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from __future__ import absolute_import
try:
import unittest2 as unittest
except:
import unittest
import numpy as np
from pyrr.objects.matrix33 import Matrix33
from pyrr.objects.matrix44 import Matrix44
from pyrr.objects.quaternion import Quaternion
from pyrr.objects.vector3 import Vector3
from pyrr.objects.vector4 import Vector4
from pyrr import matrix33
from pyrr import matrix44
from pyrr import quaternion
class test_object_quaternion(unittest.TestCase):
_shape = (4,)
_size = np.multiply.reduce(_shape)
def test_imports(self):
import pyrr
pyrr.Quaternion()
pyrr.quaternion.Quaternion()
pyrr.objects.quaternion.Quaternion()
from pyrr import Quaternion
from pyrr.objects import Quaternion
from pyrr.objects.quaternion import Quaternion
def test_create(self):
q = Quaternion()
self.assertTrue(np.array_equal(q, [0., 0., 0., 1.]))
self.assertEqual(q.shape, self._shape)
q = Quaternion([1., 2., 3., 4.])
self.assertTrue(np.array_equal(q, [1., 2., 3., 4.]))
self.assertEqual(q.shape, self._shape)
q = Quaternion(Quaternion([1., 2., 3., 4.]))
self.assertTrue(np.array_equal(q, [1., 2., 3., 4.]))
self.assertEqual(q.shape, self._shape)
def test_from_x_rotation(self):
# 180 degree turn around X axis
q = Quaternion.from_x_rotation(np.pi)
self.assertTrue(np.allclose(q, [1., 0., 0., 0.]))
self.assertTrue(np.allclose(q * Vector3([1., 0., 0.]), [1., 0., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 1., 0.]), [0.,-1., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 0., 1.]), [0., 0.,-1.]))
# 90 degree rotation around X axis
q = Quaternion.from_x_rotation(np.pi / 2.)
self.assertTrue(np.allclose(q, [np.sqrt(0.5), 0., 0., np.sqrt(0.5)]))
self.assertTrue(np.allclose(q * Vector3([1., 0., 0.]), [1., 0., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 1., 0.]), [0., 0., 1.]))
self.assertTrue(np.allclose(q * Vector3([0., 0., 1.]), [0.,-1., 0.]))
# -90 degree rotation around X axis
q = Quaternion.from_x_rotation(-np.pi / 2.)
self.assertTrue(np.allclose(q, [-np.sqrt(0.5), 0., 0., np.sqrt(0.5)]))
self.assertTrue(np.allclose(q * Vector3([1., 0., 0.]), [1., 0., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 1., 0.]), [0., 0.,-1.]))
self.assertTrue(np.allclose(q * Vector3([0., 0., 1.]), [0., 1., 0.]))
def test_from_y_rotation(self):
# 180 degree turn around Y axis
q = Quaternion.from_y_rotation(np.pi)
self.assertTrue(np.allclose(q, [0., 1., 0., 0.]))
self.assertTrue(np.allclose(q * Vector3([1., 0., 0.]), [-1., 0., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 1., 0.]), [0., 1., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 0., 1.]), [0., 0.,-1.]))
# 90 degree rotation around Y axis
q = Quaternion.from_y_rotation(np.pi / 2.)
self.assertTrue(np.allclose(q, [0., np.sqrt(0.5), 0., np.sqrt(0.5)]))
self.assertTrue(np.allclose(q * Vector3([1., 0., 0.]), [0., 0.,-1.]))
self.assertTrue(np.allclose(q * Vector3([0., 1., 0.]), [0., 1., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 0., 1.]), [1., 0., 0.]))
# -90 degree rotation around Y axis
q = Quaternion.from_y_rotation(-np.pi / 2.)
self.assertTrue(np.allclose(q, [0., -np.sqrt(0.5), 0., np.sqrt(0.5)]))
self.assertTrue(np.allclose(q * Vector3([1., 0., 0.]), [0., 0., 1.]))
self.assertTrue(np.allclose(q * Vector3([0., 1., 0.]), [0., 1., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 0., 1.]), [-1., 0., 0.]))
def test_from_z_rotation(self):
# 180 degree turn around Z axis
q = Quaternion.from_z_rotation(np.pi)
self.assertTrue(np.allclose(q, [0., 0., 1., 0.]))
self.assertTrue(np.allclose(q * Vector3([1., 0., 0.]), [-1., 0., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 1., 0.]), [0.,-1., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 0., 1.]), [0., 0., 1.]))
# 90 degree rotation around Z axis
q = Quaternion.from_z_rotation(np.pi / 2.)
self.assertTrue(np.allclose(q, [0., 0., np.sqrt(0.5), np.sqrt(0.5)]))
self.assertTrue(np.allclose(q * Vector3([1., 0., 0.]), [0., 1., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 1., 0.]), [-1., 0., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 0., 1.]), [0., 0., 1.]))
# -90 degree rotation around Z axis
q = Quaternion.from_z_rotation(-np.pi / 2.)
self.assertTrue(np.allclose(q, [0., 0., -np.sqrt(0.5), np.sqrt(0.5)]))
self.assertTrue(np.allclose(q * Vector3([1., 0., 0.]), [0.,-1., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 1., 0.]), [1., 0., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 0., 1.]), [0., 0., 1.]))
def test_from_axis_rotation(self):
q = Quaternion.from_axis_rotation([1., 0., 0.], np.pi / 2.)
self.assertTrue(np.allclose(q, [np.sqrt(0.5), 0., 0., np.sqrt(0.5)]))
self.assertTrue(np.allclose(q * Vector3([1., 0., 0.]), [1., 0., 0.]))
self.assertTrue(np.allclose(q * Vector3([0., 1., 0.]), [0., 0., 1.]))
self.assertTrue(np.allclose(q * Vector3([0., 0., 1.]), [0.,-1., 0.]))
def test_from_axis(self):
source = np.array([np.pi / 2, 0, 0])
result = Quaternion.from_axis(source)
expected = np.array([np.sqrt(0.5), 0, 0, np.sqrt(0.5)])
self.assertTrue(np.allclose(result, expected))
source = np.array([0, np.pi, 0])
result = Quaternion.from_axis(source)
expected = np.array([0, 1, 0, 0])
self.assertTrue(np.allclose(result, expected))
source = np.array([0, 0, 2 * np.pi])
result = Quaternion.from_axis(source)
expected = np.array([0, 0, 0, -1])
self.assertTrue(np.allclose(result, expected))
@unittest.skip('Not implemented')
def test_from_eulers(self):
pass
@unittest.skip('Not implemented')
def test_from_inverse_of_eulers(self):
pass
def test_length(self):
q = Quaternion.from_x_rotation(np.pi / 2.0)
self.assertTrue(np.allclose(q.length, quaternion.length(q)))
def test_normalize(self):
q = Quaternion([1., 2., 3., 4.])
self.assertFalse(np.allclose(q.length, 1.))
q.normalize()
self.assertTrue(np.allclose(q.length, 1.))
def test_normalized(self):
q1 = Quaternion([1., 2., 3., 4.])
self.assertFalse(np.allclose(q1.length, 1.))
q2 = q1.normalized
self.assertFalse(np.allclose(q1.length, 1.))
self.assertTrue(np.allclose(q2.length, 1.))
def test_angle(self):
q = Quaternion.from_x_rotation(np.pi / 2.0)
self.assertEqual(q.angle, quaternion.rotation_angle(q))
def test_axis(self):
q = Quaternion.from_x_rotation(np.pi / 2.0)
self.assertTrue(np.allclose(q.axis, quaternion.rotation_axis(q)))
def test_cross(self):
q1 = Quaternion.from_x_rotation(np.pi / 2.0)
q2 = Quaternion.from_y_rotation(np.pi / 2.0)
self.assertTrue(np.allclose(q1.cross(q2), quaternion.cross(q1, q2)))
def test_dot(self):
q1 = Quaternion.from_x_rotation(np.pi / 2.0)
q2 = Quaternion.from_y_rotation(np.pi / 2.0)
self.assertTrue(np.allclose(q1.dot(q2), quaternion.dot(q1, q2)))
def test_conjugate(self):
q = Quaternion.from_x_rotation(np.pi / 2.0)
self.assertTrue(np.allclose(q.conjugate, quaternion.conjugate(q)))
def test_inverse(self):
q = Quaternion.from_x_rotation(np.pi / 2.0)
self.assertTrue(np.allclose(q.inverse, quaternion.inverse(q)))
def test_exp(self):
source = Quaternion.from_eulers([0, np.pi / 2, 0])
result = source.exp()
expected = np.array([0, 1.31753841, 0, 1.54186346])
self.assertTrue(np.allclose(result, expected))
def test_power(self):
q1 = Quaternion.from_x_rotation(np.pi / 2.0)
q2 = Quaternion.from_x_rotation(np.pi / 2.0)
self.assertTrue(np.allclose(q1.power(2.0), quaternion.power(q2, 2.0)))
def test_negative(self):
q = Quaternion.from_x_rotation(np.pi / 2.0)
self.assertTrue(np.allclose(q.negative, quaternion.negate(q)))
def test_is_identity(self):
self.assertTrue(quaternion.is_identity(Quaternion()))
self.assertTrue(quaternion.is_identity(Quaternion([0., 0., 0., 1.])))
self.assertFalse(quaternion.is_identity(Quaternion([1., 0., 0., 0.])))
def test_matrix33(self):
q = Quaternion.from_x_rotation(np.pi / 2.0)
self.assertTrue(np.allclose(q.matrix33, matrix33.create_from_quaternion(q)))
def test_matrix44(self):
q = Quaternion.from_x_rotation(np.pi / 2.0)
self.assertTrue(np.allclose(q.matrix44, matrix44.create_from_quaternion(q)))
def test_operators_matrix33(self):
q = Quaternion()
m = Matrix33.from_x_rotation(0.5)
# add
self.assertRaises(ValueError, lambda: q + m)
# subtract
self.assertRaises(ValueError, lambda: q - m)
# multiply
self.assertTrue(np.array_equal(q * m, quaternion.cross(quaternion.create(), quaternion.create_from_matrix(matrix33.create_from_x_rotation(0.5)))))
# divide
self.assertRaises(ValueError, lambda: q / m)
def test_operators_matrix44(self):
q = Quaternion()
m = Matrix44.from_x_rotation(0.5)
# add
self.assertRaises(ValueError, lambda: q + m)
# subtract
self.assertRaises(ValueError, lambda: q - m)
# multiply
self.assertTrue(np.array_equal(q * m, quaternion.cross(quaternion.create(), quaternion.create_from_matrix(matrix44.create_from_x_rotation(0.5)))))
# divide
self.assertRaises(ValueError, lambda: q / m)
def test_operators_quaternion(self):
q1 = Quaternion()
q2 = Quaternion.from_x_rotation(0.5)
# add
self.assertRaises(ValueError, lambda: q1 + q2)
# subtract
# we had to add this to enable np.array_equal to work
# as it uses subtraction
#self.assertRaises(ValueError, lambda: q1 - q2)
# multiply
self.assertTrue(np.array_equal(q1 * q2, quaternion.cross(quaternion.create(), quaternion.create_from_x_rotation(0.5))))
# divide
self.assertRaises(ValueError, lambda: q1 / q2)
# or
self.assertTrue(np.array_equal(q1 | q2, quaternion.dot(quaternion.create(), quaternion.create_from_x_rotation(0.5))))
# inverse
self.assertTrue(np.array_equal(~q2, quaternion.conjugate(quaternion.create_from_x_rotation(0.5))))
# ==
self.assertTrue(Quaternion() == Quaternion())
self.assertFalse(Quaternion() == Quaternion([0., 0., 0., 0.]))
# !=
self.assertTrue(Quaternion() != Quaternion([1., 1., 1., 1.]))
self.assertFalse(Quaternion() != Quaternion())
def test_operators_vector3(self):
q = Quaternion.from_x_rotation(0.5)
v = Vector3([1., 0., 0.])
# add
self.assertRaises(ValueError, lambda: q + v)
# subtract
self.assertRaises(ValueError, lambda: q - v)
# multiply
self.assertTrue(np.array_equal(q * v, quaternion.apply_to_vector(quaternion.create_from_x_rotation(0.5), [1., 0., 0.])))
# divide
self.assertRaises(ValueError, lambda: q / v)
def test_operators_vector4(self):
q = Quaternion.from_x_rotation(0.5)
v = Vector4([1., 0., 0., 1.])
# add
self.assertRaises(ValueError, lambda: q + v)
# subtract
self.assertRaises(ValueError, lambda: q - v)
# multiply
self.assertTrue(np.array_equal(q * v, quaternion.apply_to_vector(quaternion.create_from_x_rotation(0.5), [1., 0., 0., 1.])))
# divide
self.assertRaises(ValueError, lambda: q / v)
def test_apply_to_vector_non_unit(self):
q = Quaternion.from_x_rotation(np.pi)
# zero length
v = Vector3([0., 0., 0.])
self.assertTrue(np.allclose(q * v, quaternion.apply_to_vector(quaternion.create_from_x_rotation(np.pi), [0., 0., 0.])))
# >1 length
v = Vector3([2., 0., 0.])
self.assertTrue(np.allclose(q * v, quaternion.apply_to_vector(quaternion.create_from_x_rotation(np.pi), [2., 0., 0.])))
v = Vector3([0., 2., 0.])
self.assertTrue(np.allclose(q * v, quaternion.apply_to_vector(quaternion.create_from_x_rotation(np.pi), [0., 2., 0.])))
v = Vector3([0., 0., 2.])
self.assertTrue(np.allclose(q * v, quaternion.apply_to_vector(quaternion.create_from_x_rotation(np.pi), [0., 0., 2.])))
def test_accessors(self):
q = Quaternion(np.arange(self._size))
self.assertTrue(np.array_equal(q.xy, [0, 1]))
self.assertTrue(np.array_equal(q.xyz, [0, 1, 2]))
self.assertTrue(np.array_equal(q.xyzw, [0, 1, 2, 3]))
self.assertTrue(np.array_equal(q.xz, [0, 2]))
self.assertTrue(np.array_equal(q.xyz, [0, 1, 2]))
self.assertTrue(np.array_equal(q.xyw, [0, 1, 3]))
self.assertTrue(np.array_equal(q.xw, [0, 3]))
self.assertEqual(q.x, 0)
self.assertEqual(q.y, 1)
self.assertEqual(q.z, 2)
self.assertEqual(q.w, 3)
q.x = 1
self.assertEqual(q.x, 1)
self.assertEqual(q[0], 1)
q.x += 1
self.assertEqual(q.x, 2)
self.assertEqual(q[0], 2)
def test_equality(self):
q1 = Quaternion([0, 0, 0, 1])
q2 = Quaternion([0, 0, 0, 1])
q3 = Quaternion([0, 0, 1, -1])
self.assertEqual(q1, q2)
self.assertNotEqual(q1, q3)
self.assertNotEqual(q2, q3)
def test_equality_negative(self):
q1 = Quaternion([0, 0, 0, 1])
q2 = Quaternion([0, 0, 0, -1])
q3 = Quaternion([0, 0, 1, -1])
self.assertEqual(q1, q2)
self.assertNotEqual(q1, q3)
if __name__ == '__main__':
unittest.main()
|
