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Version:
4.3a0.dev202505130056 ▾
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"""
GTSAM Copyright 2010-2019, Georgia Tech Research Corporation,
Atlanta, Georgia 30332-0415
All Rights Reserved
See LICENSE for the license information
Rot3 unit tests.
Author: John Lambert
"""
# pylint: disable=no-name-in-module
import unittest
import numpy as np
import gtsam
from gtsam import Point3, Rot3, Unit3
from gtsam.utils.test_case import GtsamTestCase
R1_R2_pairs = [
(
[
[0.994283, -0.10356, 0.0260251],
[0.102811, 0.994289, 0.0286205],
[-0.0288404, -0.0257812, 0.999251],
],
[
[-0.994235, 0.0918291, -0.0553602],
[-0.0987317, -0.582632, 0.806718],
[0.0418251, 0.807532, 0.588339],
],
),
(
[
[0.999823, -0.000724729, 0.0187896],
[0.00220672, 0.996874, -0.0789728],
[-0.0186736, 0.0790003, 0.9967],
],
[
[-0.99946, -0.0155217, -0.0289749],
[-0.0306159, 0.760422, 0.648707],
[0.0119641, 0.649244, -0.760487],
],
),
(
[
[0.999976, 0.00455542, -0.00529608],
[-0.00579633, 0.964214, -0.265062],
[0.00389908, 0.265086, 0.964217],
],
[
[-0.999912, -0.0123323, -0.00489179],
[-0.00739095, 0.21159, 0.977331],
[-0.0110179, 0.977281, -0.211663],
],
),
(
[
[0.998801, 0.0449026, 0.019479],
[-0.0448727, 0.998991, -0.00197348],
[-0.0195479, 0.00109704, 0.999808],
],
[
[-0.999144, -0.0406154, -0.00800012],
[0.0406017, -0.999174, 0.00185875],
[-0.00806909, 0.00153352, 0.999966],
],
),
(
[
[0.587202, 0.00034062, -0.80944],
[0.394859, 0.872825, 0.286815],
[0.706597, -0.488034, 0.51239],
],
[
[-0.999565, -0.028095, -0.00905389],
[0.0192863, -0.853838, 0.520182],
[-0.0223455, 0.519782, 0.854007],
],
),
(
[
[0.998798, 0.0370584, 0.0320815],
[-0.0355966, 0.998353, -0.0449943],
[-0.033696, 0.0437982, 0.998472],
],
[
[-0.999942, -0.010745, -0.00132538],
[-0.000998705, -0.0304045, 0.999538],
[-0.0107807, 0.999481, 0.0303914],
],
),
(
[
[0.998755, 0.00708291, -0.0493744],
[-0.00742097, 0.99995, -0.00666709],
[0.0493247, 0.0070252, 0.998758],
],
[
[-0.998434, 0.0104672, 0.0549825],
[0.0115323, 0.999751, 0.0190859],
[-0.0547691, 0.01969, -0.998307],
],
),
(
[
[0.990471, 0.0997485, -0.0949595],
[-0.117924, 0.970427, -0.210631],
[0.0711411, 0.219822, 0.972943],
],
[
[-0.99192, -0.125627, 0.0177888],
[0.126478, -0.967866, 0.217348],
[-0.0100874, 0.217839, 0.975933],
],
),
(
[
[-0.780894, -0.578319, -0.236116],
[0.34478, -0.0838381, -0.934932],
[0.520894, -0.811491, 0.264862],
],
[
[-0.99345, 0.00261746, -0.114244],
[-0.112503, 0.152922, 0.981815],
[0.0200403, 0.988236, -0.151626],
],
),
(
[
[0.968425, 0.0466097, 0.244911],
[-0.218867, 0.629346, 0.745668],
[-0.119378, -0.775726, 0.619676],
],
[
[-0.971208, 0.00666431, -0.238143],
[0.0937886, 0.929584, -0.35648],
[0.218998, -0.368551, -0.903444],
],
),
(
[
[0.998512, 0.0449168, -0.0309146],
[-0.0344032, 0.958823, 0.281914],
[0.0423043, -0.280431, 0.958941],
],
[
[-0.999713, 0.00732431, 0.0228168],
[-0.00759688, 0.806166, -0.59164],
[-0.0227275, -0.591644, -0.805879],
],
),
(
[
[0.981814, 0.00930728, 0.189617],
[-0.0084101, 0.999949, -0.00553563],
[-0.189659, 0.00384026, 0.981843],
],
[
[-0.981359, 0.00722349, -0.192051],
[0.00148564, 0.999549, 0.0300036],
[0.192182, 0.0291591, -0.980927],
],
),
(
[
[0.972544, -0.215591, 0.0876242],
[0.220661, 0.973915, -0.0529018],
[-0.0739333, 0.0707846, 0.994748],
],
[
[-0.971294, 0.215675, -0.100371],
[-0.23035, -0.747337, 0.62324],
[0.0594069, 0.628469, 0.775564],
],
),
(
[
[0.989488, 0.0152447, 0.143808],
[-0.0160974, 0.999859, 0.00476753],
[-0.143715, -0.00703235, 0.989594],
],
[
[-0.988492, 0.0124362, -0.150766],
[0.00992423, 0.999799, 0.0174037],
[0.150952, 0.0157072, -0.988417],
],
),
(
[
[0.99026, 0.109934, -0.0854388],
[-0.0973012, 0.985345, 0.140096],
[0.099588, -0.130418, 0.986445],
],
[
[-0.994239, 0.0206112, 0.1052],
[0.0227944, 0.999548, 0.0195944],
[-0.104748, 0.0218794, -0.994259],
],
),
(
[
[0.988981, 0.132742, -0.0655406],
[-0.113134, 0.963226, 0.243712],
[0.0954813, -0.233612, 0.96763],
],
[
[-0.989473, -0.144453, 0.00888153],
[0.112318, -0.727754, 0.67658],
[-0.0912697, 0.670455, 0.736317],
],
),
(
[
[0.13315, -0.722685, 0.678231],
[0.255831, 0.686195, 0.680946],
[-0.957508, 0.0828446, 0.276252],
],
[
[-0.233019, 0.0127274, -0.97239],
[-0.0143824, 0.99976, 0.0165321],
[0.972367, 0.0178377, -0.23278],
],
),
(
[
[0.906305, -0.0179617, -0.422243],
[0.0246095, 0.999644, 0.0102984],
[0.421908, -0.0197247, 0.906424],
],
[
[-0.90393, 0.0136293, 0.427466],
[0.0169755, 0.999848, 0.0040176],
[-0.427346, 0.0108879, -0.904024],
],
),
(
[
[0.999808, 0.0177784, -0.00826505],
[-0.0177075, 0.999806, 0.00856939],
[0.0084158, -0.00842139, 0.999929],
],
[
[-0.999901, -0.0141114, 0.00072392],
[0.00130602, -0.0413336, 0.999145],
[-0.0140699, 0.999047, 0.0413473],
],
),
(
[
[0.985811, -0.161425, 0.0460375],
[0.154776, 0.980269, 0.12295],
[-0.0649764, -0.11408, 0.991344],
],
[
[-0.985689, 0.137931, -0.09692],
[-0.162627, -0.626622, 0.762168],
[0.0443951, 0.767022, 0.640085],
],
),
(
[
[0.956652, -0.0116044, 0.291001],
[0.05108, 0.990402, -0.128428],
[-0.286718, 0.137726, 0.948064],
],
[
[-0.956189, 0.00996594, -0.292585],
[-0.0397033, 0.985772, 0.16333],
[0.29005, 0.167791, -0.942189],
],
),
(
[
[0.783763, -0.0181248, -0.620796],
[-0.0386421, 0.996214, -0.0778717],
[0.619857, 0.0850218, 0.780095],
],
[
[-0.780275, 0.0093644, 0.625368],
[-0.0221791, 0.998845, -0.0426297],
[-0.625045, -0.0471329, -0.779165],
],
),
(
[
[0.890984, 0.0232464, -0.453439],
[-0.0221215, 0.999725, 0.00778511],
[0.453495, 0.00309433, 0.891253],
],
[
[-0.890178, 0.0290103, 0.45469],
[0.0337152, 0.999429, 0.0022403],
[-0.454366, 0.0173244, -0.890648],
],
),
(
[
[0.998177, -0.0119546, 0.0591504],
[0.00277494, 0.988238, 0.152901],
[-0.0602825, -0.152458, 0.98647],
],
[
[-0.997444, 0.00871865, -0.0709414],
[0.0197108, 0.987598, -0.155762],
[0.0687035, -0.156762, -0.985246],
],
),
(
[
[0.985214, 0.164929, 0.0463837],
[-0.166966, 0.984975, 0.0441225],
[-0.0384096, -0.0512146, 0.997949],
],
[
[-0.999472, -0.000819214, -0.0325087],
[-0.00344291, 0.99673, 0.0807324],
[0.0323362, 0.0808019, -0.996206],
],
),
(
[
[0.998499, 0.0465241, 0.0288955],
[-0.0454764, 0.99832, -0.0359142],
[-0.0305178, 0.0345463, 0.998937],
],
[
[-0.999441, 0.00412484, -0.0332105],
[0.00374685, 0.999928, 0.0114307],
[0.0332552, 0.0112999, -0.999384],
],
),
(
[
[0.10101, -0.943239, -0.316381],
[0.841334, -0.0887423, 0.533182],
[-0.530994, -0.320039, 0.784615],
],
[
[-0.725665, 0.0153749, -0.687878],
[-0.304813, 0.889109, 0.34143],
[0.616848, 0.457438, -0.640509],
],
),
(
[
[0.843428, 0.174952, 0.507958],
[0.0435637, 0.920106, -0.389239],
[-0.535473, 0.350423, 0.768422],
],
[
[-0.835464, 0.0040872, -0.549533],
[0.00227251, 0.999989, 0.00398241],
[0.549543, 0.00207845, -0.835464],
],
),
(
[
[0.999897, -0.0142888, -0.00160177],
[0.0141561, 0.997826, -0.064364],
[0.00251798, 0.0643346, 0.997925],
],
[
[-0.999956, 0.00898988, 0.00296485],
[0.00900757, 0.999941, 0.00601779],
[-0.00291058, 0.00604429, -0.999978],
],
),
(
[
[0.999477, -0.0204859, 0.0250096],
[0.0126204, 0.959462, 0.281557],
[-0.0297637, -0.281094, 0.959219],
],
[
[-0.999384, 0.0172602, -0.0305795],
[-0.0254425, 0.24428, 0.969371],
[0.0242012, 0.969551, -0.24369],
],
),
(
[
[0.984597, 0.173474, -0.0218106],
[-0.15145, 0.783891, -0.602145],
[-0.0873592, 0.596173, 0.798089],
],
[
[-0.998608, -0.0432858, 0.0301827],
[-0.00287128, 0.615692, 0.787983],
[-0.0526917, 0.786797, -0.61496],
],
),
(
[
[0.917099, -0.3072, 0.254083],
[0.303902, 0.951219, 0.0531566],
[-0.258018, 0.0284665, 0.965721],
],
[
[-0.931191, 0.347008, -0.111675],
[-0.352102, -0.77686, 0.522032],
[0.0943935, 0.52543, 0.845586],
],
),
(
[
[0.991706, 0.0721037, -0.106393],
[-0.0995017, 0.954693, -0.280464],
[0.0813505, 0.288725, 0.95395],
],
[
[-0.995306, 0.00106317, 0.0967833],
[0.0167662, 0.986717, 0.161583],
[-0.0953259, 0.162447, -0.982103],
],
),
(
[
[0.997078, 0.0478273, -0.0595641],
[-0.0348316, 0.978617, 0.202719],
[0.067986, -0.200052, 0.977424],
],
[
[-0.997925, -0.0439691, 0.0470461],
[0.0643829, -0.695474, 0.715663],
[0.00125305, 0.717207, 0.696861],
],
),
(
[
[0.972749, -0.0233882, -0.230677],
[0.0255773, 0.999652, 0.00650349],
[0.230445, -0.0122264, 0.973009],
],
[
[-0.973286, 0.0147558, 0.229126],
[0.0145644, 0.999891, -0.00252631],
[-0.229138, 0.000878362, -0.973394],
],
),
(
[
[0.999271, 0.00700481, 0.0375381],
[-0.0348202, 0.57069, 0.820427],
[-0.0156757, -0.821136, 0.570517],
],
[
[-0.999805, -0.0198049, 0.000539906],
[0.0179848, -0.89584, 0.444015],
[-0.00831113, 0.443938, 0.89602],
],
),
(
[
[0.975255, -0.0207895, 0.220104],
[0.0252764, 0.999526, -0.0175888],
[-0.219634, 0.022717, 0.975318],
],
[
[-0.975573, 0.0128154, -0.219304],
[0.0106554, 0.999882, 0.0110292],
[0.219419, 0.00842303, -0.975594],
],
),
(
[
[-0.433961, -0.658151, -0.615236],
[0.610442, -0.717039, 0.336476],
[-0.6626, -0.229548, 0.71293],
],
[
[-0.998516, -0.00675119, -0.054067],
[-0.00405539, 0.99875, -0.0498174],
[0.0543358, -0.0495237, -0.997296],
],
),
(
[
[0.942764, -0.0126807, -0.333221],
[-0.0017175, 0.999079, -0.042879],
[0.333458, 0.0409971, 0.941873],
],
[
[-0.942228, -0.0109444, 0.334798],
[0.0110573, 0.997905, 0.0637396],
[-0.334794, 0.0637589, -0.940133],
],
),
(
[
[0.962038, 0.0147987, 0.272515],
[-0.0185974, 0.999762, 0.0113615],
[-0.272283, -0.0159982, 0.962084],
],
[
[-0.959802, 0.0113708, -0.280451],
[0.00982126, 0.999928, 0.00692958],
[0.280509, 0.00389678, -0.959845],
],
),
(
[
[0.998414, 0.0139348, 0.0545528],
[-0.0226877, 0.986318, 0.163283],
[-0.0515311, -0.164262, 0.98507],
],
[
[-0.998641, -0.000695993, -0.0521343],
[0.0182534, 0.931965, -0.362087],
[0.0488394, -0.362547, -0.930686],
],
),
(
[
[0.999705, -0.0234518, -0.00633743],
[0.0235916, 0.999458, 0.0229643],
[0.00579544, -0.023107, 0.999716],
],
[
[-0.999901, 0.004436, 0.0133471],
[-0.00306106, 0.85758, -0.514342],
[-0.0137278, -0.514332, -0.857481],
],
),
(
[
[0.998617, -0.051704, 0.0094837],
[0.0484292, 0.975079, 0.216506],
[-0.0204416, -0.215748, 0.976235],
],
[
[-0.999959, -0.00295958, -0.00862907],
[-0.00313279, 0.999792, 0.0201361],
[0.00856768, 0.0201625, -0.999761],
],
),
(
[
[0.999121, 0.0345472, -0.023733],
[-0.0333175, 0.998174, 0.0503881],
[0.0254304, -0.0495531, 0.998448],
],
[
[-0.999272, -0.0337466, 0.0178065],
[0.0200629, -0.0677624, 0.9975],
[-0.0324556, 0.997131, 0.0683898],
],
),
(
[
[0.989017, 0.139841, -0.0478525],
[-0.131355, 0.683201, -0.718319],
[-0.0677572, 0.716715, 0.694067],
],
[
[-0.995236, 0.00457798, 0.097401],
[0.097488, 0.0258334, 0.994902],
[0.00203912, 0.999657, -0.0261574],
],
),
(
[
[0.961528, 0.249402, 0.11516],
[-0.204522, 0.9298, -0.306009],
[-0.183395, 0.270684, 0.945038],
],
[
[-0.999566, -0.0233216, 0.0180679],
[0.012372, 0.224583, 0.974377],
[-0.0267822, 0.974177, -0.224197],
],
),
(
[
[0.865581, 0.0252563, -0.500131],
[0.0302583, 0.994265, 0.102578],
[0.499853, -0.103923, 0.859853],
],
[
[-0.866693, 0.0042288, 0.498824],
[0.0129331, 0.999818, 0.0139949],
[-0.498674, 0.0185807, -0.866591],
],
),
(
[
[0.998999, -0.0213419, -0.0393009],
[-0.0007582, 0.870578, -0.492031],
[0.0447153, 0.491568, 0.86969],
],
[
[-0.999207, -0.0184688, 0.0353073],
[0.00153266, 0.867625, 0.497218],
[-0.0398164, 0.496876, -0.866908],
],
),
(
[
[0.96567, -0.00482973, 0.259728],
[0.00349956, 0.999978, 0.00558359],
[-0.259749, -0.00448297, 0.965666],
],
[
[-0.962691, -0.00113074, -0.270609],
[-5.93716e-05, 0.999992, -0.00396767],
[0.270612, -0.00380337, -0.962683],
],
),
(
[
[0.948799, 0.287027, -0.131894],
[-0.300257, 0.949181, -0.0943405],
[0.0981135, 0.129112, 0.986764],
],
[
[-0.993593, -0.0406684, 0.105449],
[-0.0506857, 0.994269, -0.0941326],
[-0.101017, -0.0988741, -0.98996],
],
),
(
[
[0.998935, 0.0451118, 0.0097202],
[-0.0418086, 0.973879, -0.223183],
[-0.0195345, 0.222539, 0.974728],
],
[
[-0.999821, 0.00821522, -0.0170658],
[0.00742187, 0.998912, 0.046048],
[0.0174255, 0.0459131, -0.998794],
],
),
(
[
[0.99577, 0.00458459, 0.0917705],
[-0.00244288, 0.999722, -0.0234365],
[-0.0918524, 0.0231131, 0.995504],
],
[
[-0.995956, 0.0137721, -0.0887945],
[0.0122932, 0.999777, 0.0171801],
[0.0890113, 0.0160191, -0.995903],
],
),
(
[
[0.97931, 0.0219899, 0.201169],
[-0.0159226, 0.99937, -0.0317288],
[-0.201739, 0.0278692, 0.979043],
],
[
[-0.980952, 0.00507266, -0.19419],
[0.00310821, 0.999941, 0.010419],
[0.194231, 0.00961706, -0.98091],
],
),
(
[
[0.999616, 0.00550326, -0.0271537],
[-0.0048286, 0.99968, 0.0248495],
[0.0272817, -0.0247088, 0.999322],
],
[
[-0.999689, -0.00054899, 0.0249588],
[-0.00125497, 0.999599, -0.0282774],
[-0.0249333, -0.0282998, -0.999289],
],
),
(
[
[0.998036, -0.00755259, -0.0621791],
[0.0417502, 0.820234, 0.570502],
[0.0466927, -0.571978, 0.818939],
],
[
[-0.999135, -0.0278203, 0.0309173],
[-0.00855238, 0.864892, 0.501886],
[-0.0407029, 0.501187, -0.864382],
],
),
(
[
[0.958227, 0.00271545, 0.285997],
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[0.104649, 0.818877, -0.564348],
],
),
(
[
[0.984844, -0.0288271, 0.17103],
[0.0260588, 0.999491, 0.0184094],
[-0.171474, -0.0136736, 0.985094],
],
[
[-0.984637, -0.00367691, -0.174577],
[-0.00649229, 0.999858, 0.0155587],
[0.174495, 0.0164532, -0.984521],
],
),
(
[
[0.99985, 0.000720773, -0.0172841],
[-0.00075051, 0.999998, -0.0017141],
[0.0172828, 0.00172682, 0.999849],
],
[
[-0.999926, -0.00413456, 0.0114842],
[-0.00368343, 0.999231, 0.0390359],
[-0.0116368, 0.0389908, -0.999172],
],
),
(
[
[0.997976, 0.0603523, -0.0200139],
[-0.0558618, 0.982551, 0.177404],
[0.0303714, -0.175927, 0.983935],
],
[
[-0.996867, -0.0790953, 0.00217996],
[0.0318842, -0.376338, 0.925935],
[-0.0724181, 0.923101, 0.37768],
],
),
(
[
[0.94678, -0.00538407, -0.321837],
[0.00249113, 0.999953, -0.0094],
[0.321872, 0.008098, 0.946749],
],
[
[-0.945694, 0.0255694, 0.324053],
[0.0240377, 0.999673, -0.00872898],
[-0.32417, -0.000465377, -0.945999],
],
),
(
[
[0.846059, 0.435245, -0.307807],
[0.318073, 0.0512036, 0.946682],
[0.4278, -0.898855, -0.0951187],
],
[
[-0.217213, -0.0389124, 0.975352],
[0.742195, 0.642416, 0.190918],
[-0.634011, 0.765368, -0.11066],
],
),
(
[
[0.914988, -0.0538229, -0.399875],
[-0.0459455, 0.970717, -0.23579],
[0.400857, 0.234117, 0.885722],
],
[
[-0.919706, 0.00194642, 0.392606],
[0.105539, 0.964406, 0.242451],
[-0.378159, 0.264418, -0.887176],
],
),
(
[
[0.970915, -0.183858, 0.153365],
[0.209801, 0.96196, -0.174974],
[-0.115361, 0.202061, 0.972555],
],
[
[-0.975509, 0.21077, -0.0629391],
[-0.218082, -0.964089, 0.151576],
[-0.0287314, 0.161588, 0.986441],
],
),
(
[
[0.99369, -0.00515149, -0.112044],
[0.00366664, 0.999903, -0.0134545],
[0.112102, 0.0129588, 0.993612],
],
[
[-0.99406, 0.00631892, 0.108668],
[0.00878985, 0.999713, 0.022273],
[-0.108496, 0.0230956, -0.99383],
],
),
(
[
[0.995917, 0.0137529, 0.089215],
[-0.0145079, 0.999864, 0.00781912],
[-0.0890954, -0.00908151, 0.995982],
],
[
[-0.996188, 0.012059, -0.0864113],
[0.0126654, 0.999899, -0.00647346],
[0.0863245, -0.00754306, -0.99624],
],
),
(
[
[0.84563, -0.0032436, -0.533759],
[0.0040093, 0.999992, 0.000275049],
[0.533754, -0.00237259, 0.845636],
],
[
[-0.849818, -0.00755214, 0.527023],
[-0.00734806, 0.99997, 0.00248074],
[-0.527026, -0.00176415, -0.849848],
],
),
(
[
[0.736067, -0.212675, -0.642631],
[-0.447028, 0.560168, -0.697408],
[0.508303, 0.800613, 0.31725],
],
[
[-0.684029, 0.0061039, 0.729431],
[0.0260275, 0.999532, 0.0160434],
[-0.728992, 0.0299595, -0.683868],
],
),
(
[
[0.993949, 0.00461705, -0.109742],
[-0.00653155, 0.999833, -0.0170925],
[0.109644, 0.0177058, 0.993813],
],
[
[-0.994446, 0.0218439, 0.102965],
[0.0227578, 0.999711, 0.00770966],
[-0.102767, 0.0100102, -0.994656],
],
),
(
[
[0.996005, -0.0103388, 0.0886959],
[-0.0291635, 0.901147, 0.432531],
[-0.0843999, -0.43339, 0.897246],
],
[
[-0.999947, 0.00833193, -0.00598923],
[-0.0101526, -0.887864, 0.459993],
[-0.00148526, 0.46003, 0.887902],
],
),
(
[
[0.981518, 0.0114609, 0.191025],
[-0.0104683, 0.999926, -0.00620422],
[-0.191082, 0.00408984, 0.981565],
],
[
[-0.979556, 0.000134379, -0.201176],
[-0.00817302, 0.999148, 0.0404628],
[0.20101, 0.0412799, -0.97872],
],
),
(
[
[0.997665, -0.0372296, -0.0572574],
[0.0379027, 0.999224, 0.0107148],
[0.0568141, -0.01286, 0.998302],
],
[
[-0.997794, 0.00389749, 0.0662921],
[0.00639122, 0.999278, 0.0374446],
[-0.0660983, 0.0377856, -0.997099],
],
),
(
[
[0.981618, -0.0105643, -0.190564],
[0.00329498, 0.999256, -0.0384229],
[0.190828, 0.0370887, 0.980923],
],
[
[-0.981673, -0.000810695, 0.190576],
[0.00398375, 0.999685, 0.0247729],
[-0.190536, 0.0250779, -0.981361],
],
),
(
[
[-0.544941, -0.812151, -0.208446],
[0.812337, -0.449791, -0.37121],
[0.207722, -0.371617, 0.90485],
],
[
[-0.121327, -0.000366672, -0.992614],
[-0.955208, 0.271977, 0.116655],
[0.269926, 0.962303, -0.0333484],
],
),
(
[
[0.637701, -0.219537, 0.738336],
[0.735715, 0.457522, -0.499397],
[-0.228168, 0.861671, 0.453279],
],
[
[-0.741797, 0.0196167, -0.670339],
[-0.00209087, 0.9995, 0.0315629],
[0.670623, 0.0248149, -0.741385],
],
),
(
[
[0.99813, -0.0590625, -0.0157485],
[0.0589086, 0.998213, -0.0100649],
[0.0163148, 0.00911833, 0.999825],
],
[
[-0.99893, 0.0258783, -0.0383385],
[-0.0440455, -0.279068, 0.959261],
[0.014125, 0.959924, 0.279908],
],
),
(
[
[0.999558, 0.0028395, -0.0296019],
[-0.00492321, 0.997496, -0.0705578],
[0.0293274, 0.0706723, 0.997068],
],
[
[-0.999532, -0.0305627, -0.00231546],
[0.00957406, -0.38309, 0.923664],
[-0.0291167, 0.923206, 0.383202],
],
),
(
[
[0.99814, -0.0528437, -0.0303853],
[0.0590889, 0.96123, 0.269341],
[0.0149743, -0.270636, 0.962565],
],
[
[-0.999464, 0.00781117, 0.0318024],
[-0.000588355, 0.966696, -0.255928],
[-0.0327423, -0.255809, -0.966173],
],
),
(
[
[-0.936685, 0.234194, 0.260336],
[-0.233325, -0.97178, 0.034698],
[0.261116, -0.0282419, 0.964894],
],
[
[0.999511, 0.00582072, 0.0307461],
[0.0289012, 0.204922, -0.978352],
[-0.0119956, 0.978762, 0.204654],
],
),
(
[
[0.973616, -0.019218, -0.227384],
[0.0030011, 0.99744, -0.0714512],
[0.228175, 0.0688836, 0.97118],
],
[
[-0.974738, 0.0190271, 0.222547],
[0.0222378, 0.999682, 0.0119297],
[-0.222249, 0.0165771, -0.97485],
],
),
(
[
[0.997273, 0.0453471, -0.0582173],
[-0.0234007, 0.942529, 0.333303],
[0.0699858, -0.331032, 0.941021],
],
[
[-0.996269, -0.0613496, 0.0607196],
[-0.0100285, 0.780948, 0.624516],
[-0.0857328, 0.621576, -0.77865],
],
),
(
[
[0.999511, 0.0274482, -0.0149865],
[-0.0305945, 0.957511, -0.286769],
[0.00647846, 0.287087, 0.957883],
],
[
[-0.999443, -0.0260559, 0.0209038],
[0.0148505, 0.213942, 0.976734],
[-0.0299225, 0.976499, -0.213437],
],
),
(
[
[0.621123, 0.722893, 0.302708],
[-0.48353, 0.657448, -0.577894],
[-0.61677, 0.212574, 0.757896],
],
[
[-0.996888, -0.0217614, -0.0757776],
[-0.0783897, 0.376159, 0.923234],
[0.00841386, 0.926299, -0.376694],
],
),
(
[
[0.974426, 0.0128384, -0.224341],
[-0.0123842, 0.999917, 0.00343166],
[0.224367, -0.00056561, 0.974505],
],
[
[-0.973234, -0.00506667, 0.229763],
[-0.000498848, 0.999801, 0.0199346],
[-0.229818, 0.0192865, -0.973043],
],
),
(
[
[0.994721, -0.0881097, 0.0526082],
[0.0972904, 0.972774, -0.210345],
[-0.0326424, 0.214353, 0.976211],
],
[
[-0.994309, 0.0920529, -0.0536268],
[-0.105538, -0.782431, 0.613729],
[0.0145358, 0.615896, 0.787694],
],
),
(
[
[0.998677, -0.0372894, 0.0354002],
[0.0242326, 0.948589, 0.315583],
[-0.0453481, -0.314308, 0.948237],
],
[
[-0.999066, -0.00910724, -0.0422707],
[-0.024629, 0.923353, 0.383161],
[0.0355411, 0.383844, -0.922715],
],
),
(
[
[0.931525, 0.00831028, 0.363583],
[0.0192806, 0.997204, -0.0721909],
[-0.363167, 0.0742577, 0.92876],
],
[
[-0.930052, -0.00174384, -0.367425],
[-0.0268673, 0.997634, 0.0632737],
[0.366445, 0.0687194, -0.927899],
],
),
(
[
[-0.50483, -0.819216, 0.272087],
[0.775688, -0.568816, -0.273414],
[0.378753, 0.0730272, 0.922612],
],
[
[-0.981596, 0.00031926, 0.190974],
[0.00652401, 0.999471, 0.0318616],
[-0.190863, 0.0325211, -0.981079],
],
),
(
[
[0.990518, -0.00195099, -0.137368],
[-0.00164696, 0.999659, -0.0260735],
[0.137372, 0.0260526, 0.990177],
],
[
[-0.991078, 0.00934835, 0.132961],
[0.0106057, 0.999905, 0.00875176],
[-0.132866, 0.0100839, -0.991083],
],
),
(
[
[0.935049, -0.353081, 0.0318997],
[0.257018, 0.737114, 0.624984],
[-0.244184, -0.576192, 0.779985],
],
[
[-0.977342, -0.00167896, -0.211667],
[-0.0448634, 0.978894, 0.199386],
[0.206864, 0.204364, -0.956789],
],
),
(
[
[0.998464, 0.0501172, 0.0236119],
[-0.0498618, 0.998692, -0.0112844],
[-0.0241466, 0.0100898, 0.999658],
],
[
[-0.999931, -0.0037971, -0.0112195],
[-0.00640916, 0.970027, 0.242913],
[0.00996085, 0.242968, -0.969984],
],
),
(
[
[0.999893, -0.0108217, 0.00984537],
[0.011201, 0.999164, -0.0393194],
[-0.00941164, 0.0394255, 0.999178],
],
[
[-0.999886, 0.00730461, -0.0133396],
[-0.0118202, -0.925163, 0.379391],
[-0.00956982, 0.379504, 0.925142],
],
),
(
[
[0.990922, -0.086745, 0.102709],
[0.0847349, 0.99612, 0.0237834],
[-0.104373, -0.0148644, 0.994427],
],
[
[-0.994922, -0.00197458, -0.10064],
[-0.00242513, 0.999988, 0.00435525],
[0.10063, 0.00457739, -0.994914],
],
),
(
[
[0.999856, 0.00210734, -0.0168511],
[-0.00557165, 0.978053, -0.20828],
[0.0160424, 0.208344, 0.977924],
],
[
[-0.999698, 0.0048691, 0.0241226],
[-0.00154306, 0.965899, -0.258915],
[-0.0245606, -0.258874, -0.9656],
],
),
(
[
[0.992858, -0.0249864, -0.116659],
[0.0419872, 0.988447, 0.145634],
[0.111673, -0.149492, 0.982436],
],
[
[-0.992324, 0.0357741, 0.118384],
[-0.0419528, 0.803113, -0.594348],
[-0.116338, -0.594752, -0.795447],
],
),
(
[
[0.986821, -0.00531913, 0.161729],
[0.00797365, 0.999844, -0.0157688],
[-0.16162, 0.0168505, 0.986709],
],
[
[-0.985867, 0.0119402, -0.167109],
[0.0141227, 0.99983, -0.0118784],
[0.166939, -0.0140704, -0.985868],
],
),
(
[
[0.999693, -0.0158939, -0.0190113],
[0.0103599, 0.96501, -0.262007],
[0.0225104, 0.261729, 0.964879],
],
[
[-0.999344, -0.0314781, -0.0180051],
[-0.0250895, 0.241673, 0.970034],
[-0.0261833, 0.969847, -0.242305],
],
),
(
[
[0.977445, 0.0293661, 0.209138],
[-0.0723687, 0.976903, 0.201057],
[-0.198403, -0.211657, 0.956994],
],
[
[-0.976437, 0.00895131, -0.215624],
[0.0552894, 0.976169, -0.20985],
[0.208607, -0.216827, -0.953663],
],
),
(
[
[0.994593, 0.0974797, -0.0358119],
[-0.0822288, 0.949838, 0.301737],
[0.0634288, -0.297161, 0.952718],
],
[
[-0.994192, -0.10746, -0.00604622],
[0.078812, -0.7651, 0.639071],
[-0.0733003, 0.634882, 0.769124],
],
),
(
[
[0.365674, 0.282077, -0.88697],
[-0.609177, 0.793033, 0.00105565],
[0.703694, 0.539936, 0.461826],
],
[
[-0.469534, 0.0109062, 0.882848],
[0.0060785, 0.99994, -0.00911984],
[-0.882894, 0.00108445, -0.469572],
],
),
(
[
[0.999956, 0.00903085, 0.0025358],
[-0.00862738, 0.991574, -0.129252],
[-0.00368169, 0.129224, 0.991609],
],
[
[-0.999976, 0.00322491, -0.00637541],
[0.00379751, 0.995755, -0.0919687],
[0.00605176, -0.0919907, -0.995743],
],
),
(
[
[0.999982, -0.00398882, -0.00441072],
[0.00411881, 0.999545, 0.0298655],
[0.00428959, -0.0298832, 0.999544],
],
[
[-0.999931, -0.00315547, -0.0114491],
[0.00300966, -0.999914, 0.0128304],
[-0.0114875, 0.012796, 0.999853],
],
),
(
[
[0.996613, 0.0781452, -0.0256245],
[-0.0610516, 0.91178, 0.406116],
[0.0550999, -0.403175, 0.913462],
],
[
[-0.996368, -0.084671, 0.00909851],
[0.0540149, -0.545774, 0.83619],
[-0.0658352, 0.833644, 0.548365],
],
),
(
[
[0.961059, 0.139318, 0.238654],
[-0.117488, 0.987672, -0.103448],
[-0.250124, 0.0713812, 0.965579],
],
[
[-0.973397, 0.00782581, -0.228998],
[-0.0621109, 0.952986, 0.296581],
[0.220553, 0.302913, -0.927147],
],
),
(
[
[0.156415, -0.982138, 0.104589],
[-0.568896, -0.176149, -0.803323],
[0.807398, 0.0661518, -0.586287],
],
[
[-0.992155, 0.0934304, -0.0830664],
[-0.121171, -0.555137, 0.822887],
[0.0307694, 0.826496, 0.562102],
],
),
(
[
[0.997973, 0.0130328, -0.0622976],
[-0.011111, 0.999455, 0.0310968],
[0.0626689, -0.0303416, 0.997573],
],
[
[-0.997391, -0.00094697, 0.0722014],
[-0.00271076, 0.9997, -0.024334],
[-0.0721567, -0.024466, -0.997094],
],
),
(
[
[0.913504, -0.0125928, -0.406634],
[-0.108363, 0.95588, -0.27304],
[0.392132, 0.293487, 0.871836],
],
[
[-0.909813, 0.0115348, 0.414861],
[0.128636, 0.958223, 0.255464],
[-0.394582, 0.28579, -0.873287],
],
),
(
[
[0.932595, -0.0693644, 0.354197],
[0.0984415, 0.993036, -0.0647231],
[-0.347241, 0.0952281, 0.932928],
],
[
[-0.930498, 0.00578599, -0.366252],
[-0.106202, 0.952666, 0.284867],
[0.350564, 0.303964, -0.885839],
],
),
(
[
[0.995668, -0.00475737, 0.0928567],
[0.00890154, 0.99898, -0.0442667],
[-0.0925514, 0.0449015, 0.994695],
],
[
[-0.996077, -0.0107986, -0.0878355],
[0.00749423, 0.978669, -0.205305],
[0.0881789, -0.205158, -0.974749],
],
),
(
[
[0.99948, 0.0321999, 0.00146151],
[-0.0321302, 0.998886, -0.0345513],
[-0.00257243, 0.0344864, 0.999402],
],
[
[-0.999953, 0.00726142, -0.0065326],
[0.00488529, 0.950962, 0.30927],
[0.00845801, 0.309223, -0.950953],
],
),
]
class TestRot3(GtsamTestCase):
"""Test selected Rot3 methods."""
def test_axisangle(self) -> None:
"""Test .axisAngle() method."""
# fmt: off
R = np.array(
[
[ -0.999957, 0.00922903, 0.00203116],
[ 0.00926964, 0.999739, 0.0208927],
[ -0.0018374, 0.0209105, -0.999781]
])
# fmt: on
# get back angle in radians
_, actual_angle = Rot3(R).axisAngle()
expected_angle = 3.1396582
np.testing.assert_almost_equal(actual_angle, expected_angle, 1e-7)
def test_axis_angle_stress_test(self) -> None:
"""Test that .axisAngle() yields angles less than 180 degrees for specific inputs."""
for (R1, R2) in R1_R2_pairs:
R1 = Rot3(np.array(R1))
R2 = Rot3(np.array(R2))
i1Ri2 = R1.between(R2)
axis, angle = i1Ri2.axisAngle()
angle_deg = np.rad2deg(angle)
assert angle_deg < 180
def test_rotate(self) -> None:
"""Test that rotate() works for both Point3 and Unit3."""
R = Rot3(np.array([[1, 0, 0], [0, -1, 0], [0, 0, -1]]))
p = Point3(1., 1., 1.)
u = Unit3(np.array([1, 1, 1]))
actual_p = R.rotate(p)
actual_u = R.rotate(u)
expected_p = Point3(np.array([1, -1, -1]))
expected_u = Unit3(np.array([1, -1, -1]))
np.testing.assert_array_equal(actual_p, expected_p)
np.testing.assert_array_equal(actual_u.point3(), expected_u.point3())
def test_unrotate(self) -> None:
"""Test that unrotate() after rotate() yields original Point3/Unit3."""
wRc = Rot3(np.array(R1_R2_pairs[0][0]))
c_p = Point3(1., 1., 1.)
c_u = Unit3(np.array([1, 1, 1]))
w_p = wRc.rotate(c_p)
w_u = wRc.rotate(c_u)
actual_p = wRc.unrotate(w_p)
actual_u = wRc.unrotate(w_u)
np.testing.assert_almost_equal(actual_p, c_p, decimal=6)
np.testing.assert_almost_equal(actual_u.point3(), c_u.point3(), decimal=6)
if __name__ == "__main__":
unittest.main()