demo + utils venv
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"""
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========================================================
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Spatial Transformations (:mod:`scipy.spatial.transform`)
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========================================================
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.. currentmodule:: scipy.spatial.transform
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This package implements various spatial transformations. For now,
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only rotations are supported.
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Rotations in 3 dimensions
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=========================
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.. autosummary::
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:toctree: generated/
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Rotation
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Slerp
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"""
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from __future__ import division, print_function, absolute_import
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from .rotation import Rotation, Slerp
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__all__ = ['Rotation', 'Slerp']
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from scipy._lib._testutils import PytestTester
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test = PytestTester(__name__)
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del PytestTester
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from __future__ import division, print_function, absolute_import
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def configuration(parent_package='', top_path=None):
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from numpy.distutils.misc_util import Configuration
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config = Configuration('transform', parent_package, top_path)
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config.add_data_dir('tests')
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return config
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from __future__ import division, print_function, absolute_import
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import pytest
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import numpy as np
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from numpy.testing import assert_equal, assert_array_almost_equal
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from numpy.testing import assert_allclose
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from scipy.spatial.transform import Rotation, Slerp
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from scipy.stats import special_ortho_group
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from itertools import permutations
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def test_generic_quat_matrix():
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x = np.array([[3, 4, 0, 0], [5, 12, 0, 0]])
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r = Rotation.from_quat(x)
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expected_quat = x / np.array([[5], [13]])
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assert_array_almost_equal(r.as_quat(), expected_quat)
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def test_from_single_1d_quaternion():
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x = np.array([3, 4, 0, 0])
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r = Rotation.from_quat(x)
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expected_quat = x / 5
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assert_array_almost_equal(r.as_quat(), expected_quat)
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def test_from_single_2d_quaternion():
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x = np.array([[3, 4, 0, 0]])
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r = Rotation.from_quat(x)
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expected_quat = x / 5
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assert_array_almost_equal(r.as_quat(), expected_quat)
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def test_from_square_quat_matrix():
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# Ensure proper norm array broadcasting
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x = np.array([
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[3, 0, 0, 4],
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[5, 0, 12, 0],
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[0, 0, 0, 1],
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[0, 0, 0, -1]
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])
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r = Rotation.from_quat(x)
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expected_quat = x / np.array([[5], [13], [1], [1]])
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assert_array_almost_equal(r.as_quat(), expected_quat)
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def test_malformed_1d_from_quat():
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with pytest.raises(ValueError):
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Rotation.from_quat(np.array([1, 2, 3]))
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def test_malformed_2d_from_quat():
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with pytest.raises(ValueError):
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Rotation.from_quat(np.array([
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[1, 2, 3, 4, 5],
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[4, 5, 6, 7, 8]
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]))
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def test_zero_norms_from_quat():
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x = np.array([
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[3, 4, 0, 0],
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[0, 0, 0, 0],
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[5, 0, 12, 0]
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])
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with pytest.raises(ValueError):
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Rotation.from_quat(x)
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def test_as_dcm_single_1d_quaternion():
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quat = [0, 0, 0, 1]
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mat = Rotation.from_quat(quat).as_dcm()
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# mat.shape == (3,3) due to 1d input
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assert_array_almost_equal(mat, np.eye(3))
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def test_as_dcm_single_2d_quaternion():
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quat = [[0, 0, 1, 1]]
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mat = Rotation.from_quat(quat).as_dcm()
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assert_equal(mat.shape, (1, 3, 3))
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expected_mat = np.array([
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[0, -1, 0],
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[1, 0, 0],
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[0, 0, 1]
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])
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assert_array_almost_equal(mat[0], expected_mat)
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def test_as_dcm_from_square_input():
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quats = [
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[0, 0, 1, 1],
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[0, 1, 0, 1],
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[0, 0, 0, 1],
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[0, 0, 0, -1]
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]
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mat = Rotation.from_quat(quats).as_dcm()
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assert_equal(mat.shape, (4, 3, 3))
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expected0 = np.array([
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[0, -1, 0],
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[1, 0, 0],
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[0, 0, 1]
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])
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assert_array_almost_equal(mat[0], expected0)
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expected1 = np.array([
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[0, 0, 1],
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[0, 1, 0],
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[-1, 0, 0]
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])
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assert_array_almost_equal(mat[1], expected1)
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assert_array_almost_equal(mat[2], np.eye(3))
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assert_array_almost_equal(mat[3], np.eye(3))
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def test_as_dcm_from_generic_input():
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quats = [
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[0, 0, 1, 1],
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[0, 1, 0, 1],
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[1, 2, 3, 4]
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]
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mat = Rotation.from_quat(quats).as_dcm()
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assert_equal(mat.shape, (3, 3, 3))
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expected0 = np.array([
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[0, -1, 0],
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[1, 0, 0],
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[0, 0, 1]
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])
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assert_array_almost_equal(mat[0], expected0)
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expected1 = np.array([
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[0, 0, 1],
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[0, 1, 0],
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[-1, 0, 0]
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])
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assert_array_almost_equal(mat[1], expected1)
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expected2 = np.array([
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[0.4, -2, 2.2],
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[2.8, 1, 0.4],
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[-1, 2, 2]
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]) / 3
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assert_array_almost_equal(mat[2], expected2)
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def test_from_single_2d_dcm():
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dcm = [
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[0, 0, 1],
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[1, 0, 0],
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[0, 1, 0]
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]
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expected_quat = [0.5, 0.5, 0.5, 0.5]
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assert_array_almost_equal(
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Rotation.from_dcm(dcm).as_quat(),
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expected_quat)
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def test_from_single_3d_dcm():
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dcm = np.array([
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[0, 0, 1],
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[1, 0, 0],
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[0, 1, 0]
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]).reshape((1, 3, 3))
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expected_quat = np.array([0.5, 0.5, 0.5, 0.5]).reshape((1, 4))
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assert_array_almost_equal(
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Rotation.from_dcm(dcm).as_quat(),
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expected_quat)
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def test_from_dcm_calculation():
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expected_quat = np.array([1, 1, 6, 1]) / np.sqrt(39)
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dcm = np.array([
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[-0.8974359, -0.2564103, 0.3589744],
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[0.3589744, -0.8974359, 0.2564103],
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[0.2564103, 0.3589744, 0.8974359]
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])
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assert_array_almost_equal(
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Rotation.from_dcm(dcm).as_quat(),
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expected_quat)
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assert_array_almost_equal(
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Rotation.from_dcm(dcm.reshape((1, 3, 3))).as_quat(),
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expected_quat.reshape((1, 4)))
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def test_dcm_calculation_pipeline():
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dcm = special_ortho_group.rvs(3, size=10, random_state=0)
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assert_array_almost_equal(Rotation.from_dcm(dcm).as_dcm(), dcm)
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def test_from_dcm_ortho_output():
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np.random.seed(0)
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dcm = np.random.random((100, 3, 3))
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ortho_dcm = Rotation.from_dcm(dcm).as_dcm()
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mult_result = np.einsum('...ij,...jk->...ik', ortho_dcm,
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ortho_dcm.transpose((0, 2, 1)))
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eye3d = np.zeros((100, 3, 3))
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for i in range(3):
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eye3d[:, i, i] = 1.0
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assert_array_almost_equal(mult_result, eye3d)
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def test_from_1d_single_rotvec():
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rotvec = [1, 0, 0]
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expected_quat = np.array([0.4794255, 0, 0, 0.8775826])
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result = Rotation.from_rotvec(rotvec)
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assert_array_almost_equal(result.as_quat(), expected_quat)
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def test_from_2d_single_rotvec():
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rotvec = [[1, 0, 0]]
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expected_quat = np.array([[0.4794255, 0, 0, 0.8775826]])
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result = Rotation.from_rotvec(rotvec)
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assert_array_almost_equal(result.as_quat(), expected_quat)
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def test_from_generic_rotvec():
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rotvec = [
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[1, 2, 2],
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[1, -1, 0.5],
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[0, 0, 0]
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]
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expected_quat = np.array([
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[0.3324983, 0.6649967, 0.6649967, 0.0707372],
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[0.4544258, -0.4544258, 0.2272129, 0.7316889],
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[0, 0, 0, 1]
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])
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assert_array_almost_equal(
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Rotation.from_rotvec(rotvec).as_quat(),
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expected_quat)
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def test_from_rotvec_small_angle():
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rotvec = np.array([
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[5e-4 / np.sqrt(3), -5e-4 / np.sqrt(3), 5e-4 / np.sqrt(3)],
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[0.2, 0.3, 0.4],
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[0, 0, 0]
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])
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quat = Rotation.from_rotvec(rotvec).as_quat()
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# cos(theta/2) ~~ 1 for small theta
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assert_allclose(quat[0, 3], 1)
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# sin(theta/2) / theta ~~ 0.5 for small theta
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assert_allclose(quat[0, :3], rotvec[0] * 0.5)
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assert_allclose(quat[1, 3], 0.9639685)
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assert_allclose(
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quat[1, :3],
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np.array([
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0.09879603932153465,
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0.14819405898230198,
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0.19759207864306931
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]))
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assert_equal(quat[2], np.array([0, 0, 0, 1]))
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def test_malformed_1d_from_rotvec():
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with pytest.raises(ValueError, match='Expected `rot_vec` to have shape'):
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Rotation.from_rotvec([1, 2])
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def test_malformed_2d_from_rotvec():
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with pytest.raises(ValueError, match='Expected `rot_vec` to have shape'):
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Rotation.from_rotvec([
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[1, 2, 3, 4],
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[5, 6, 7, 8]
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])
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def test_as_generic_rotvec():
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quat = np.array([
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[1, 2, -1, 0.5],
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[1, -1, 1, 0.0003],
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[0, 0, 0, 1]
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])
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quat /= np.linalg.norm(quat, axis=1)[:, None]
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rotvec = Rotation.from_quat(quat).as_rotvec()
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angle = np.linalg.norm(rotvec, axis=1)
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assert_allclose(quat[:, 3], np.cos(angle/2))
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assert_allclose(np.cross(rotvec, quat[:, :3]), np.zeros((3, 3)))
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def test_as_rotvec_single_1d_input():
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quat = np.array([1, 2, -3, 2])
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expected_rotvec = np.array([0.5772381, 1.1544763, -1.7317144])
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actual_rotvec = Rotation.from_quat(quat).as_rotvec()
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assert_equal(actual_rotvec.shape, (3,))
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assert_allclose(actual_rotvec, expected_rotvec)
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def test_as_rotvec_single_2d_input():
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quat = np.array([[1, 2, -3, 2]])
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expected_rotvec = np.array([[0.5772381, 1.1544763, -1.7317144]])
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actual_rotvec = Rotation.from_quat(quat).as_rotvec()
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assert_equal(actual_rotvec.shape, (1, 3))
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assert_allclose(actual_rotvec, expected_rotvec)
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def test_rotvec_calc_pipeline():
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# Include small angles
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rotvec = np.array([
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[0, 0, 0],
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[1, -1, 2],
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[-3e-4, 3.5e-4, 7.5e-5]
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])
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assert_allclose(Rotation.from_rotvec(rotvec).as_rotvec(), rotvec)
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def test_from_euler_single_rotation():
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quat = Rotation.from_euler('z', 90, degrees=True).as_quat()
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expected_quat = np.array([0, 0, 1, 1]) / np.sqrt(2)
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assert_allclose(quat, expected_quat)
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def test_single_intrinsic_extrinsic_rotation():
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extrinsic = Rotation.from_euler('z', 90, degrees=True).as_dcm()
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intrinsic = Rotation.from_euler('Z', 90, degrees=True).as_dcm()
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assert_allclose(extrinsic, intrinsic)
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def test_from_euler_rotation_order():
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# Intrinsic rotation is same as extrinsic with order reversed
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np.random.seed(0)
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a = np.random.randint(low=0, high=180, size=(6, 3))
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b = a[:, ::-1]
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x = Rotation.from_euler('xyz', a, degrees=True).as_quat()
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y = Rotation.from_euler('ZYX', b, degrees=True).as_quat()
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assert_allclose(x, y)
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def test_from_euler_elementary_extrinsic_rotation():
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# Simple test to check if extrinsic rotations are implemented correctly
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dcm = Rotation.from_euler('zx', [90, 90], degrees=True).as_dcm()
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expected_dcm = np.array([
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[0, -1, 0],
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[0, 0, -1],
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[1, 0, 0]
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])
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assert_array_almost_equal(dcm, expected_dcm)
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def test_from_euler_intrinsic_rotation_312():
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angles = [
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[30, 60, 45],
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[30, 60, 30],
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[45, 30, 60]
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]
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dcm = Rotation.from_euler('ZXY', angles, degrees=True).as_dcm()
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assert_array_almost_equal(dcm[0], np.array([
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[0.3061862, -0.2500000, 0.9185587],
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[0.8838835, 0.4330127, -0.1767767],
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[-0.3535534, 0.8660254, 0.3535534]
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]))
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assert_array_almost_equal(dcm[1], np.array([
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[0.5334936, -0.2500000, 0.8080127],
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[0.8080127, 0.4330127, -0.3995191],
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[-0.2500000, 0.8660254, 0.4330127]
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]))
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assert_array_almost_equal(dcm[2], np.array([
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[0.0473672, -0.6123725, 0.7891491],
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[0.6597396, 0.6123725, 0.4355958],
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[-0.7500000, 0.5000000, 0.4330127]
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]))
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def test_from_euler_intrinsic_rotation_313():
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angles = [
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[30, 60, 45],
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[30, 60, 30],
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[45, 30, 60]
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]
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dcm = Rotation.from_euler('ZXZ', angles, degrees=True).as_dcm()
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assert_array_almost_equal(dcm[0], np.array([
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[0.43559574, -0.78914913, 0.4330127],
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[0.65973961, -0.04736717, -0.750000],
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[0.61237244, 0.61237244, 0.500000]
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]))
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assert_array_almost_equal(dcm[1], np.array([
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[0.6250000, -0.64951905, 0.4330127],
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[0.64951905, 0.1250000, -0.750000],
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[0.4330127, 0.750000, 0.500000]
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]))
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assert_array_almost_equal(dcm[2], np.array([
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[-0.1767767, -0.91855865, 0.35355339],
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[0.88388348, -0.30618622, -0.35355339],
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[0.4330127, 0.25000000, 0.8660254]
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]))
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def test_from_euler_extrinsic_rotation_312():
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angles = [
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[30, 60, 45],
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[30, 60, 30],
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[45, 30, 60]
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||||
]
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dcm = Rotation.from_euler('zxy', angles, degrees=True).as_dcm()
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||||
|
||||
assert_array_almost_equal(dcm[0], np.array([
|
||||
[0.91855865, 0.1767767, 0.35355339],
|
||||
[0.25000000, 0.4330127, -0.8660254],
|
||||
[-0.30618622, 0.88388348, 0.35355339]
|
||||
]))
|
||||
|
||||
assert_array_almost_equal(dcm[1], np.array([
|
||||
[0.96650635, -0.0580127, 0.2500000],
|
||||
[0.25000000, 0.4330127, -0.8660254],
|
||||
[-0.0580127, 0.89951905, 0.4330127]
|
||||
]))
|
||||
|
||||
assert_array_almost_equal(dcm[2], np.array([
|
||||
[0.65973961, -0.04736717, 0.7500000],
|
||||
[0.61237244, 0.61237244, -0.5000000],
|
||||
[-0.43559574, 0.78914913, 0.4330127]
|
||||
]))
|
||||
|
||||
|
||||
def test_from_euler_extrinsic_rotation_313():
|
||||
angles = [
|
||||
[30, 60, 45],
|
||||
[30, 60, 30],
|
||||
[45, 30, 60]
|
||||
]
|
||||
dcm = Rotation.from_euler('zxz', angles, degrees=True).as_dcm()
|
||||
|
||||
assert_array_almost_equal(dcm[0], np.array([
|
||||
[0.43559574, -0.65973961, 0.61237244],
|
||||
[0.78914913, -0.04736717, -0.61237244],
|
||||
[0.4330127, 0.75000000, 0.500000]
|
||||
]))
|
||||
|
||||
assert_array_almost_equal(dcm[1], np.array([
|
||||
[0.62500000, -0.64951905, 0.4330127],
|
||||
[0.64951905, 0.12500000, -0.750000],
|
||||
[0.4330127, 0.75000000, 0.500000]
|
||||
]))
|
||||
|
||||
assert_array_almost_equal(dcm[2], np.array([
|
||||
[-0.1767767, -0.88388348, 0.4330127],
|
||||
[0.91855865, -0.30618622, -0.250000],
|
||||
[0.35355339, 0.35355339, 0.8660254]
|
||||
]))
|
||||
|
||||
|
||||
def test_as_euler_asymmetric_axes():
|
||||
np.random.seed(0)
|
||||
n = 10
|
||||
angles = np.empty((n, 3))
|
||||
angles[:, 0] = np.random.uniform(low=-np.pi, high=np.pi, size=(n,))
|
||||
angles[:, 1] = np.random.uniform(low=-np.pi / 2, high=np.pi / 2, size=(n,))
|
||||
angles[:, 2] = np.random.uniform(low=-np.pi, high=np.pi, size=(n,))
|
||||
|
||||
for seq_tuple in permutations('xyz'):
|
||||
# Extrinsic rotations
|
||||
seq = ''.join(seq_tuple)
|
||||
assert_allclose(angles, Rotation.from_euler(seq, angles).as_euler(seq))
|
||||
# Intrinsic rotations
|
||||
seq = seq.upper()
|
||||
assert_allclose(angles, Rotation.from_euler(seq, angles).as_euler(seq))
|
||||
|
||||
|
||||
def test_as_euler_symmetric_axes():
|
||||
np.random.seed(0)
|
||||
n = 10
|
||||
angles = np.empty((n, 3))
|
||||
angles[:, 0] = np.random.uniform(low=-np.pi, high=np.pi, size=(n,))
|
||||
angles[:, 1] = np.random.uniform(low=0, high=np.pi, size=(n,))
|
||||
angles[:, 2] = np.random.uniform(low=-np.pi, high=np.pi, size=(n,))
|
||||
|
||||
for axis1 in ['x', 'y', 'z']:
|
||||
for axis2 in ['x', 'y', 'z']:
|
||||
if axis1 == axis2:
|
||||
continue
|
||||
# Extrinsic rotations
|
||||
seq = axis1 + axis2 + axis1
|
||||
assert_allclose(
|
||||
angles, Rotation.from_euler(seq, angles).as_euler(seq))
|
||||
# Intrinsic rotations
|
||||
seq = seq.upper()
|
||||
assert_allclose(
|
||||
angles, Rotation.from_euler(seq, angles).as_euler(seq))
|
||||
|
||||
|
||||
def test_as_euler_degenerate_asymmetric_axes():
|
||||
# Since we cannot check for angle equality, we check for dcm equality
|
||||
angles = np.array([
|
||||
[45, 90, 35],
|
||||
[35, -90, 20],
|
||||
[35, 90, 25],
|
||||
[25, -90, 15]
|
||||
])
|
||||
|
||||
with pytest.warns(UserWarning, match="Gimbal lock"):
|
||||
for seq_tuple in permutations('xyz'):
|
||||
# Extrinsic rotations
|
||||
seq = ''.join(seq_tuple)
|
||||
rotation = Rotation.from_euler(seq, angles, degrees=True)
|
||||
dcm_expected = rotation.as_dcm()
|
||||
|
||||
angle_estimates = rotation.as_euler(seq, degrees=True)
|
||||
dcm_estimated = Rotation.from_euler(
|
||||
seq, angle_estimates, degrees=True
|
||||
).as_dcm()
|
||||
|
||||
assert_array_almost_equal(dcm_expected, dcm_estimated)
|
||||
|
||||
# Intrinsic rotations
|
||||
seq = seq.upper()
|
||||
rotation = Rotation.from_euler(seq, angles, degrees=True)
|
||||
dcm_expected = rotation.as_dcm()
|
||||
|
||||
angle_estimates = rotation.as_euler(seq, degrees=True)
|
||||
dcm_estimated = Rotation.from_euler(
|
||||
seq, angle_estimates, degrees=True
|
||||
).as_dcm()
|
||||
|
||||
assert_array_almost_equal(dcm_expected, dcm_estimated)
|
||||
|
||||
|
||||
def test_as_euler_degenerate_symmetric_axes():
|
||||
# Since we cannot check for angle equality, we check for dcm equality
|
||||
angles = np.array([
|
||||
[15, 0, 60],
|
||||
[35, 0, 75],
|
||||
[60, 180, 35],
|
||||
[15, -180, 25],
|
||||
])
|
||||
|
||||
with pytest.warns(UserWarning, match="Gimbal lock"):
|
||||
for axis1 in ['x', 'y', 'z']:
|
||||
for axis2 in ['x', 'y', 'z']:
|
||||
if axis1 == axis2:
|
||||
continue
|
||||
|
||||
# Extrinsic rotations
|
||||
seq = axis1 + axis2 + axis1
|
||||
rotation = Rotation.from_euler(seq, angles, degrees=True)
|
||||
dcm_expected = rotation.as_dcm()
|
||||
|
||||
angle_estimates = rotation.as_euler(seq, degrees=True)
|
||||
dcm_estimated = Rotation.from_euler(
|
||||
seq, angle_estimates, degrees=True
|
||||
).as_dcm()
|
||||
|
||||
assert_array_almost_equal(dcm_expected, dcm_estimated)
|
||||
|
||||
# Intrinsic rotations
|
||||
seq = seq.upper()
|
||||
rotation = Rotation.from_euler(seq, angles, degrees=True)
|
||||
dcm_expected = rotation.as_dcm()
|
||||
|
||||
angle_estimates = rotation.as_euler(seq, degrees=True)
|
||||
dcm_estimated = Rotation.from_euler(
|
||||
seq, angle_estimates, degrees=True
|
||||
).as_dcm()
|
||||
|
||||
assert_array_almost_equal(dcm_expected, dcm_estimated)
|
||||
|
||||
|
||||
def test_inv():
|
||||
np.random.seed(0)
|
||||
n = 10
|
||||
p = Rotation.from_quat(np.random.normal(size=(n, 4)))
|
||||
q = p.inv()
|
||||
|
||||
p_dcm = p.as_dcm()
|
||||
q_dcm = q.as_dcm()
|
||||
result1 = np.einsum('...ij,...jk->...ik', p_dcm, q_dcm)
|
||||
result2 = np.einsum('...ij,...jk->...ik', q_dcm, p_dcm)
|
||||
|
||||
eye3d = np.empty((n, 3, 3))
|
||||
eye3d[:] = np.eye(3)
|
||||
|
||||
assert_array_almost_equal(result1, eye3d)
|
||||
assert_array_almost_equal(result2, eye3d)
|
||||
|
||||
|
||||
def test_inv_single_rotation():
|
||||
np.random.seed(0)
|
||||
p = Rotation.from_quat(np.random.normal(size=(4,)))
|
||||
q = p.inv()
|
||||
|
||||
p_dcm = p.as_dcm()
|
||||
q_dcm = q.as_dcm()
|
||||
res1 = np.dot(p_dcm, q_dcm)
|
||||
res2 = np.dot(q_dcm, p_dcm)
|
||||
|
||||
eye = np.eye(3)
|
||||
|
||||
assert_array_almost_equal(res1, eye)
|
||||
assert_array_almost_equal(res2, eye)
|
||||
|
||||
x = Rotation.from_quat(np.random.normal(size=(1, 4)))
|
||||
y = x.inv()
|
||||
|
||||
x_dcm = x.as_dcm()
|
||||
y_dcm = y.as_dcm()
|
||||
result1 = np.einsum('...ij,...jk->...ik', x_dcm, y_dcm)
|
||||
result2 = np.einsum('...ij,...jk->...ik', y_dcm, x_dcm)
|
||||
|
||||
eye3d = np.empty((1, 3, 3))
|
||||
eye3d[:] = np.eye(3)
|
||||
|
||||
assert_array_almost_equal(result1, eye3d)
|
||||
assert_array_almost_equal(result2, eye3d)
|
||||
|
||||
|
||||
def test_apply_single_rotation_single_point():
|
||||
dcm = np.array([
|
||||
[0, -1, 0],
|
||||
[1, 0, 0],
|
||||
[0, 0, 1]
|
||||
])
|
||||
r_1d = Rotation.from_dcm(dcm)
|
||||
r_2d = Rotation.from_dcm(np.expand_dims(dcm, axis=0))
|
||||
|
||||
v_1d = np.array([1, 2, 3])
|
||||
v_2d = np.expand_dims(v_1d, axis=0)
|
||||
v1d_rotated = np.array([-2, 1, 3])
|
||||
v2d_rotated = np.expand_dims(v1d_rotated, axis=0)
|
||||
|
||||
assert_allclose(r_1d.apply(v_1d), v1d_rotated)
|
||||
assert_allclose(r_1d.apply(v_2d), v2d_rotated)
|
||||
assert_allclose(r_2d.apply(v_1d), v2d_rotated)
|
||||
assert_allclose(r_2d.apply(v_2d), v2d_rotated)
|
||||
|
||||
v1d_inverse = np.array([2, -1, 3])
|
||||
v2d_inverse = np.expand_dims(v1d_inverse, axis=0)
|
||||
|
||||
assert_allclose(r_1d.apply(v_1d, inverse=True), v1d_inverse)
|
||||
assert_allclose(r_1d.apply(v_2d, inverse=True), v2d_inverse)
|
||||
assert_allclose(r_2d.apply(v_1d, inverse=True), v2d_inverse)
|
||||
assert_allclose(r_2d.apply(v_2d, inverse=True), v2d_inverse)
|
||||
|
||||
|
||||
def test_apply_single_rotation_multiple_points():
|
||||
dcm = np.array([
|
||||
[0, -1, 0],
|
||||
[1, 0, 0],
|
||||
[0, 0, 1]
|
||||
])
|
||||
r1 = Rotation.from_dcm(dcm)
|
||||
r2 = Rotation.from_dcm(np.expand_dims(dcm, axis=0))
|
||||
|
||||
v = np.array([[1, 2, 3], [4, 5, 6]])
|
||||
v_rotated = np.array([[-2, 1, 3], [-5, 4, 6]])
|
||||
|
||||
assert_allclose(r1.apply(v), v_rotated)
|
||||
assert_allclose(r2.apply(v), v_rotated)
|
||||
|
||||
v_inverse = np.array([[2, -1, 3], [5, -4, 6]])
|
||||
|
||||
assert_allclose(r1.apply(v, inverse=True), v_inverse)
|
||||
assert_allclose(r2.apply(v, inverse=True), v_inverse)
|
||||
|
||||
|
||||
def test_apply_multiple_rotations_single_point():
|
||||
dcm = np.empty((2, 3, 3))
|
||||
dcm[0] = np.array([
|
||||
[0, -1, 0],
|
||||
[1, 0, 0],
|
||||
[0, 0, 1]
|
||||
])
|
||||
dcm[1] = np.array([
|
||||
[1, 0, 0],
|
||||
[0, 0, -1],
|
||||
[0, 1, 0]
|
||||
])
|
||||
r = Rotation.from_dcm(dcm)
|
||||
|
||||
v1 = np.array([1, 2, 3])
|
||||
v2 = np.expand_dims(v1, axis=0)
|
||||
|
||||
v_rotated = np.array([[-2, 1, 3], [1, -3, 2]])
|
||||
|
||||
assert_allclose(r.apply(v1), v_rotated)
|
||||
assert_allclose(r.apply(v2), v_rotated)
|
||||
|
||||
v_inverse = np.array([[2, -1, 3], [1, 3, -2]])
|
||||
|
||||
assert_allclose(r.apply(v1, inverse=True), v_inverse)
|
||||
assert_allclose(r.apply(v2, inverse=True), v_inverse)
|
||||
|
||||
|
||||
def test_apply_multiple_rotations_multiple_points():
|
||||
dcm = np.empty((2, 3, 3))
|
||||
dcm[0] = np.array([
|
||||
[0, -1, 0],
|
||||
[1, 0, 0],
|
||||
[0, 0, 1]
|
||||
])
|
||||
dcm[1] = np.array([
|
||||
[1, 0, 0],
|
||||
[0, 0, -1],
|
||||
[0, 1, 0]
|
||||
])
|
||||
r = Rotation.from_dcm(dcm)
|
||||
|
||||
v = np.array([[1, 2, 3], [4, 5, 6]])
|
||||
v_rotated = np.array([[-2, 1, 3], [4, -6, 5]])
|
||||
assert_allclose(r.apply(v), v_rotated)
|
||||
|
||||
v_inverse = np.array([[2, -1, 3], [4, 6, -5]])
|
||||
assert_allclose(r.apply(v, inverse=True), v_inverse)
|
||||
|
||||
|
||||
def test_getitem():
|
||||
dcm = np.empty((2, 3, 3))
|
||||
dcm[0] = np.array([
|
||||
[0, -1, 0],
|
||||
[1, 0, 0],
|
||||
[0, 0, 1]
|
||||
])
|
||||
dcm[1] = np.array([
|
||||
[1, 0, 0],
|
||||
[0, 0, -1],
|
||||
[0, 1, 0]
|
||||
])
|
||||
r = Rotation.from_dcm(dcm)
|
||||
|
||||
assert_allclose(r[0].as_dcm(), dcm[0])
|
||||
assert_allclose(r[1].as_dcm(), dcm[1])
|
||||
assert_allclose(r[:-1].as_dcm(), np.expand_dims(dcm[0], axis=0))
|
||||
|
||||
|
||||
def test_n_rotations():
|
||||
dcm = np.empty((2, 3, 3))
|
||||
dcm[0] = np.array([
|
||||
[0, -1, 0],
|
||||
[1, 0, 0],
|
||||
[0, 0, 1]
|
||||
])
|
||||
dcm[1] = np.array([
|
||||
[1, 0, 0],
|
||||
[0, 0, -1],
|
||||
[0, 1, 0]
|
||||
])
|
||||
r = Rotation.from_dcm(dcm)
|
||||
|
||||
assert_equal(len(r), 2)
|
||||
assert_equal(len(r[0]), 1)
|
||||
assert_equal(len(r[1]), 1)
|
||||
assert_equal(len(r[:-1]), 1)
|
||||
|
||||
|
||||
def test_quat_ownership():
|
||||
# Ensure that users cannot accidentally corrupt object
|
||||
quat = np.array([
|
||||
[1, 0, 0, 0],
|
||||
[0, 1, 0, 0],
|
||||
[0, 0, 1, 0]
|
||||
])
|
||||
r = Rotation.from_quat(quat, normalized=True)
|
||||
s = r[0:2]
|
||||
|
||||
r._quat[0] = np.array([0, -1, 0, 0])
|
||||
assert_allclose(s._quat[0], np.array([1, 0, 0, 0]))
|
||||
|
||||
|
||||
def test_match_vectors_no_rotation():
|
||||
x = np.array([[1, 2, 3], [4, 5, 6]])
|
||||
y = x.copy()
|
||||
|
||||
r, p = Rotation.match_vectors(x, y)
|
||||
assert_array_almost_equal(r.as_dcm(), np.eye(3))
|
||||
|
||||
|
||||
def test_match_vectors_no_noise():
|
||||
np.random.seed(0)
|
||||
c = Rotation.from_quat(np.random.normal(size=4))
|
||||
b = np.random.normal(size=(5, 3))
|
||||
a = c.apply(b)
|
||||
|
||||
est, cov = Rotation.match_vectors(a, b)
|
||||
assert_allclose(c.as_quat(), est.as_quat())
|
||||
|
||||
|
||||
def test_match_vectors_noise():
|
||||
np.random.seed(0)
|
||||
n_vectors = 100
|
||||
rot = Rotation.from_euler('xyz', np.random.normal(size=3))
|
||||
vectors = np.random.normal(size=(n_vectors, 3))
|
||||
result = rot.apply(vectors)
|
||||
|
||||
# The paper adds noise as indepedently distributed angular errors
|
||||
sigma = np.deg2rad(1)
|
||||
tolerance = 1.5 * sigma
|
||||
noise = Rotation.from_rotvec(
|
||||
np.random.normal(
|
||||
size=(n_vectors, 3),
|
||||
scale=sigma
|
||||
)
|
||||
)
|
||||
|
||||
# Attitude errors must preserve norm. Hence apply individual random
|
||||
# rotations to each vector.
|
||||
noisy_result = noise.apply(result)
|
||||
|
||||
est, cov = Rotation.match_vectors(noisy_result, vectors)
|
||||
|
||||
# Use rotation compositions to find out closeness
|
||||
error_vector = (rot * est.inv()).as_rotvec()
|
||||
assert_allclose(error_vector[0], 0, atol=tolerance)
|
||||
assert_allclose(error_vector[1], 0, atol=tolerance)
|
||||
assert_allclose(error_vector[2], 0, atol=tolerance)
|
||||
|
||||
# Check error bounds using covariance matrix
|
||||
cov *= sigma
|
||||
assert_allclose(cov[0, 0], 0, atol=tolerance)
|
||||
assert_allclose(cov[1, 1], 0, atol=tolerance)
|
||||
assert_allclose(cov[2, 2], 0, atol=tolerance)
|
||||
|
||||
|
||||
def test_random_rotation_shape():
|
||||
assert_equal(Rotation.random().as_quat().shape, (4,))
|
||||
assert_equal(Rotation.random(None).as_quat().shape, (4,))
|
||||
|
||||
assert_equal(Rotation.random(1).as_quat().shape, (1, 4))
|
||||
assert_equal(Rotation.random(5).as_quat().shape, (5, 4))
|
||||
|
||||
|
||||
def test_slerp():
|
||||
np.random.seed(0)
|
||||
|
||||
key_rots = Rotation.from_quat(np.random.uniform(size=(5, 4)))
|
||||
key_quats = key_rots.as_quat()
|
||||
|
||||
key_times = [0, 1, 2, 3, 4]
|
||||
interpolator = Slerp(key_times, key_rots)
|
||||
|
||||
times = [0, 0.5, 0.25, 1, 1.5, 2, 2.75, 3, 3.25, 3.60, 4]
|
||||
interp_rots = interpolator(times)
|
||||
interp_quats = interp_rots.as_quat()
|
||||
|
||||
# Dot products are affected by sign of quaternions
|
||||
interp_quats[interp_quats[:, -1] < 0] *= -1
|
||||
# Checking for quaternion equality, perform same operation
|
||||
key_quats[key_quats[:, -1] < 0] *= -1
|
||||
|
||||
# Equality at keyframes, including both endpoints
|
||||
assert_allclose(interp_quats[0], key_quats[0])
|
||||
assert_allclose(interp_quats[3], key_quats[1])
|
||||
assert_allclose(interp_quats[5], key_quats[2])
|
||||
assert_allclose(interp_quats[7], key_quats[3])
|
||||
assert_allclose(interp_quats[10], key_quats[4])
|
||||
|
||||
# Constant angular velocity between keyframes. Check by equating
|
||||
# cos(theta) between quaternion pairs with equal time difference.
|
||||
cos_theta1 = np.sum(interp_quats[0] * interp_quats[2])
|
||||
cos_theta2 = np.sum(interp_quats[2] * interp_quats[1])
|
||||
assert_allclose(cos_theta1, cos_theta2)
|
||||
|
||||
cos_theta4 = np.sum(interp_quats[3] * interp_quats[4])
|
||||
cos_theta5 = np.sum(interp_quats[4] * interp_quats[5])
|
||||
assert_allclose(cos_theta4, cos_theta5)
|
||||
|
||||
# theta1: 0 -> 0.25, theta3 : 0.5 -> 1
|
||||
# Use double angle formula for double the time difference
|
||||
cos_theta3 = np.sum(interp_quats[1] * interp_quats[3])
|
||||
assert_allclose(cos_theta3, 2 * (cos_theta1**2) - 1)
|
||||
|
||||
# Miscellaneous checks
|
||||
assert_equal(len(interp_rots), len(times))
|
||||
|
||||
|
||||
def test_slerp_single_rot():
|
||||
with pytest.raises(ValueError, match="at least 2 rotations"):
|
||||
r = Rotation.from_quat([1, 2, 3, 4])
|
||||
Slerp([1], r)
|
||||
|
||||
|
||||
def test_slerp_time_dim_mismatch():
|
||||
with pytest.raises(ValueError,
|
||||
match="times to be specified in a 1 dimensional array"):
|
||||
np.random.seed(0)
|
||||
r = Rotation.from_quat(np.random.uniform(size=(2, 4)))
|
||||
t = np.array([[1],
|
||||
[2]])
|
||||
Slerp(t, r)
|
||||
|
||||
|
||||
def test_slerp_num_rotations_mismatch():
|
||||
with pytest.raises(ValueError, match="number of rotations to be equal to "
|
||||
"number of timestamps"):
|
||||
np.random.seed(0)
|
||||
r = Rotation.from_quat(np.random.uniform(size=(5, 4)))
|
||||
t = np.arange(7)
|
||||
Slerp(t, r)
|
||||
|
||||
|
||||
def test_slerp_equal_times():
|
||||
with pytest.raises(ValueError, match="strictly increasing order"):
|
||||
np.random.seed(0)
|
||||
r = Rotation.from_quat(np.random.uniform(size=(5, 4)))
|
||||
t = [0, 1, 2, 2, 4]
|
||||
Slerp(t, r)
|
||||
|
||||
|
||||
def test_slerp_decreasing_times():
|
||||
with pytest.raises(ValueError, match="strictly increasing order"):
|
||||
np.random.seed(0)
|
||||
r = Rotation.from_quat(np.random.uniform(size=(5, 4)))
|
||||
t = [0, 1, 3, 2, 4]
|
||||
Slerp(t, r)
|
||||
|
||||
|
||||
def test_slerp_call_time_dim_mismatch():
|
||||
np.random.seed(0)
|
||||
r = Rotation.from_quat(np.random.uniform(size=(5, 4)))
|
||||
t = np.arange(5)
|
||||
s = Slerp(t, r)
|
||||
|
||||
with pytest.raises(ValueError,
|
||||
match="times to be specified in a 1 dimensional array"):
|
||||
interp_times = np.array([[3.5],
|
||||
[4.2]])
|
||||
s(interp_times)
|
||||
|
||||
|
||||
def test_slerp_call_time_out_of_range():
|
||||
np.random.seed(0)
|
||||
r = Rotation.from_quat(np.random.uniform(size=(5, 4)))
|
||||
t = np.arange(5) + 1
|
||||
s = Slerp(t, r)
|
||||
|
||||
with pytest.raises(ValueError, match="times must be within the range"):
|
||||
s([0, 1, 2])
|
||||
with pytest.raises(ValueError, match="times must be within the range"):
|
||||
s([1, 2, 6])
|
||||
Reference in New Issue
Block a user