test_Rot3.py

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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],
        ],
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    (
        [
            [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()