test_Rot3.py
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1 """
2 GTSAM Copyright 2010-2019, Georgia Tech Research Corporation,
3 Atlanta, Georgia 30332-0415
4 All Rights Reserved
5 See LICENSE for the license information
6 Rot3 unit tests.
7 Author: John Lambert
8 """
9 # pylint: disable=no-name-in-module
10 
11 import unittest
12 
13 import numpy as np
14 
15 import gtsam
16 from gtsam import Point3, Rot3, Unit3
17 from gtsam.utils.test_case import GtsamTestCase
18 
19 
20 R1_R2_pairs = [
21  (
22  [
23  [0.994283, -0.10356, 0.0260251],
24  [0.102811, 0.994289, 0.0286205],
25  [-0.0288404, -0.0257812, 0.999251],
26  ],
27  [
28  [-0.994235, 0.0918291, -0.0553602],
29  [-0.0987317, -0.582632, 0.806718],
30  [0.0418251, 0.807532, 0.588339],
31  ],
32  ),
33  (
34  [
35  [0.999823, -0.000724729, 0.0187896],
36  [0.00220672, 0.996874, -0.0789728],
37  [-0.0186736, 0.0790003, 0.9967],
38  ],
39  [
40  [-0.99946, -0.0155217, -0.0289749],
41  [-0.0306159, 0.760422, 0.648707],
42  [0.0119641, 0.649244, -0.760487],
43  ],
44  ),
45  (
46  [
47  [0.999976, 0.00455542, -0.00529608],
48  [-0.00579633, 0.964214, -0.265062],
49  [0.00389908, 0.265086, 0.964217],
50  ],
51  [
52  [-0.999912, -0.0123323, -0.00489179],
53  [-0.00739095, 0.21159, 0.977331],
54  [-0.0110179, 0.977281, -0.211663],
55  ],
56  ),
57  (
58  [
59  [0.998801, 0.0449026, 0.019479],
60  [-0.0448727, 0.998991, -0.00197348],
61  [-0.0195479, 0.00109704, 0.999808],
62  ],
63  [
64  [-0.999144, -0.0406154, -0.00800012],
65  [0.0406017, -0.999174, 0.00185875],
66  [-0.00806909, 0.00153352, 0.999966],
67  ],
68  ),
69  (
70  [
71  [0.587202, 0.00034062, -0.80944],
72  [0.394859, 0.872825, 0.286815],
73  [0.706597, -0.488034, 0.51239],
74  ],
75  [
76  [-0.999565, -0.028095, -0.00905389],
77  [0.0192863, -0.853838, 0.520182],
78  [-0.0223455, 0.519782, 0.854007],
79  ],
80  ),
81  (
82  [
83  [0.998798, 0.0370584, 0.0320815],
84  [-0.0355966, 0.998353, -0.0449943],
85  [-0.033696, 0.0437982, 0.998472],
86  ],
87  [
88  [-0.999942, -0.010745, -0.00132538],
89  [-0.000998705, -0.0304045, 0.999538],
90  [-0.0107807, 0.999481, 0.0303914],
91  ],
92  ),
93  (
94  [
95  [0.998755, 0.00708291, -0.0493744],
96  [-0.00742097, 0.99995, -0.00666709],
97  [0.0493247, 0.0070252, 0.998758],
98  ],
99  [
100  [-0.998434, 0.0104672, 0.0549825],
101  [0.0115323, 0.999751, 0.0190859],
102  [-0.0547691, 0.01969, -0.998307],
103  ],
104  ),
105  (
106  [
107  [0.990471, 0.0997485, -0.0949595],
108  [-0.117924, 0.970427, -0.210631],
109  [0.0711411, 0.219822, 0.972943],
110  ],
111  [
112  [-0.99192, -0.125627, 0.0177888],
113  [0.126478, -0.967866, 0.217348],
114  [-0.0100874, 0.217839, 0.975933],
115  ],
116  ),
117  (
118  [
119  [-0.780894, -0.578319, -0.236116],
120  [0.34478, -0.0838381, -0.934932],
121  [0.520894, -0.811491, 0.264862],
122  ],
123  [
124  [-0.99345, 0.00261746, -0.114244],
125  [-0.112503, 0.152922, 0.981815],
126  [0.0200403, 0.988236, -0.151626],
127  ],
128  ),
129  (
130  [
131  [0.968425, 0.0466097, 0.244911],
132  [-0.218867, 0.629346, 0.745668],
133  [-0.119378, -0.775726, 0.619676],
134  ],
135  [
136  [-0.971208, 0.00666431, -0.238143],
137  [0.0937886, 0.929584, -0.35648],
138  [0.218998, -0.368551, -0.903444],
139  ],
140  ),
141  (
142  [
143  [0.998512, 0.0449168, -0.0309146],
144  [-0.0344032, 0.958823, 0.281914],
145  [0.0423043, -0.280431, 0.958941],
146  ],
147  [
148  [-0.999713, 0.00732431, 0.0228168],
149  [-0.00759688, 0.806166, -0.59164],
150  [-0.0227275, -0.591644, -0.805879],
151  ],
152  ),
153  (
154  [
155  [0.981814, 0.00930728, 0.189617],
156  [-0.0084101, 0.999949, -0.00553563],
157  [-0.189659, 0.00384026, 0.981843],
158  ],
159  [
160  [-0.981359, 0.00722349, -0.192051],
161  [0.00148564, 0.999549, 0.0300036],
162  [0.192182, 0.0291591, -0.980927],
163  ],
164  ),
165  (
166  [
167  [0.972544, -0.215591, 0.0876242],
168  [0.220661, 0.973915, -0.0529018],
169  [-0.0739333, 0.0707846, 0.994748],
170  ],
171  [
172  [-0.971294, 0.215675, -0.100371],
173  [-0.23035, -0.747337, 0.62324],
174  [0.0594069, 0.628469, 0.775564],
175  ],
176  ),
177  (
178  [
179  [0.989488, 0.0152447, 0.143808],
180  [-0.0160974, 0.999859, 0.00476753],
181  [-0.143715, -0.00703235, 0.989594],
182  ],
183  [
184  [-0.988492, 0.0124362, -0.150766],
185  [0.00992423, 0.999799, 0.0174037],
186  [0.150952, 0.0157072, -0.988417],
187  ],
188  ),
189  (
190  [
191  [0.99026, 0.109934, -0.0854388],
192  [-0.0973012, 0.985345, 0.140096],
193  [0.099588, -0.130418, 0.986445],
194  ],
195  [
196  [-0.994239, 0.0206112, 0.1052],
197  [0.0227944, 0.999548, 0.0195944],
198  [-0.104748, 0.0218794, -0.994259],
199  ],
200  ),
201  (
202  [
203  [0.988981, 0.132742, -0.0655406],
204  [-0.113134, 0.963226, 0.243712],
205  [0.0954813, -0.233612, 0.96763],
206  ],
207  [
208  [-0.989473, -0.144453, 0.00888153],
209  [0.112318, -0.727754, 0.67658],
210  [-0.0912697, 0.670455, 0.736317],
211  ],
212  ),
213  (
214  [
215  [0.13315, -0.722685, 0.678231],
216  [0.255831, 0.686195, 0.680946],
217  [-0.957508, 0.0828446, 0.276252],
218  ],
219  [
220  [-0.233019, 0.0127274, -0.97239],
221  [-0.0143824, 0.99976, 0.0165321],
222  [0.972367, 0.0178377, -0.23278],
223  ],
224  ),
225  (
226  [
227  [0.906305, -0.0179617, -0.422243],
228  [0.0246095, 0.999644, 0.0102984],
229  [0.421908, -0.0197247, 0.906424],
230  ],
231  [
232  [-0.90393, 0.0136293, 0.427466],
233  [0.0169755, 0.999848, 0.0040176],
234  [-0.427346, 0.0108879, -0.904024],
235  ],
236  ),
237  (
238  [
239  [0.999808, 0.0177784, -0.00826505],
240  [-0.0177075, 0.999806, 0.00856939],
241  [0.0084158, -0.00842139, 0.999929],
242  ],
243  [
244  [-0.999901, -0.0141114, 0.00072392],
245  [0.00130602, -0.0413336, 0.999145],
246  [-0.0140699, 0.999047, 0.0413473],
247  ],
248  ),
249  (
250  [
251  [0.985811, -0.161425, 0.0460375],
252  [0.154776, 0.980269, 0.12295],
253  [-0.0649764, -0.11408, 0.991344],
254  ],
255  [
256  [-0.985689, 0.137931, -0.09692],
257  [-0.162627, -0.626622, 0.762168],
258  [0.0443951, 0.767022, 0.640085],
259  ],
260  ),
261  (
262  [
263  [0.956652, -0.0116044, 0.291001],
264  [0.05108, 0.990402, -0.128428],
265  [-0.286718, 0.137726, 0.948064],
266  ],
267  [
268  [-0.956189, 0.00996594, -0.292585],
269  [-0.0397033, 0.985772, 0.16333],
270  [0.29005, 0.167791, -0.942189],
271  ],
272  ),
273  (
274  [
275  [0.783763, -0.0181248, -0.620796],
276  [-0.0386421, 0.996214, -0.0778717],
277  [0.619857, 0.0850218, 0.780095],
278  ],
279  [
280  [-0.780275, 0.0093644, 0.625368],
281  [-0.0221791, 0.998845, -0.0426297],
282  [-0.625045, -0.0471329, -0.779165],
283  ],
284  ),
285  (
286  [
287  [0.890984, 0.0232464, -0.453439],
288  [-0.0221215, 0.999725, 0.00778511],
289  [0.453495, 0.00309433, 0.891253],
290  ],
291  [
292  [-0.890178, 0.0290103, 0.45469],
293  [0.0337152, 0.999429, 0.0022403],
294  [-0.454366, 0.0173244, -0.890648],
295  ],
296  ),
297  (
298  [
299  [0.998177, -0.0119546, 0.0591504],
300  [0.00277494, 0.988238, 0.152901],
301  [-0.0602825, -0.152458, 0.98647],
302  ],
303  [
304  [-0.997444, 0.00871865, -0.0709414],
305  [0.0197108, 0.987598, -0.155762],
306  [0.0687035, -0.156762, -0.985246],
307  ],
308  ),
309  (
310  [
311  [0.985214, 0.164929, 0.0463837],
312  [-0.166966, 0.984975, 0.0441225],
313  [-0.0384096, -0.0512146, 0.997949],
314  ],
315  [
316  [-0.999472, -0.000819214, -0.0325087],
317  [-0.00344291, 0.99673, 0.0807324],
318  [0.0323362, 0.0808019, -0.996206],
319  ],
320  ),
321  (
322  [
323  [0.998499, 0.0465241, 0.0288955],
324  [-0.0454764, 0.99832, -0.0359142],
325  [-0.0305178, 0.0345463, 0.998937],
326  ],
327  [
328  [-0.999441, 0.00412484, -0.0332105],
329  [0.00374685, 0.999928, 0.0114307],
330  [0.0332552, 0.0112999, -0.999384],
331  ],
332  ),
333  (
334  [
335  [0.10101, -0.943239, -0.316381],
336  [0.841334, -0.0887423, 0.533182],
337  [-0.530994, -0.320039, 0.784615],
338  ],
339  [
340  [-0.725665, 0.0153749, -0.687878],
341  [-0.304813, 0.889109, 0.34143],
342  [0.616848, 0.457438, -0.640509],
343  ],
344  ),
345  (
346  [
347  [0.843428, 0.174952, 0.507958],
348  [0.0435637, 0.920106, -0.389239],
349  [-0.535473, 0.350423, 0.768422],
350  ],
351  [
352  [-0.835464, 0.0040872, -0.549533],
353  [0.00227251, 0.999989, 0.00398241],
354  [0.549543, 0.00207845, -0.835464],
355  ],
356  ),
357  (
358  [
359  [0.999897, -0.0142888, -0.00160177],
360  [0.0141561, 0.997826, -0.064364],
361  [0.00251798, 0.0643346, 0.997925],
362  ],
363  [
364  [-0.999956, 0.00898988, 0.00296485],
365  [0.00900757, 0.999941, 0.00601779],
366  [-0.00291058, 0.00604429, -0.999978],
367  ],
368  ),
369  (
370  [
371  [0.999477, -0.0204859, 0.0250096],
372  [0.0126204, 0.959462, 0.281557],
373  [-0.0297637, -0.281094, 0.959219],
374  ],
375  [
376  [-0.999384, 0.0172602, -0.0305795],
377  [-0.0254425, 0.24428, 0.969371],
378  [0.0242012, 0.969551, -0.24369],
379  ],
380  ),
381  (
382  [
383  [0.984597, 0.173474, -0.0218106],
384  [-0.15145, 0.783891, -0.602145],
385  [-0.0873592, 0.596173, 0.798089],
386  ],
387  [
388  [-0.998608, -0.0432858, 0.0301827],
389  [-0.00287128, 0.615692, 0.787983],
390  [-0.0526917, 0.786797, -0.61496],
391  ],
392  ),
393  (
394  [
395  [0.917099, -0.3072, 0.254083],
396  [0.303902, 0.951219, 0.0531566],
397  [-0.258018, 0.0284665, 0.965721],
398  ],
399  [
400  [-0.931191, 0.347008, -0.111675],
401  [-0.352102, -0.77686, 0.522032],
402  [0.0943935, 0.52543, 0.845586],
403  ],
404  ),
405  (
406  [
407  [0.991706, 0.0721037, -0.106393],
408  [-0.0995017, 0.954693, -0.280464],
409  [0.0813505, 0.288725, 0.95395],
410  ],
411  [
412  [-0.995306, 0.00106317, 0.0967833],
413  [0.0167662, 0.986717, 0.161583],
414  [-0.0953259, 0.162447, -0.982103],
415  ],
416  ),
417  (
418  [
419  [0.997078, 0.0478273, -0.0595641],
420  [-0.0348316, 0.978617, 0.202719],
421  [0.067986, -0.200052, 0.977424],
422  ],
423  [
424  [-0.997925, -0.0439691, 0.0470461],
425  [0.0643829, -0.695474, 0.715663],
426  [0.00125305, 0.717207, 0.696861],
427  ],
428  ),
429  (
430  [
431  [0.972749, -0.0233882, -0.230677],
432  [0.0255773, 0.999652, 0.00650349],
433  [0.230445, -0.0122264, 0.973009],
434  ],
435  [
436  [-0.973286, 0.0147558, 0.229126],
437  [0.0145644, 0.999891, -0.00252631],
438  [-0.229138, 0.000878362, -0.973394],
439  ],
440  ),
441  (
442  [
443  [0.999271, 0.00700481, 0.0375381],
444  [-0.0348202, 0.57069, 0.820427],
445  [-0.0156757, -0.821136, 0.570517],
446  ],
447  [
448  [-0.999805, -0.0198049, 0.000539906],
449  [0.0179848, -0.89584, 0.444015],
450  [-0.00831113, 0.443938, 0.89602],
451  ],
452  ),
453  (
454  [
455  [0.975255, -0.0207895, 0.220104],
456  [0.0252764, 0.999526, -0.0175888],
457  [-0.219634, 0.022717, 0.975318],
458  ],
459  [
460  [-0.975573, 0.0128154, -0.219304],
461  [0.0106554, 0.999882, 0.0110292],
462  [0.219419, 0.00842303, -0.975594],
463  ],
464  ),
465  (
466  [
467  [-0.433961, -0.658151, -0.615236],
468  [0.610442, -0.717039, 0.336476],
469  [-0.6626, -0.229548, 0.71293],
470  ],
471  [
472  [-0.998516, -0.00675119, -0.054067],
473  [-0.00405539, 0.99875, -0.0498174],
474  [0.0543358, -0.0495237, -0.997296],
475  ],
476  ),
477  (
478  [
479  [0.942764, -0.0126807, -0.333221],
480  [-0.0017175, 0.999079, -0.042879],
481  [0.333458, 0.0409971, 0.941873],
482  ],
483  [
484  [-0.942228, -0.0109444, 0.334798],
485  [0.0110573, 0.997905, 0.0637396],
486  [-0.334794, 0.0637589, -0.940133],
487  ],
488  ),
489  (
490  [
491  [0.962038, 0.0147987, 0.272515],
492  [-0.0185974, 0.999762, 0.0113615],
493  [-0.272283, -0.0159982, 0.962084],
494  ],
495  [
496  [-0.959802, 0.0113708, -0.280451],
497  [0.00982126, 0.999928, 0.00692958],
498  [0.280509, 0.00389678, -0.959845],
499  ],
500  ),
501  (
502  [
503  [0.998414, 0.0139348, 0.0545528],
504  [-0.0226877, 0.986318, 0.163283],
505  [-0.0515311, -0.164262, 0.98507],
506  ],
507  [
508  [-0.998641, -0.000695993, -0.0521343],
509  [0.0182534, 0.931965, -0.362087],
510  [0.0488394, -0.362547, -0.930686],
511  ],
512  ),
513  (
514  [
515  [0.999705, -0.0234518, -0.00633743],
516  [0.0235916, 0.999458, 0.0229643],
517  [0.00579544, -0.023107, 0.999716],
518  ],
519  [
520  [-0.999901, 0.004436, 0.0133471],
521  [-0.00306106, 0.85758, -0.514342],
522  [-0.0137278, -0.514332, -0.857481],
523  ],
524  ),
525  (
526  [
527  [0.998617, -0.051704, 0.0094837],
528  [0.0484292, 0.975079, 0.216506],
529  [-0.0204416, -0.215748, 0.976235],
530  ],
531  [
532  [-0.999959, -0.00295958, -0.00862907],
533  [-0.00313279, 0.999792, 0.0201361],
534  [0.00856768, 0.0201625, -0.999761],
535  ],
536  ),
537  (
538  [
539  [0.999121, 0.0345472, -0.023733],
540  [-0.0333175, 0.998174, 0.0503881],
541  [0.0254304, -0.0495531, 0.998448],
542  ],
543  [
544  [-0.999272, -0.0337466, 0.0178065],
545  [0.0200629, -0.0677624, 0.9975],
546  [-0.0324556, 0.997131, 0.0683898],
547  ],
548  ),
549  (
550  [
551  [0.989017, 0.139841, -0.0478525],
552  [-0.131355, 0.683201, -0.718319],
553  [-0.0677572, 0.716715, 0.694067],
554  ],
555  [
556  [-0.995236, 0.00457798, 0.097401],
557  [0.097488, 0.0258334, 0.994902],
558  [0.00203912, 0.999657, -0.0261574],
559  ],
560  ),
561  (
562  [
563  [0.961528, 0.249402, 0.11516],
564  [-0.204522, 0.9298, -0.306009],
565  [-0.183395, 0.270684, 0.945038],
566  ],
567  [
568  [-0.999566, -0.0233216, 0.0180679],
569  [0.012372, 0.224583, 0.974377],
570  [-0.0267822, 0.974177, -0.224197],
571  ],
572  ),
573  (
574  [
575  [0.865581, 0.0252563, -0.500131],
576  [0.0302583, 0.994265, 0.102578],
577  [0.499853, -0.103923, 0.859853],
578  ],
579  [
580  [-0.866693, 0.0042288, 0.498824],
581  [0.0129331, 0.999818, 0.0139949],
582  [-0.498674, 0.0185807, -0.866591],
583  ],
584  ),
585  (
586  [
587  [0.998999, -0.0213419, -0.0393009],
588  [-0.0007582, 0.870578, -0.492031],
589  [0.0447153, 0.491568, 0.86969],
590  ],
591  [
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1700  ),
1701  (
1702  [
1703  [0.998677, -0.0372894, 0.0354002],
1704  [0.0242326, 0.948589, 0.315583],
1705  [-0.0453481, -0.314308, 0.948237],
1706  ],
1707  [
1708  [-0.999066, -0.00910724, -0.0422707],
1709  [-0.024629, 0.923353, 0.383161],
1710  [0.0355411, 0.383844, -0.922715],
1711  ],
1712  ),
1713  (
1714  [
1715  [0.931525, 0.00831028, 0.363583],
1716  [0.0192806, 0.997204, -0.0721909],
1717  [-0.363167, 0.0742577, 0.92876],
1718  ],
1719  [
1720  [-0.930052, -0.00174384, -0.367425],
1721  [-0.0268673, 0.997634, 0.0632737],
1722  [0.366445, 0.0687194, -0.927899],
1723  ],
1724  ),
1725  (
1726  [
1727  [-0.50483, -0.819216, 0.272087],
1728  [0.775688, -0.568816, -0.273414],
1729  [0.378753, 0.0730272, 0.922612],
1730  ],
1731  [
1732  [-0.981596, 0.00031926, 0.190974],
1733  [0.00652401, 0.999471, 0.0318616],
1734  [-0.190863, 0.0325211, -0.981079],
1735  ],
1736  ),
1737  (
1738  [
1739  [0.990518, -0.00195099, -0.137368],
1740  [-0.00164696, 0.999659, -0.0260735],
1741  [0.137372, 0.0260526, 0.990177],
1742  ],
1743  [
1744  [-0.991078, 0.00934835, 0.132961],
1745  [0.0106057, 0.999905, 0.00875176],
1746  [-0.132866, 0.0100839, -0.991083],
1747  ],
1748  ),
1749  (
1750  [
1751  [0.935049, -0.353081, 0.0318997],
1752  [0.257018, 0.737114, 0.624984],
1753  [-0.244184, -0.576192, 0.779985],
1754  ],
1755  [
1756  [-0.977342, -0.00167896, -0.211667],
1757  [-0.0448634, 0.978894, 0.199386],
1758  [0.206864, 0.204364, -0.956789],
1759  ],
1760  ),
1761  (
1762  [
1763  [0.998464, 0.0501172, 0.0236119],
1764  [-0.0498618, 0.998692, -0.0112844],
1765  [-0.0241466, 0.0100898, 0.999658],
1766  ],
1767  [
1768  [-0.999931, -0.0037971, -0.0112195],
1769  [-0.00640916, 0.970027, 0.242913],
1770  [0.00996085, 0.242968, -0.969984],
1771  ],
1772  ),
1773  (
1774  [
1775  [0.999893, -0.0108217, 0.00984537],
1776  [0.011201, 0.999164, -0.0393194],
1777  [-0.00941164, 0.0394255, 0.999178],
1778  ],
1779  [
1780  [-0.999886, 0.00730461, -0.0133396],
1781  [-0.0118202, -0.925163, 0.379391],
1782  [-0.00956982, 0.379504, 0.925142],
1783  ],
1784  ),
1785  (
1786  [
1787  [0.990922, -0.086745, 0.102709],
1788  [0.0847349, 0.99612, 0.0237834],
1789  [-0.104373, -0.0148644, 0.994427],
1790  ],
1791  [
1792  [-0.994922, -0.00197458, -0.10064],
1793  [-0.00242513, 0.999988, 0.00435525],
1794  [0.10063, 0.00457739, -0.994914],
1795  ],
1796  ),
1797  (
1798  [
1799  [0.999856, 0.00210734, -0.0168511],
1800  [-0.00557165, 0.978053, -0.20828],
1801  [0.0160424, 0.208344, 0.977924],
1802  ],
1803  [
1804  [-0.999698, 0.0048691, 0.0241226],
1805  [-0.00154306, 0.965899, -0.258915],
1806  [-0.0245606, -0.258874, -0.9656],
1807  ],
1808  ),
1809  (
1810  [
1811  [0.992858, -0.0249864, -0.116659],
1812  [0.0419872, 0.988447, 0.145634],
1813  [0.111673, -0.149492, 0.982436],
1814  ],
1815  [
1816  [-0.992324, 0.0357741, 0.118384],
1817  [-0.0419528, 0.803113, -0.594348],
1818  [-0.116338, -0.594752, -0.795447],
1819  ],
1820  ),
1821  (
1822  [
1823  [0.986821, -0.00531913, 0.161729],
1824  [0.00797365, 0.999844, -0.0157688],
1825  [-0.16162, 0.0168505, 0.986709],
1826  ],
1827  [
1828  [-0.985867, 0.0119402, -0.167109],
1829  [0.0141227, 0.99983, -0.0118784],
1830  [0.166939, -0.0140704, -0.985868],
1831  ],
1832  ),
1833  (
1834  [
1835  [0.999693, -0.0158939, -0.0190113],
1836  [0.0103599, 0.96501, -0.262007],
1837  [0.0225104, 0.261729, 0.964879],
1838  ],
1839  [
1840  [-0.999344, -0.0314781, -0.0180051],
1841  [-0.0250895, 0.241673, 0.970034],
1842  [-0.0261833, 0.969847, -0.242305],
1843  ],
1844  ),
1845  (
1846  [
1847  [0.977445, 0.0293661, 0.209138],
1848  [-0.0723687, 0.976903, 0.201057],
1849  [-0.198403, -0.211657, 0.956994],
1850  ],
1851  [
1852  [-0.976437, 0.00895131, -0.215624],
1853  [0.0552894, 0.976169, -0.20985],
1854  [0.208607, -0.216827, -0.953663],
1855  ],
1856  ),
1857  (
1858  [
1859  [0.994593, 0.0974797, -0.0358119],
1860  [-0.0822288, 0.949838, 0.301737],
1861  [0.0634288, -0.297161, 0.952718],
1862  ],
1863  [
1864  [-0.994192, -0.10746, -0.00604622],
1865  [0.078812, -0.7651, 0.639071],
1866  [-0.0733003, 0.634882, 0.769124],
1867  ],
1868  ),
1869  (
1870  [
1871  [0.365674, 0.282077, -0.88697],
1872  [-0.609177, 0.793033, 0.00105565],
1873  [0.703694, 0.539936, 0.461826],
1874  ],
1875  [
1876  [-0.469534, 0.0109062, 0.882848],
1877  [0.0060785, 0.99994, -0.00911984],
1878  [-0.882894, 0.00108445, -0.469572],
1879  ],
1880  ),
1881  (
1882  [
1883  [0.999956, 0.00903085, 0.0025358],
1884  [-0.00862738, 0.991574, -0.129252],
1885  [-0.00368169, 0.129224, 0.991609],
1886  ],
1887  [
1888  [-0.999976, 0.00322491, -0.00637541],
1889  [0.00379751, 0.995755, -0.0919687],
1890  [0.00605176, -0.0919907, -0.995743],
1891  ],
1892  ),
1893  (
1894  [
1895  [0.999982, -0.00398882, -0.00441072],
1896  [0.00411881, 0.999545, 0.0298655],
1897  [0.00428959, -0.0298832, 0.999544],
1898  ],
1899  [
1900  [-0.999931, -0.00315547, -0.0114491],
1901  [0.00300966, -0.999914, 0.0128304],
1902  [-0.0114875, 0.012796, 0.999853],
1903  ],
1904  ),
1905  (
1906  [
1907  [0.996613, 0.0781452, -0.0256245],
1908  [-0.0610516, 0.91178, 0.406116],
1909  [0.0550999, -0.403175, 0.913462],
1910  ],
1911  [
1912  [-0.996368, -0.084671, 0.00909851],
1913  [0.0540149, -0.545774, 0.83619],
1914  [-0.0658352, 0.833644, 0.548365],
1915  ],
1916  ),
1917  (
1918  [
1919  [0.961059, 0.139318, 0.238654],
1920  [-0.117488, 0.987672, -0.103448],
1921  [-0.250124, 0.0713812, 0.965579],
1922  ],
1923  [
1924  [-0.973397, 0.00782581, -0.228998],
1925  [-0.0621109, 0.952986, 0.296581],
1926  [0.220553, 0.302913, -0.927147],
1927  ],
1928  ),
1929  (
1930  [
1931  [0.156415, -0.982138, 0.104589],
1932  [-0.568896, -0.176149, -0.803323],
1933  [0.807398, 0.0661518, -0.586287],
1934  ],
1935  [
1936  [-0.992155, 0.0934304, -0.0830664],
1937  [-0.121171, -0.555137, 0.822887],
1938  [0.0307694, 0.826496, 0.562102],
1939  ],
1940  ),
1941  (
1942  [
1943  [0.997973, 0.0130328, -0.0622976],
1944  [-0.011111, 0.999455, 0.0310968],
1945  [0.0626689, -0.0303416, 0.997573],
1946  ],
1947  [
1948  [-0.997391, -0.00094697, 0.0722014],
1949  [-0.00271076, 0.9997, -0.024334],
1950  [-0.0721567, -0.024466, -0.997094],
1951  ],
1952  ),
1953  (
1954  [
1955  [0.913504, -0.0125928, -0.406634],
1956  [-0.108363, 0.95588, -0.27304],
1957  [0.392132, 0.293487, 0.871836],
1958  ],
1959  [
1960  [-0.909813, 0.0115348, 0.414861],
1961  [0.128636, 0.958223, 0.255464],
1962  [-0.394582, 0.28579, -0.873287],
1963  ],
1964  ),
1965  (
1966  [
1967  [0.932595, -0.0693644, 0.354197],
1968  [0.0984415, 0.993036, -0.0647231],
1969  [-0.347241, 0.0952281, 0.932928],
1970  ],
1971  [
1972  [-0.930498, 0.00578599, -0.366252],
1973  [-0.106202, 0.952666, 0.284867],
1974  [0.350564, 0.303964, -0.885839],
1975  ],
1976  ),
1977  (
1978  [
1979  [0.995668, -0.00475737, 0.0928567],
1980  [0.00890154, 0.99898, -0.0442667],
1981  [-0.0925514, 0.0449015, 0.994695],
1982  ],
1983  [
1984  [-0.996077, -0.0107986, -0.0878355],
1985  [0.00749423, 0.978669, -0.205305],
1986  [0.0881789, -0.205158, -0.974749],
1987  ],
1988  ),
1989  (
1990  [
1991  [0.99948, 0.0321999, 0.00146151],
1992  [-0.0321302, 0.998886, -0.0345513],
1993  [-0.00257243, 0.0344864, 0.999402],
1994  ],
1995  [
1996  [-0.999953, 0.00726142, -0.0065326],
1997  [0.00488529, 0.950962, 0.30927],
1998  [0.00845801, 0.309223, -0.950953],
1999  ],
2000  ),
2001 ]
2002 
2003 
2004 class TestRot3(GtsamTestCase):
2005  """Test selected Rot3 methods."""
2006 
2007  def test_axisangle(self) -> None:
2008  """Test .axisAngle() method."""
2009  # fmt: off
2010  R = np.array(
2011  [
2012  [ -0.999957, 0.00922903, 0.00203116],
2013  [ 0.00926964, 0.999739, 0.0208927],
2014  [ -0.0018374, 0.0209105, -0.999781]
2015  ])
2016  # fmt: on
2017 
2018  # get back angle in radians
2019  _, actual_angle = Rot3(R).axisAngle()
2020  expected_angle = 3.1396582
2021  np.testing.assert_almost_equal(actual_angle, expected_angle, 1e-7)
2022 
2023  def test_axis_angle_stress_test(self) -> None:
2024  """Test that .axisAngle() yields angles less than 180 degrees for specific inputs."""
2025  for (R1, R2) in R1_R2_pairs:
2026  R1 = Rot3(np.array(R1))
2027  R2 = Rot3(np.array(R2))
2028 
2029  i1Ri2 = R1.between(R2)
2030 
2031  axis, angle = i1Ri2.axisAngle()
2032  angle_deg = np.rad2deg(angle)
2033  assert angle_deg < 180
2034 
2035  def test_rotate(self) -> None:
2036  """Test that rotate() works for both Point3 and Unit3."""
2037  R = Rot3(np.array([[1, 0, 0], [0, -1, 0], [0, 0, -1]]))
2038  p = Point3(1., 1., 1.)
2039  u = Unit3(np.array([1, 1, 1]))
2040  actual_p = R.rotate(p)
2041  actual_u = R.rotate(u)
2042  expected_p = Point3(np.array([1, -1, -1]))
2043  expected_u = Unit3(np.array([1, -1, -1]))
2044  np.testing.assert_array_equal(actual_p, expected_p)
2045  np.testing.assert_array_equal(actual_u.point3(), expected_u.point3())
2046 
2047  def test_unrotate(self) -> None:
2048  """Test that unrotate() after rotate() yields original Point3/Unit3."""
2049  wRc = Rot3(np.array(R1_R2_pairs[0][0]))
2050  c_p = Point3(1., 1., 1.)
2051  c_u = Unit3(np.array([1, 1, 1]))
2052  w_p = wRc.rotate(c_p)
2053  w_u = wRc.rotate(c_u)
2054  actual_p = wRc.unrotate(w_p)
2055  actual_u = wRc.unrotate(w_u)
2056 
2057  np.testing.assert_almost_equal(actual_p, c_p, decimal=6)
2058  np.testing.assert_almost_equal(actual_u.point3(), c_u.point3(), decimal=6)
2059 
2060 
2061 if __name__ == "__main__":
2062  unittest.main()
gtsam::Rot3
Rot3 is a 3D rotation represented as a rotation matrix if the preprocessor symbol GTSAM_USE_QUATERNIO...
Definition: Rot3.h:58
gtsam::utils.test_case
Definition: test_case.py:1
test_Rot3.TestRot3
Definition: test_Rot3.py:2004
test_Rot3.TestRot3.test_unrotate
None test_unrotate(self)
Definition: test_Rot3.py:2047
gtsam::utils.test_case.GtsamTestCase
Definition: test_case.py:16
gtsam::Point3
Vector3 Point3
Definition: Point3.h:38
gtsam::Unit3
Represents a 3D point on a unit sphere.
Definition: Unit3.h:42
test_Rot3.TestRot3.test_axis_angle_stress_test
None test_axis_angle_stress_test(self)
Definition: test_Rot3.py:2023
test_Rot3.TestRot3.test_rotate
None test_rotate(self)
Definition: test_Rot3.py:2035
test_Rot3.TestRot3.test_axisangle
None test_axisangle(self)
Definition: test_Rot3.py:2007

gtsam
Author(s):
autogenerated on Sun Dec 22 2024 04:16:00