cd3fe20990a5ac1d683806f605110962aac3f1)</span>
</div>
</td>
<td> <div id="MSearchBox" class="MSearchBoxInactive">
<span class="left">
<span id="MSearchSelect" onmouseover="return searchBox.OnSearchSelectShow()" onmouseout="return searchBox.OnSearchSelectHide()"> </span>
<input type="text" id="MSearchField" value="" placeholder="Search" accesskey="S"
onfocus="searchBox.OnSearchFieldFocus(true)"
onblur="searchBox.OnSearchFieldFocus(false)"
onkeyup="searchBox.OnSearchFieldChange(event)"/>
</span><span class="right">
<a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.svg" alt=""/></a>
</span>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.9.7 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
var searchBox = new SearchBox("searchBox", "search/",'.html');
/* @license-end */
</script>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
<div id="nav-tree">
<div id="nav-tree-contents">
<div id="nav-sync" class="sync"></div>
</div>
</div>
<div id="splitbar" style="-moz-user-select:none;"
class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
$(document).ready(function(){initNavTree('EulerAngles_8h_source.html',''); initResizable(); });
/* @license-end */
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<div id="MSearchResults">
<div class="SRPage">
<div id="SRIndex">
<div id="SRResults"></div>
<div class="SRStatus" id="Loading">Loading...</div>
<div class="SRStatus" id="Searching">Searching...</div>
<div class="SRStatus" id="NoMatches">No Matches</div>
</div>
</div>
</div>
</div>
<div class="header">
<div class="headertitle"><div class="title">EulerAngles.h</div></div>
</div><!--header-->
<div class="contents">
<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// for linear algebra.</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">//</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr></span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">// Copyright (C) 2023 Juraj Oršulić, University of Zagreb <juraj.orsulic@fer.hr></span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">//</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="preprocessor">#ifndef EIGEN_EULERANGLES_H</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#define EIGEN_EULERANGLES_H</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include "./InternalHeaderCheck.h"</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span>EIGEN_DEVICE_FUNC <span class="keyword">inline</span> Matrix<typename MatrixBase<Derived>::Scalar,3,1></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"><a class="line" href="group__Geometry__Module.html#gaf67ac87150a889f5e320e39186b1c432"> 43</a></span><a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::canonicalEulerAngles</a>(<a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> a0, <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> a1, <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> a2)<span class="keyword"> const</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="comment">/* Implemented from Graphics Gems IV */</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> </div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <a class="code hl_class" href="classEigen_1_1Matrix.html">Matrix<Scalar, 3, 1></a> res;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> odd = ((a0 + 1) % 3 == a1) ? 0 : 1;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = a0;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = (a0 + 1 + odd) % 3;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = (a0 + 2 - odd) % 3;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordflow">if</span> (a0 == a2)</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// Proper Euler angles (same first and last axis).</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// The i, j, k indices enable addressing the input matrix as the XYX archetype matrix (see Graphics Gems IV),</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// where e.g. coeff(k, i) means third column, first row in the XYX archetype matrix:</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// c2 s2s1 s2c1</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// s2s3 -c2s1s3 + c1c3 -c2c1s3 - s1c3</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// -s2c3 c2s1c3 + c1s3 c2c1c3 - s1s3</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// Note: s2 is always positive.</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a> s2 = numext::hypot(coeff(j, i), coeff(k, i));</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">if</span> (odd)</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> {</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> res[0] = numext::atan2(coeff(j, i), coeff(k, i));</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// s2 is always positive, so res[1] will be within the canonical [0, pi] range</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> res[1] = numext::atan2(s2, coeff(i, i));</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> }</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> {</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// In the !odd case, signs of all three angles are flipped at the very end. To keep the solution within the canonical range,</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// we flip the solution and make res[1] always negative here (since s2 is always positive, -atan2(s2, c2) will always be negative).</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// The final flip at the end due to !odd will thus make res[1] positive and canonical.</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// NB: in the general case, there are two correct solutions, but only one is canonical. For proper Euler angles,</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// flipping from one solution to the other involves flipping the sign of the second angle res[1] and adding/subtracting pi</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// to the first and third angles. The addition/subtraction of pi to the first angle res[0] is handled here by flipping</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// the signs of arguments to atan2, while the calculation of the third angle does not need special adjustment since</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// it uses the adjusted res[0] as the input and produces a correct result.</span></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> res[0] = numext::atan2(-coeff(j, i), -coeff(k, i));</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> res[1] = -numext::atan2(s2, coeff(i, i));</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> }</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// we can compute their respective rotation, and apply its inverse to M. Since the result must</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// be a rotation around x, we have:</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="comment">//</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// c2 s1.s2 c1.s2 1 0 0</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// 0 c1 -s1 * M = 0 c3 s3</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// -s2 s1.c2 c1.c2 0 -s3 c3</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="comment">//</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a> s1 = numext::sin(res[0]);</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a> c1 = numext::cos(res[0]);</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> res[2] = numext::atan2(c1 * coeff(j, k) - s1 * coeff(k, k), c1 * coeff(j, j) - s1 * coeff(k, j));</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> }</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> {</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// Tait-Bryan angles (all three axes are different; typically used for yaw-pitch-roll calculations).</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// The i, j, k indices enable addressing the input matrix as the XYZ archetype matrix (see Graphics Gems IV),</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="comment">// where e.g. coeff(k, i) means third column, first row in the XYZ archetype matrix:</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="comment">// c2c3 s2s1c3 - c1s3 s2c1c3 + s1s3</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="comment">// c2s3 s2s1s3 + c1c3 s2c1s3 - s1c3</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="comment">// -s2 c2s1 c2c1</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> res[0] = numext::atan2(coeff(j, k), coeff(k, k));</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> </div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a> c2 = numext::hypot(coeff(i, i), coeff(i, j));</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="comment">// c2 is always positive, so the following atan2 will always return a result in the correct canonical middle angle range [-pi/2, pi/2]</span></div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> res[1] = numext::atan2(-coeff(i, k), c2);</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a> s1 = numext::sin(res[0]);</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a> c1 = numext::cos(res[0]);</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> res[2] = numext::atan2(s1 * coeff(k, i) - c1 * coeff(j, i), c1 * coeff(j, j) - s1 * coeff(k, j));</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> }</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordflow">if</span> (!odd)</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> {</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> res = -res;</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> }</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> </div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">return</span> res;</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span>}</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> </div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span>EIGEN_DEPRECATED EIGEN_DEVICE_FUNC <span class="keyword">inline</span> <a class="code hl_class" href="classEigen_1_1Matrix.html">Matrix<typename MatrixBase<Derived>::Scalar</a>,3,1></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"><a class="line" href="group__Geometry__Module.html#ga5a61d4a29ac24ace7043a6301c21e52c"> 139</a></span><a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::eulerAngles</a>(<a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> a0, <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> a1, <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> a2)<span class="keyword"> const</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="comment">/* Implemented from Graphics Gems IV */</span></div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> </div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <a class="code hl_class" href="classEigen_1_1Matrix.html">Matrix<Scalar, 3, 1></a> res;</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> odd = ((a0 + 1) % 3 == a1) ? 0 : 1;</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = a0;</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = (a0 + 1 + odd) % 3;</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = (a0 + 2 - odd) % 3;</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> </div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keywordflow">if</span> (a0 == a2)</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> {</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> res[0] = numext::atan2(coeff(j, i), coeff(k, i));</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keywordflow">if</span> ((odd && res[0] < <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a>(0)) || ((!odd) && res[0] > <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a>(0)))</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> {</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordflow">if</span> (res[0] > <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a>(0))</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> {</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> res[0] -= <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a>(EIGEN_PI);</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> }</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> {</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> res[0] += <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a>(EIGEN_PI);</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> }</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> </div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a> s2 = numext::hypot(coeff(j, i), coeff(k, i));</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> res[1] = -numext::atan2(s2, coeff(i, i));</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> }</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> {</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a> s2 = numext::hypot(coeff(j, i), coeff(k, i));</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> res[1] = numext::atan2(s2, coeff(i, i));</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> }</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> </div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="comment">// With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,</span></div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="comment">// we can compute their respective rotation, and apply its inverse to M. Since the result must</span></div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="comment">// be a rotation around x, we have:</span></div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="comment">//</span></div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="comment">// c2 s1.s2 c1.s2 1 0 0</span></div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="comment">// 0 c1 -s1 * M = 0 c3 s3</span></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="comment">// -s2 s1.c2 c1.c2 0 -s3 c3</span></div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="comment">//</span></div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> </div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a> s1 = numext::sin(res[0]);</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a> c1 = numext::cos(res[0]);</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> res[2] = numext::atan2(c1 * coeff(j, k) - s1 * coeff(k, k), c1 * coeff(j, j) - s1 * coeff(k, j));</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> }</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> {</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> res[0] = numext::atan2(coeff(j, k), coeff(k, k));</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a> c2 = numext::hypot(coeff(i, i), coeff(i, j));</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="keywordflow">if</span> ((odd && res[0] < <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a>(0)) || ((!odd) && res[0] > <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a>(0)))</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> {</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keywordflow">if</span> (res[0] > <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a>(0))</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> {</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> res[0] -= <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a>(EIGEN_PI);</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> }</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> {</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> res[0] += <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a>(EIGEN_PI);</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> }</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> res[1] = numext::atan2(-coeff(i, k), -c2);</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> }</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> {</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> res[1] = numext::atan2(-coeff(i, k), c2);</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> }</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a> s1 = numext::sin(res[0]);</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a> c1 = numext::cos(res[0]);</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> res[2] = numext::atan2(s1 * coeff(k, i) - c1 * coeff(j, i), c1 * coeff(j, j) - s1 * coeff(k, j));</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> }</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="keywordflow">if</span> (!odd)</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> {</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> res = -res;</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> }</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> </div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="keywordflow">return</span> res;</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span>}</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> </div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span>} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> </div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span><span class="preprocessor">#endif </span><span class="comment">// EIGEN_EULERANGLES_H</span></div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_a5feed465b3a8e60c47e73ecce83e39a2"><div class="ttname"><a href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Eigen::DenseBase::Scalar</a></div><div class="ttdeci">internal::traits< Derived >::Scalar Scalar</div><div class="ttdef"><b>Definition</b> DenseBase.h:61</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions.</div><div class="ttdef"><b>Definition</b> MatrixBase.h:52</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix</a></div><div class="ttdoc">The matrix class, also used for vectors and row-vectors.</div><div class="ttdef"><b>Definition</b> Matrix.h:182</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition</b> Meta.h:82</div></div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="dir_a62d91f57b5fefafb116d3f5c1ce792a.html">Eigen</a></li><li class="navelem"><a class="el" href="dir_f84311377820247c2dbcf5d6a63ab308.html">src</a></li><li class="navelem"><a class="el" href="dir_02f13bb04c88c5da299a51110c156190.html">Geometry</a></li><li class="navelem"><b>EulerAngles.h</b></li>
<li class="footer">Generated on Tue Jul 11 2023 17:10:20 for Eigen by
<a href="http://www.doxygen.org/index.html">
<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.9.7 </li>
</ul>
</div>
</body>
</html>