2063 lines
56 KiB
Python
2063 lines
56 KiB
Python
"""
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GTSAM Copyright 2010-2019, Georgia Tech Research Corporation,
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Atlanta, Georgia 30332-0415
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All Rights Reserved
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See LICENSE for the license information
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Rot3 unit tests.
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Author: John Lambert
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"""
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# pylint: disable=no-name-in-module
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import unittest
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import numpy as np
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import gtsam
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from gtsam import Point3, Rot3, Unit3
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from gtsam.utils.test_case import GtsamTestCase
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R1_R2_pairs = [
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(
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[
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[0.994283, -0.10356, 0.0260251],
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[0.102811, 0.994289, 0.0286205],
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|
[-0.0288404, -0.0257812, 0.999251],
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],
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|
[
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|
[-0.994235, 0.0918291, -0.0553602],
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|
[-0.0987317, -0.582632, 0.806718],
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[0.0418251, 0.807532, 0.588339],
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],
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|
),
|
|
(
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|
[
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|
[0.999823, -0.000724729, 0.0187896],
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|
[0.00220672, 0.996874, -0.0789728],
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|
[-0.0186736, 0.0790003, 0.9967],
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],
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|
[
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|
[-0.99946, -0.0155217, -0.0289749],
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|
[-0.0306159, 0.760422, 0.648707],
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|
[0.0119641, 0.649244, -0.760487],
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],
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),
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|
(
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|
[
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|
[0.999976, 0.00455542, -0.00529608],
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|
[-0.00579633, 0.964214, -0.265062],
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|
[0.00389908, 0.265086, 0.964217],
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|
],
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|
[
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|
[-0.999912, -0.0123323, -0.00489179],
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|
[-0.00739095, 0.21159, 0.977331],
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|
[-0.0110179, 0.977281, -0.211663],
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|
],
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|
),
|
|
(
|
|
[
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|
[0.998801, 0.0449026, 0.019479],
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|
[-0.0448727, 0.998991, -0.00197348],
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|
[-0.0195479, 0.00109704, 0.999808],
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|
],
|
|
[
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|
[-0.999144, -0.0406154, -0.00800012],
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|
[0.0406017, -0.999174, 0.00185875],
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|
[-0.00806909, 0.00153352, 0.999966],
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],
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|
),
|
|
(
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|
[
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|
[0.587202, 0.00034062, -0.80944],
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|
[0.394859, 0.872825, 0.286815],
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|
[0.706597, -0.488034, 0.51239],
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|
],
|
|
[
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|
[-0.999565, -0.028095, -0.00905389],
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|
[0.0192863, -0.853838, 0.520182],
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|
[-0.0223455, 0.519782, 0.854007],
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],
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),
|
|
(
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|
[
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|
[0.998798, 0.0370584, 0.0320815],
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|
[-0.0355966, 0.998353, -0.0449943],
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|
[-0.033696, 0.0437982, 0.998472],
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],
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|
[
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|
[-0.999942, -0.010745, -0.00132538],
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|
[-0.000998705, -0.0304045, 0.999538],
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|
[-0.0107807, 0.999481, 0.0303914],
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],
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),
|
|
(
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|
[
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|
[0.998755, 0.00708291, -0.0493744],
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|
[-0.00742097, 0.99995, -0.00666709],
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|
[0.0493247, 0.0070252, 0.998758],
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],
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|
[
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|
[-0.998434, 0.0104672, 0.0549825],
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|
[0.0115323, 0.999751, 0.0190859],
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|
[-0.0547691, 0.01969, -0.998307],
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],
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),
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|
(
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|
[
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|
[0.990471, 0.0997485, -0.0949595],
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|
[-0.117924, 0.970427, -0.210631],
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|
[0.0711411, 0.219822, 0.972943],
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],
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|
[
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[-0.99192, -0.125627, 0.0177888],
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|
[0.126478, -0.967866, 0.217348],
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[-0.0100874, 0.217839, 0.975933],
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],
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),
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|
(
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|
[
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[-0.780894, -0.578319, -0.236116],
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|
[0.34478, -0.0838381, -0.934932],
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|
[0.520894, -0.811491, 0.264862],
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],
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[
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[-0.99345, 0.00261746, -0.114244],
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[-0.112503, 0.152922, 0.981815],
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[0.0200403, 0.988236, -0.151626],
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],
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),
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(
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[
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[0.968425, 0.0466097, 0.244911],
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[-0.218867, 0.629346, 0.745668],
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[-0.119378, -0.775726, 0.619676],
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],
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[
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[-0.971208, 0.00666431, -0.238143],
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[0.0937886, 0.929584, -0.35648],
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[0.218998, -0.368551, -0.903444],
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],
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),
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(
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[
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[0.998512, 0.0449168, -0.0309146],
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[-0.0344032, 0.958823, 0.281914],
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[0.0423043, -0.280431, 0.958941],
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],
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[
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[-0.999713, 0.00732431, 0.0228168],
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[-0.00759688, 0.806166, -0.59164],
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[-0.0227275, -0.591644, -0.805879],
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],
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),
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(
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[
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[0.981814, 0.00930728, 0.189617],
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[-0.0084101, 0.999949, -0.00553563],
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[-0.189659, 0.00384026, 0.981843],
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],
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[
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[-0.981359, 0.00722349, -0.192051],
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[0.00148564, 0.999549, 0.0300036],
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[0.192182, 0.0291591, -0.980927],
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],
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),
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(
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[
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[0.972544, -0.215591, 0.0876242],
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[0.220661, 0.973915, -0.0529018],
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[-0.0739333, 0.0707846, 0.994748],
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],
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[
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[-0.971294, 0.215675, -0.100371],
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[-0.23035, -0.747337, 0.62324],
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[0.0594069, 0.628469, 0.775564],
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],
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),
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(
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[
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[0.989488, 0.0152447, 0.143808],
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[-0.0160974, 0.999859, 0.00476753],
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[-0.143715, -0.00703235, 0.989594],
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],
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[
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[-0.988492, 0.0124362, -0.150766],
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[0.00992423, 0.999799, 0.0174037],
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[0.150952, 0.0157072, -0.988417],
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],
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),
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|
(
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|
[
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|
[0.99026, 0.109934, -0.0854388],
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|
[-0.0973012, 0.985345, 0.140096],
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|
[0.099588, -0.130418, 0.986445],
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],
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|
[
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|
[-0.994239, 0.0206112, 0.1052],
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|
[0.0227944, 0.999548, 0.0195944],
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|
[-0.104748, 0.0218794, -0.994259],
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],
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),
|
|
(
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|
[
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|
[0.988981, 0.132742, -0.0655406],
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|
[-0.113134, 0.963226, 0.243712],
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|
[0.0954813, -0.233612, 0.96763],
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],
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|
[
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|
[-0.989473, -0.144453, 0.00888153],
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|
[0.112318, -0.727754, 0.67658],
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|
[-0.0912697, 0.670455, 0.736317],
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],
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),
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|
(
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|
[
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[0.13315, -0.722685, 0.678231],
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|
[0.255831, 0.686195, 0.680946],
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|
[-0.957508, 0.0828446, 0.276252],
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],
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|
[
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|
[-0.233019, 0.0127274, -0.97239],
|
|
[-0.0143824, 0.99976, 0.0165321],
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|
[0.972367, 0.0178377, -0.23278],
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],
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),
|
|
(
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|
[
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|
[0.906305, -0.0179617, -0.422243],
|
|
[0.0246095, 0.999644, 0.0102984],
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|
[0.421908, -0.0197247, 0.906424],
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|
],
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|
[
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|
[-0.90393, 0.0136293, 0.427466],
|
|
[0.0169755, 0.999848, 0.0040176],
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|
[-0.427346, 0.0108879, -0.904024],
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],
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),
|
|
(
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|
[
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[0.999808, 0.0177784, -0.00826505],
|
|
[-0.0177075, 0.999806, 0.00856939],
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|
[0.0084158, -0.00842139, 0.999929],
|
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],
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|
[
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|
[-0.999901, -0.0141114, 0.00072392],
|
|
[0.00130602, -0.0413336, 0.999145],
|
|
[-0.0140699, 0.999047, 0.0413473],
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],
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),
|
|
(
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|
[
|
|
[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],
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|
[0.0443951, 0.767022, 0.640085],
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],
|
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),
|
|
(
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|
[
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|
[0.956652, -0.0116044, 0.291001],
|
|
[0.05108, 0.990402, -0.128428],
|
|
[-0.286718, 0.137726, 0.948064],
|
|
],
|
|
[
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|
[-0.956189, 0.00996594, -0.292585],
|
|
[-0.0397033, 0.985772, 0.16333],
|
|
[0.29005, 0.167791, -0.942189],
|
|
],
|
|
),
|
|
(
|
|
[
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|
[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],
|
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],
|
|
),
|
|
(
|
|
[
|
|
[0.998177, -0.0119546, 0.0591504],
|
|
[0.00277494, 0.988238, 0.152901],
|
|
[-0.0602825, -0.152458, 0.98647],
|
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],
|
|
[
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[-0.997444, 0.00871865, -0.0709414],
|
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[0.0197108, 0.987598, -0.155762],
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[0.0687035, -0.156762, -0.985246],
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],
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),
|
|
(
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[
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[0.985214, 0.164929, 0.0463837],
|
|
[-0.166966, 0.984975, 0.0441225],
|
|
[-0.0384096, -0.0512146, 0.997949],
|
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],
|
|
[
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|
[-0.999472, -0.000819214, -0.0325087],
|
|
[-0.00344291, 0.99673, 0.0807324],
|
|
[0.0323362, 0.0808019, -0.996206],
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],
|
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),
|
|
(
|
|
[
|
|
[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],
|
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],
|
|
),
|
|
(
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|
[
|
|
[0.10101, -0.943239, -0.316381],
|
|
[0.841334, -0.0887423, 0.533182],
|
|
[-0.530994, -0.320039, 0.784615],
|
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],
|
|
[
|
|
[-0.725665, 0.0153749, -0.687878],
|
|
[-0.304813, 0.889109, 0.34143],
|
|
[0.616848, 0.457438, -0.640509],
|
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],
|
|
),
|
|
(
|
|
[
|
|
[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],
|
|
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|
|
[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()
|