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test_transforms3d.py
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executable file
·811 lines (671 loc) · 30.8 KB
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Fri Apr 10 14:19:04 2020
@author: corkep
"""
import numpy as np
import numpy.testing as nt
import unittest
from math import pi
from scipy.linalg import logm
from spatialmath.base.transforms3d import *
from spatialmath.base.transformsNd import isR, t2r, r2t, rt2tr, skew
class Test3D(unittest.TestCase):
def test_checks(self):
# 2D case, with rotation matrix
R = np.eye(2)
nt.assert_equal(isR(R), True)
nt.assert_equal(isrot(R), False)
nt.assert_equal(ishom(R), False)
nt.assert_equal(isrot(R, True), False)
nt.assert_equal(ishom(R, True), False)
# 2D case, invalid rotation matrix
R = np.array([[1, 1], [0, 1]])
nt.assert_equal(isR(R), False)
nt.assert_equal(isrot(R), False)
nt.assert_equal(ishom(R), False)
nt.assert_equal(isrot(R, True), False)
nt.assert_equal(ishom(R, True), False)
# 2D case, with homogeneous transformation matrix
T = np.array([[1, 0, 3], [0, 1, 4], [0, 0, 1]])
nt.assert_equal(isR(T), False)
nt.assert_equal(isrot(T), True)
nt.assert_equal(ishom(T), False)
nt.assert_equal(isrot(T, True), False)
nt.assert_equal(ishom(T, True), False)
# 2D case, invalid rotation matrix
T = np.array([[1, 1, 3], [0, 1, 4], [0, 0, 1]])
nt.assert_equal(isR(T), False)
nt.assert_equal(isrot(T), True)
nt.assert_equal(ishom(T), False)
nt.assert_equal(isrot(T, True), False)
nt.assert_equal(ishom(T, True), False)
# 2D case, invalid bottom row
T = np.array([[1, 1, 3], [0, 1, 4], [9, 0, 1]])
nt.assert_equal(isR(T), False)
nt.assert_equal(isrot(T), True)
nt.assert_equal(ishom(T), False)
nt.assert_equal(isrot(T, True), False)
nt.assert_equal(ishom(T, True), False)
# reflection case
T = np.array([[-1, 0, 0], [0, 1, 0], [0, 0, 1]])
nt.assert_equal(isR(T), False)
nt.assert_equal(isrot(T), True)
nt.assert_equal(ishom(T), False)
nt.assert_equal(isrot(T, True), False)
nt.assert_equal(ishom(T, True), False)
def test_trinv(self):
T = np.eye(4)
nt.assert_array_almost_equal(trinv(T), T)
T = trotx(0.3)
nt.assert_array_almost_equal(trinv(T) @ T, np.eye(4))
T = transl(1, 2, 3)
nt.assert_array_almost_equal(trinv(T) @ T, np.eye(4))
def test_rotx(self):
R = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
nt.assert_array_almost_equal(rotx(0), R)
nt.assert_array_almost_equal(rotx(0, unit="rad"), R)
nt.assert_array_almost_equal(rotx(0, unit="deg"), R)
nt.assert_array_almost_equal(rotx(0, "deg"), R)
nt.assert_almost_equal(np.linalg.det(rotx(0)), 1)
R = np.array([[1, 0, 0], [0, 0, -1], [0, 1, 0]])
nt.assert_array_almost_equal(rotx(pi / 2), R)
nt.assert_array_almost_equal(rotx(pi / 2, unit="rad"), R)
nt.assert_array_almost_equal(rotx(90, unit="deg"), R)
nt.assert_array_almost_equal(rotx(90, "deg"), R)
nt.assert_almost_equal(np.linalg.det(rotx(pi / 2)), 1)
R = np.array([[1, 0, 0], [0, -1, 0], [0, 0, -1]])
nt.assert_array_almost_equal(rotx(pi), R)
nt.assert_array_almost_equal(rotx(pi, unit="rad"), R)
nt.assert_array_almost_equal(rotx(180, unit="deg"), R)
nt.assert_array_almost_equal(rotx(180, "deg"), R)
nt.assert_almost_equal(np.linalg.det(rotx(pi)), 1)
def test_roty(self):
R = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
nt.assert_array_almost_equal(roty(0), R)
nt.assert_array_almost_equal(roty(0, unit="rad"), R)
nt.assert_array_almost_equal(roty(0, unit="deg"), R)
nt.assert_array_almost_equal(roty(0, "deg"), R)
nt.assert_almost_equal(np.linalg.det(roty(0)), 1)
R = np.array([[0, 0, 1], [0, 1, 0], [-1, 0, 0]])
nt.assert_array_almost_equal(roty(pi / 2), R)
nt.assert_array_almost_equal(roty(pi / 2, unit="rad"), R)
nt.assert_array_almost_equal(roty(90, unit="deg"), R)
nt.assert_array_almost_equal(roty(90, "deg"), R)
nt.assert_almost_equal(np.linalg.det(roty(pi / 2)), 1)
R = np.array([[-1, 0, 0], [0, 1, 0], [0, 0, -1]])
nt.assert_array_almost_equal(roty(pi), R)
nt.assert_array_almost_equal(roty(pi, unit="rad"), R)
nt.assert_array_almost_equal(roty(180, unit="deg"), R)
nt.assert_array_almost_equal(roty(180, "deg"), R)
nt.assert_almost_equal(np.linalg.det(roty(pi)), 1)
def test_rotz(self):
R = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
nt.assert_array_almost_equal(rotz(0), R)
nt.assert_array_almost_equal(rotz(0, unit="rad"), R)
nt.assert_array_almost_equal(rotz(0, unit="deg"), R)
nt.assert_array_almost_equal(rotz(0, "deg"), R)
nt.assert_almost_equal(np.linalg.det(rotz(0)), 1)
R = np.array([[0, -1, 0], [1, 0, 0], [0, 0, 1]])
nt.assert_array_almost_equal(rotz(pi / 2), R)
nt.assert_array_almost_equal(rotz(pi / 2, unit="rad"), R)
nt.assert_array_almost_equal(rotz(90, unit="deg"), R)
nt.assert_array_almost_equal(rotz(90, "deg"), R)
nt.assert_almost_equal(np.linalg.det(rotz(pi / 2)), 1)
R = np.array([[-1, 0, 0], [0, -1, 0], [0, 0, 1]])
nt.assert_array_almost_equal(rotz(pi), R)
nt.assert_array_almost_equal(rotz(pi, unit="rad"), R)
nt.assert_array_almost_equal(rotz(180, unit="deg"), R)
nt.assert_array_almost_equal(rotz(180, "deg"), R)
nt.assert_almost_equal(np.linalg.det(rotz(pi)), 1)
def test_trotX(self):
T = np.array([[1, 0, 0, 3], [0, 0, -1, 4], [0, 1, 0, 5], [0, 0, 0, 1]])
nt.assert_array_almost_equal(trotx(pi / 2, t=[3, 4, 5]), T)
nt.assert_array_almost_equal(trotx(pi / 2, t=(3, 4, 5)), T)
nt.assert_array_almost_equal(trotx(pi / 2, t=np.array([3, 4, 5])), T)
T = np.array([[0, 0, 1, 3], [0, 1, 0, 4], [-1, 0, 0, 5], [0, 0, 0, 1]])
nt.assert_array_almost_equal(troty(pi / 2, t=[3, 4, 5]), T)
nt.assert_array_almost_equal(troty(pi / 2, t=(3, 4, 5)), T)
nt.assert_array_almost_equal(troty(pi / 2, t=np.array([3, 4, 5])), T)
T = np.array([[0, -1, 0, 3], [1, 0, 0, 4], [0, 0, 1, 5], [0, 0, 0, 1]])
nt.assert_array_almost_equal(trotz(pi / 2, t=[3, 4, 5]), T)
nt.assert_array_almost_equal(trotz(pi / 2, t=(3, 4, 5)), T)
nt.assert_array_almost_equal(trotz(pi / 2, t=np.array([3, 4, 5])), T)
def test_rpy2r(self):
r2d = 180 / pi
# default zyx order
R = rotz(0.3) @ roty(0.2) @ rotx(0.1)
nt.assert_array_almost_equal(rpy2r(0.1, 0.2, 0.3), R)
nt.assert_array_almost_equal(rpy2r([0.1, 0.2, 0.3]), R)
nt.assert_array_almost_equal(
rpy2r(0.1 * r2d, 0.2 * r2d, 0.3 * r2d, unit="deg"), R
)
nt.assert_array_almost_equal(
rpy2r([0.1 * r2d, 0.2 * r2d, 0.3 * r2d], unit="deg"), R
)
# xyz order
R = rotx(0.3) @ roty(0.2) @ rotz(0.1)
nt.assert_array_almost_equal(rpy2r(0.1, 0.2, 0.3, order="xyz"), R)
nt.assert_array_almost_equal(rpy2r([0.1, 0.2, 0.3], order="xyz"), R)
nt.assert_array_almost_equal(
rpy2r(0.1 * r2d, 0.2 * r2d, 0.3 * r2d, unit="deg", order="xyz"), R
)
nt.assert_array_almost_equal(
rpy2r([0.1 * r2d, 0.2 * r2d, 0.3 * r2d], unit="deg", order="xyz"), R
)
# yxz order
R = roty(0.3) @ rotx(0.2) @ rotz(0.1)
nt.assert_array_almost_equal(rpy2r(0.1, 0.2, 0.3, order="yxz"), R)
nt.assert_array_almost_equal(rpy2r([0.1, 0.2, 0.3], order="yxz"), R)
nt.assert_array_almost_equal(
rpy2r(0.1 * r2d, 0.2 * r2d, 0.3 * r2d, unit="deg", order="yxz"), R
)
nt.assert_array_almost_equal(
rpy2r([0.1 * r2d, 0.2 * r2d, 0.3 * r2d], unit="deg", order="yxz"), R
)
def test_rpy2tr(self):
r2d = 180 / pi
# default zyx order
T = trotz(0.3) @ troty(0.2) @ trotx(0.1)
nt.assert_array_almost_equal(rpy2tr(0.1, 0.2, 0.3), T)
nt.assert_array_almost_equal(rpy2tr([0.1, 0.2, 0.3]), T)
nt.assert_array_almost_equal(
rpy2tr(0.1 * r2d, 0.2 * r2d, 0.3 * r2d, unit="deg"), T
)
nt.assert_array_almost_equal(
rpy2tr([0.1 * r2d, 0.2 * r2d, 0.3 * r2d], unit="deg"), T
)
# xyz order
T = trotx(0.3) @ troty(0.2) @ trotz(0.1)
nt.assert_array_almost_equal(rpy2tr(0.1, 0.2, 0.3, order="xyz"), T)
nt.assert_array_almost_equal(rpy2tr([0.1, 0.2, 0.3], order="xyz"), T)
nt.assert_array_almost_equal(
rpy2tr(0.1 * r2d, 0.2 * r2d, 0.3 * r2d, unit="deg", order="xyz"), T
)
nt.assert_array_almost_equal(
rpy2tr([0.1 * r2d, 0.2 * r2d, 0.3 * r2d], unit="deg", order="xyz"), T
)
# yxz order
T = troty(0.3) @ trotx(0.2) @ trotz(0.1)
nt.assert_array_almost_equal(rpy2tr(0.1, 0.2, 0.3, order="yxz"), T)
nt.assert_array_almost_equal(rpy2tr([0.1, 0.2, 0.3], order="yxz"), T)
nt.assert_array_almost_equal(
rpy2tr(0.1 * r2d, 0.2 * r2d, 0.3 * r2d, unit="deg", order="yxz"), T
)
nt.assert_array_almost_equal(
rpy2tr([0.1 * r2d, 0.2 * r2d, 0.3 * r2d], unit="deg", order="yxz"), T
)
def test_eul2r(self):
r2d = 180 / pi
# default zyx order
R = rotz(0.1) @ roty(0.2) @ rotz(0.3)
nt.assert_array_almost_equal(eul2r(0.1, 0.2, 0.3), R)
nt.assert_array_almost_equal(eul2r([0.1, 0.2, 0.3]), R)
nt.assert_array_almost_equal(
eul2r(0.1 * r2d, 0.2 * r2d, 0.3 * r2d, unit="deg"), R
)
nt.assert_array_almost_equal(
eul2r([0.1 * r2d, 0.2 * r2d, 0.3 * r2d], unit="deg"), R
)
def test_eul2tr(self):
r2d = 180 / pi
# default zyx order
T = trotz(0.1) @ troty(0.2) @ trotz(0.3)
nt.assert_array_almost_equal(eul2tr(0.1, 0.2, 0.3), T)
nt.assert_array_almost_equal(eul2tr([0.1, 0.2, 0.3]), T)
nt.assert_array_almost_equal(
eul2tr(0.1 * r2d, 0.2 * r2d, 0.3 * r2d, unit="deg"), T
)
nt.assert_array_almost_equal(
eul2tr([0.1 * r2d, 0.2 * r2d, 0.3 * r2d], unit="deg"), T
)
def test_angvec2r(self):
r2d = 180 / pi
nt.assert_array_almost_equal(angvec2r(0, [1, 0, 0]), rotx(0))
nt.assert_array_almost_equal(angvec2r(pi / 4, [1, 0, 0]), rotx(pi / 4))
nt.assert_array_almost_equal(angvec2r(-pi / 4, [1, 0, 0]), rotx(-pi / 4))
nt.assert_array_almost_equal(angvec2r(0, [0, 1, 0]), roty(0))
nt.assert_array_almost_equal(angvec2r(pi / 4, [0, 1, 0]), roty(pi / 4))
nt.assert_array_almost_equal(angvec2r(-pi / 4, [0, 1, 0]), roty(-pi / 4))
nt.assert_array_almost_equal(angvec2r(0, [0, 0, 1]), rotz(0))
nt.assert_array_almost_equal(angvec2r(pi / 4, [0, 0, 1]), rotz(pi / 4))
nt.assert_array_almost_equal(angvec2r(-pi / 4, [0, 0, 1]), rotz(-pi / 4))
def test_angvec2tr(self):
r2d = 180 / pi
nt.assert_array_almost_equal(angvec2tr(0, [1, 0, 0]), trotx(0))
nt.assert_array_almost_equal(angvec2tr(pi / 4, [1, 0, 0]), trotx(pi / 4))
nt.assert_array_almost_equal(angvec2tr(-pi / 4, [1, 0, 0]), trotx(-pi / 4))
nt.assert_array_almost_equal(angvec2tr(0, [0, 1, 0]), troty(0))
nt.assert_array_almost_equal(angvec2tr(pi / 4, [0, 1, 0]), troty(pi / 4))
nt.assert_array_almost_equal(angvec2tr(-pi / 4, [0, 1, 0]), troty(-pi / 4))
nt.assert_array_almost_equal(angvec2tr(0, [0, 0, 1]), trotz(0))
nt.assert_array_almost_equal(angvec2tr(pi / 4, [0, 0, 1]), trotz(pi / 4))
nt.assert_array_almost_equal(angvec2tr(-pi / 4, [0, 0, 1]), trotz(-pi / 4))
r2d = 180 / pi
nt.assert_array_almost_equal(angvec2r(0, [1, 0, 0]), rotx(0))
nt.assert_array_almost_equal(angvec2r(pi / 4, [1, 0, 0]), rotx(pi / 4))
nt.assert_array_almost_equal(angvec2r(-pi / 4, [1, 0, 0]), rotx(-pi / 4))
def test_trlog(self):
R = np.eye(3)
nt.assert_array_almost_equal(trlog(R), skew([0, 0, 0]))
nt.assert_array_almost_equal(trlog(R, twist=True), [0, 0, 0])
R = rotx(0.5)
nt.assert_array_almost_equal(trlog(R), skew([0.5, 0, 0]))
nt.assert_array_almost_equal(trlog(R, twist=True), [0.5, 0, 0])
R = roty(0.5)
nt.assert_array_almost_equal(trlog(R), skew([0, 0.5, 0]))
nt.assert_array_almost_equal(trlog(R, twist=True), [0, 0.5, 0])
R = rotz(0.5)
nt.assert_array_almost_equal(trlog(R), skew([0, 0, 0.5]))
nt.assert_array_almost_equal(trlog(R, twist=True), [0, 0, 0.5])
R = rpy2r(0.1, 0.2, 0.3)
nt.assert_array_almost_equal(logm(R), trlog(R))
T = transl(1, 2, 3) @ rpy2tr(0.1, 0.2, 0.3)
nt.assert_array_almost_equal(logm(T), trlog(T))
def test_trexp(self):
R = trexp(skew([0.5, 0, 0]))
nt.assert_array_almost_equal(R, rotx(0.5))
R = trexp(skew([0, 0.5, 0]))
nt.assert_array_almost_equal(R, roty(0.5))
R = trexp(skew([0, 0, 0.5]))
nt.assert_array_almost_equal(R, rotz(0.5))
R = rpy2r(0.1, 0.2, 0.3)
nt.assert_array_almost_equal(trexp(logm(R)), R)
T = transl(1, 2, 3) @ rpy2tr(0.1, 0.2, 0.3)
nt.assert_array_almost_equal(trexp(logm(T)), T)
def test_exp2r(self):
r2d = 180 / pi
nt.assert_array_almost_equal(exp2r([0, 0, 0]), rotx(0))
nt.assert_array_almost_equal(exp2r([pi / 4, 0, 0]), rotx(pi / 4))
nt.assert_array_almost_equal(exp2r([-pi / 4, 0, 0]), rotx(-pi / 4))
nt.assert_array_almost_equal(exp2r([0, 0, 0]), roty(0))
nt.assert_array_almost_equal(exp2r([0, pi / 4, 0]), roty(pi / 4))
nt.assert_array_almost_equal(exp2r([0, -pi / 4, 0]), roty(-pi / 4))
nt.assert_array_almost_equal(exp2r([0, 0, 0]), rotz(0))
nt.assert_array_almost_equal(exp2r([0, 0, pi / 4]), rotz(pi / 4))
nt.assert_array_almost_equal(exp2r([0, 0, -pi / 4]), rotz(-pi / 4))
def test_exp2tr(self):
r2d = 180 / pi
nt.assert_array_almost_equal(exp2tr([0, 0, 0]), trotx(0))
nt.assert_array_almost_equal(exp2tr([pi / 4, 0, 0]), trotx(pi / 4))
nt.assert_array_almost_equal(exp2tr([-pi / 4, 0, 0]), trotx(-pi / 4))
nt.assert_array_almost_equal(exp2tr([0, 0, 0]), troty(0))
nt.assert_array_almost_equal(exp2tr([0, pi / 4, 0]), troty(pi / 4))
nt.assert_array_almost_equal(exp2tr([0, -pi / 4, 0]), troty(-pi / 4))
nt.assert_array_almost_equal(exp2tr([0, 0, 0]), trotz(0))
nt.assert_array_almost_equal(exp2tr([0, 0, pi / 4]), trotz(pi / 4))
nt.assert_array_almost_equal(exp2tr([0, 0, -pi / 4]), trotz(-pi / 4))
def test_tr2rpy(self):
rpy = np.r_[0.1, 0.2, 0.3]
R = rpy2r(rpy)
nt.assert_array_almost_equal(tr2rpy(R), rpy)
nt.assert_array_almost_equal(tr2rpy(R, unit="deg"), rpy * 180 / pi)
T = rpy2tr(rpy)
nt.assert_array_almost_equal(
tr2rpy(T),
rpy,
)
nt.assert_array_almost_equal(tr2rpy(T, unit="deg"), rpy * 180 / pi)
# xyz order
R = rpy2r(rpy, order="xyz")
nt.assert_array_almost_equal(tr2rpy(R, order="xyz"), rpy)
nt.assert_array_almost_equal(tr2rpy(R, unit="deg", order="xyz"), rpy * 180 / pi)
T = rpy2tr(rpy, order="xyz")
nt.assert_array_almost_equal(tr2rpy(T, order="xyz"), rpy)
nt.assert_array_almost_equal(tr2rpy(T, unit="deg", order="xyz"), rpy * 180 / pi)
# corner cases
seq = "zyx"
ang = [pi, 0, 0]
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
ang = [0, pi, 0]
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
ang = [0, 0, pi]
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
ang = [0, pi / 2, 0] # singularity
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
ang = [0, -pi / 2, 0]
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
seq = "xyz"
ang = [pi, 0, 0]
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
ang = [0, pi, 0]
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
ang = [0, 0, pi]
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
ang = [0, pi / 2, 0] # singularity
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
ang = [0, -pi / 2, 0]
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
seq = "yxz"
ang = [pi, 0, 0]
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
ang = [0, pi, 0]
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
ang = [0, 0, pi]
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
ang = [0, pi / 2, 0] # singularity
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
ang = [0, -pi / 2, 0]
a = rpy2tr(ang, order=seq)
nt.assert_array_almost_equal(rpy2tr(tr2rpy(a, order=seq), order=seq), a)
def test_trnorm(self):
R = rpy2r(0.2, 0.3, 0.4)
R = np.round(R, 3) # approx SO(3)
R = trnorm(R)
self.assertTrue(isrot(R, check=True))
R = rpy2r(0.2, 0.3, 0.4)
R = np.round(R, 3) # approx SO(3)
T = rt2tr(R, [3, 4, 5])
T = trnorm(T)
self.assertTrue(ishom(T, check=True))
nt.assert_almost_equal(T[:3, 3], [3, 4, 5])
def test_tr2eul(self):
eul = np.r_[0.1, 0.2, 0.3]
R = eul2r(eul)
nt.assert_array_almost_equal(tr2eul(R), eul)
nt.assert_array_almost_equal(tr2eul(R, unit="deg"), eul * 180 / pi)
T = eul2tr(eul)
nt.assert_array_almost_equal(tr2eul(T), eul)
nt.assert_array_almost_equal(tr2eul(T, unit="deg"), eul * 180 / pi)
# test singularity case
eul = [0.1, 0, 0.3]
R = eul2r(eul)
nt.assert_array_almost_equal(eul2r(tr2eul(R)), R)
nt.assert_array_almost_equal(eul2r(tr2eul(R, unit="deg"), unit="deg"), R)
# test flip
eul = [-0.1, 0.2, 0.3]
R = eul2r(eul)
eul2 = tr2eul(R, flip=True)
nt.assert_equal(eul2[0] > 0, True)
nt.assert_array_almost_equal(eul2r(eul2), R)
def test_tr2angvec(self):
# null rotation
# - vector isn't defined here, but RTB sets it (0 0 0)
[theta, v] = tr2angvec(np.eye(3, 3))
nt.assert_array_almost_equal(theta, 0.0)
nt.assert_array_almost_equal(v, np.r_[0, 0, 0])
# canonic rotations
[theta, v] = tr2angvec(rotx(pi / 2))
nt.assert_array_almost_equal(theta, pi / 2)
nt.assert_array_almost_equal(v, np.r_[1, 0, 0])
[theta, v] = tr2angvec(roty(pi / 2))
nt.assert_array_almost_equal(theta, pi / 2)
nt.assert_array_almost_equal(v, np.r_[0, 1, 0])
[theta, v] = tr2angvec(rotz(pi / 2))
nt.assert_array_almost_equal(theta, pi / 2)
nt.assert_array_almost_equal(v, np.r_[0, 0, 1])
# null rotation
[theta, v] = tr2angvec(np.eye(4))
nt.assert_array_almost_equal(theta, 0.0)
nt.assert_array_almost_equal(v, np.r_[0, 0, 0])
# canonic rotations
[theta, v] = tr2angvec(trotx(pi / 2))
nt.assert_array_almost_equal(theta, pi / 2)
nt.assert_array_almost_equal(v, np.r_[1, 0, 0])
[theta, v] = tr2angvec(troty(pi / 2))
nt.assert_array_almost_equal(theta, pi / 2)
nt.assert_array_almost_equal(v, np.r_[0, 1, 0])
[theta, v] = tr2angvec(trotz(pi / 2))
nt.assert_array_almost_equal(theta, pi / 2)
nt.assert_array_almost_equal(v, np.r_[0, 0, 1])
[theta, v] = tr2angvec(roty(pi / 2), unit="deg")
nt.assert_array_almost_equal(theta, 90)
nt.assert_array_almost_equal(v, np.r_[0, 1, 0])
true_ang = 1.51
true_vec = np.array([0.0, 1.0, 0.0])
eps = 1e-08
# show that tr2angvec works on true rotation matrix
ang, vec = tr2angvec(roty(true_ang), check=True)
nt.assert_almost_equal(ang, true_ang)
nt.assert_almost_equal(vec, true_vec)
# check a rotation matrix that should fail
badR = roty(true_ang) + eps
with self.assertRaises(ValueError):
tr2angvec(badR, check=True)
# run without check
ang, vec = tr2angvec(badR, check=False)
nt.assert_almost_equal(ang, true_ang)
nt.assert_almost_equal(vec, true_vec)
def test_print(self):
R = rotx(0.3) @ roty(0.4)
s = trprint(R, file=None)
self.assertIsInstance(s, str)
self.assertEqual(len(s), 30)
T = transl(1, 2, 3) @ trotx(0.3) @ troty(0.4)
s = trprint(T, file=None)
self.assertIsInstance(s, str)
self.assertEqual(len(s), 42)
self.assertTrue("rpy" in s)
self.assertTrue("zyx" in s)
s = trprint(T, file=None, orient="rpy/xyz")
self.assertIsInstance(s, str)
self.assertEqual(len(s), 39)
self.assertTrue("rpy" in s)
self.assertTrue("xyz" in s)
s = trprint(T, file=None, orient="eul")
self.assertIsInstance(s, str)
self.assertEqual(len(s), 37)
self.assertTrue("eul" in s)
self.assertFalse("zyx" in s)
def test_trinterp(self):
R0 = rotx(-0.3)
R1 = rotx(0.3)
nt.assert_array_almost_equal(trinterp(start=R0, end=R1, s=0), R0)
nt.assert_array_almost_equal(trinterp(start=R0, end=R1, s=1), R1)
nt.assert_array_almost_equal(trinterp(start=R0, end=R1, s=0.5), np.eye(3))
nt.assert_array_almost_equal(trinterp(start=None, end=R1, s=0), np.eye(3))
nt.assert_array_almost_equal(trinterp(start=None, end=R1, s=1), R1)
nt.assert_array_almost_equal(trinterp(start=None, end=R1, s=0.5), rotx(0.3 / 2))
T0 = trotx(-0.3)
T1 = trotx(0.3)
nt.assert_array_almost_equal(trinterp(start=T0, end=T1, s=0), T0)
nt.assert_array_almost_equal(trinterp(start=T0, end=T1, s=1), T1)
nt.assert_array_almost_equal(trinterp(start=T0, end=T1, s=0.5), np.eye(4))
nt.assert_array_almost_equal(trinterp(start=None, end=T1, s=0), np.eye(4))
nt.assert_array_almost_equal(trinterp(start=None, end=T1, s=1), T1)
nt.assert_array_almost_equal(
trinterp(start=None, end=T1, s=0.5), trotx(0.3 / 2)
)
T0 = transl(-1, -2, -3)
T1 = transl(1, 2, 3)
nt.assert_array_almost_equal(trinterp(start=T0, end=T1, s=0), T0)
nt.assert_array_almost_equal(trinterp(start=T0, end=T1, s=1), T1)
nt.assert_array_almost_equal(trinterp(start=T0, end=T1, s=0.5), np.eye(4))
T0 = transl(-1, -2, -3) @ trotx(-0.3)
T1 = transl(1, 2, 3) @ trotx(0.3)
nt.assert_array_almost_equal(trinterp(start=T0, end=T1, s=0), T0)
nt.assert_array_almost_equal(trinterp(start=T0, end=T1, s=1), T1)
nt.assert_array_almost_equal(trinterp(start=T0, end=T1, s=0.5), np.eye(4))
nt.assert_array_almost_equal(trinterp(start=T0, end=T1, s=0), T0)
nt.assert_array_almost_equal(trinterp(start=T0, end=T1, s=1), T1)
nt.assert_array_almost_equal(trinterp(start=T0, end=T1, s=0.5), np.eye(4))
def test_tr2delta(self):
# unit testing tr2delta with a tr matrix
nt.assert_array_almost_equal(
tr2delta(transl(0.1, 0.2, 0.3)), np.r_[0.1, 0.2, 0.3, 0, 0, 0]
)
nt.assert_array_almost_equal(
tr2delta(transl(0.1, 0.2, 0.3), transl(0.2, 0.4, 0.6)),
np.r_[0.1, 0.2, 0.3, 0, 0, 0],
)
nt.assert_array_almost_equal(
tr2delta(trotx(0.001)), np.r_[0, 0, 0, 0.001, 0, 0]
)
nt.assert_array_almost_equal(
tr2delta(troty(0.001)), np.r_[0, 0, 0, 0, 0.001, 0]
)
nt.assert_array_almost_equal(
tr2delta(trotz(0.001)), np.r_[0, 0, 0, 0, 0, 0.001]
)
nt.assert_array_almost_equal(
tr2delta(trotx(0.001), trotx(0.002)), np.r_[0, 0, 0, 0.001, 0, 0]
)
# %Testing with a scalar number input
# verifyError(tc, @()tr2delta(1),'SMTB:tr2delta:badarg');
# verifyError(tc, @()tr2delta( ones(3,3) ),'SMTB:tr2delta:badarg');
def test_delta2tr(self):
# test with standard numbers
nt.assert_array_almost_equal(
delta2tr([0.1, 0.2, 0.3, 0.4, 0.5, 0.6]),
np.array(
[
[1.0, -0.6, 0.5, 0.1],
[0.6, 1.0, -0.4, 0.2],
[-0.5, 0.4, 1.0, 0.3],
[0, 0, 0, 1.0],
]
),
)
# test, with, zeros
nt.assert_array_almost_equal(delta2tr([0, 0, 0, 0, 0, 0]), np.eye(4))
# test with scalar input
# verifyError(testCase, @()delta2tr(1),'MATLAB:badsubscript');
def test_tr2jac(self):
# NOTE, create these matrices using pyprint() in MATLAB
# TODO change to forming it from block R matrices directly
nt.assert_array_almost_equal(
tr2jac(trotx(pi / 2)).T,
np.array(
[
[1, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, -1, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, -1, 0],
]
),
)
nt.assert_array_almost_equal(
tr2jac(transl(1, 2, 3)).T,
np.array(
[
[1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1],
]
),
)
# test with scalar value
# verifyError(tc, @()tr2jac(1),'SMTB:t2r:badarg');
def test_r2x(self):
R = rpy2r(0.2, 0.3, 0.4)
nt.assert_array_almost_equal(r2x(R, representation="eul"), tr2eul(R))
nt.assert_array_almost_equal(
r2x(R, representation="rpy/xyz"), tr2rpy(R, order="xyz")
)
nt.assert_array_almost_equal(
r2x(R, representation="rpy/zyx"), tr2rpy(R, order="zyx")
)
nt.assert_array_almost_equal(
r2x(R, representation="rpy/yxz"), tr2rpy(R, order="yxz")
)
nt.assert_array_almost_equal(
r2x(R, representation="arm"), tr2rpy(R, order="xyz")
)
nt.assert_array_almost_equal(
r2x(R, representation="vehicle"), tr2rpy(R, order="zyx")
)
nt.assert_array_almost_equal(
r2x(R, representation="camera"), tr2rpy(R, order="yxz")
)
nt.assert_array_almost_equal(r2x(R, representation="exp"), trlog(R, twist=True))
def test_x2r(self):
x = [0.2, 0.3, 0.4]
nt.assert_array_almost_equal(x2r(x, representation="eul"), eul2r(x))
nt.assert_array_almost_equal(
x2r(x, representation="rpy/xyz"), rpy2r(x, order="xyz")
)
nt.assert_array_almost_equal(
x2r(x, representation="rpy/zyx"), rpy2r(x, order="zyx")
)
nt.assert_array_almost_equal(
x2r(x, representation="rpy/yxz"), rpy2r(x, order="yxz")
)
nt.assert_array_almost_equal(
x2r(x, representation="arm"), rpy2r(x, order="xyz")
)
nt.assert_array_almost_equal(
x2r(x, representation="vehicle"), rpy2r(x, order="zyx")
)
nt.assert_array_almost_equal(
x2r(x, representation="camera"), rpy2r(x, order="yxz")
)
nt.assert_array_almost_equal(x2r(x, representation="exp"), trexp(x))
def test_tr2x(self):
t = [1, 2, 3]
R = rpy2tr(0.2, 0.3, 0.4)
T = transl(t) @ R
x = tr2x(T, representation="eul")
nt.assert_array_almost_equal(x[:3], t)
nt.assert_array_almost_equal(x[3:], tr2eul(R))
x = tr2x(T, representation="rpy/xyz")
nt.assert_array_almost_equal(x[:3], t)
nt.assert_array_almost_equal(x[3:], tr2rpy(R, order="xyz"))
x = tr2x(T, representation="rpy/zyx")
nt.assert_array_almost_equal(x[:3], t)
nt.assert_array_almost_equal(x[3:], tr2rpy(R, order="zyx"))
x = tr2x(T, representation="rpy/yxz")
nt.assert_array_almost_equal(x[:3], t)
nt.assert_array_almost_equal(x[3:], tr2rpy(R, order="yxz"))
x = tr2x(T, representation="arm")
nt.assert_array_almost_equal(x[:3], t)
nt.assert_array_almost_equal(x[3:], tr2rpy(R, order="xyz"))
x = tr2x(T, representation="vehicle")
nt.assert_array_almost_equal(x[:3], t)
nt.assert_array_almost_equal(x[3:], tr2rpy(R, order="zyx"))
x = tr2x(T, representation="camera")
nt.assert_array_almost_equal(x[:3], t)
nt.assert_array_almost_equal(x[3:], tr2rpy(R, order="yxz"))
x = tr2x(T, representation="exp")
nt.assert_array_almost_equal(x[:3], t)
nt.assert_array_almost_equal(x[3:], trlog(t2r(R), twist=True))
def test_x2tr(self):
t = [1, 2, 3]
gamma = [0.3, 0.2, 0.1]
x = np.r_[t, gamma]
nt.assert_array_almost_equal(
x2tr(x, representation="eul"), transl(t) @ eul2tr(gamma)
)
nt.assert_array_almost_equal(
x2tr(x, representation="rpy/xyz"), transl(t) @ rpy2tr(gamma, order="xyz")
)
nt.assert_array_almost_equal(
x2tr(x, representation="rpy/zyx"), transl(t) @ rpy2tr(gamma, order="zyx")
)
nt.assert_array_almost_equal(
x2tr(x, representation="rpy/yxz"), transl(t) @ rpy2tr(gamma, order="yxz")
)
nt.assert_array_almost_equal(
x2tr(x, representation="arm"), transl(t) @ rpy2tr(gamma, order="xyz")
)
nt.assert_array_almost_equal(
x2tr(x, representation="vehicle"), transl(t) @ rpy2tr(gamma, order="zyx")
)
nt.assert_array_almost_equal(
x2tr(x, representation="camera"), transl(t) @ rpy2tr(gamma, order="yxz")
)
nt.assert_array_almost_equal(
x2tr(x, representation="exp"), transl(t) @ r2t(trexp(gamma))
)
# ---------------------------------------------------------------------------------------#
if __name__ == "__main__":
unittest.main()