def update(self, x, z):
rotation_x = quaternion.Quaternion(
quaternion.create_from_eulers([x, 0, 0]))
rotation_z = self.rotation_x.conjugate.cross(
quaternion.Quaternion(quaternion.create_from_eulers([0, 0, z])))
self.rotation_x = self.rotation_x.cross(rotation_x)
self.matrix = numpy.matmul(
self.matrix,
matrix44.create_from_quaternion(rotation_z.cross(self.rotation_x)))
self.inverse_matrix = numpy.linalg.inv(self.matrix)
def test_exp(self):
source = np.array([0, 0, 0, 1.0])
result = quaternion.exp(source)
expected = np.array([0, 0, 0, np.exp(1)])
np.testing.assert_almost_equal(result, expected)
source = quaternion.create_from_eulers([np.pi, 0, 0])
result = quaternion.exp(source)
expected = np.array([0.84147098, 0, 0, 0.54030231])
np.testing.assert_almost_equal(result, expected)
# Tests from the boost::math::quaternion
source = np.array([4 * np.arctan(1), 0, 0, 0])
result = quaternion.exp(source) + [0, 0, 0, 1.0]
result = np.linalg.norm(result)
expected = 2 * np.finfo(result.dtype).eps
np.testing.assert_almost_equal(result, expected)
source = np.array([0, 4 * np.arctan(1), 0, 0])
result = quaternion.exp(source) + [0, 0, 0, 1.0]
result = np.linalg.norm(result)
expected = 2 * np.finfo(result.dtype).eps
np.testing.assert_almost_equal(result, expected)
source = np.array([0, 0, 4 * np.arctan(1), 0])
result = quaternion.exp(source) + [0, 0, 0, 1.0]
result = np.linalg.norm(result)
expected = 2 * np.finfo(result.dtype).eps
np.testing.assert_almost_equal(result, expected)
def test_exp(self):
source = np.array([0, 0, 0, 1.0])
result = quaternion.exp(source)
expected = np.array([0, 0, 0, np.exp(1)])
np.testing.assert_almost_equal(result, expected)
source = quaternion.create_from_eulers([np.pi, 0, 0])
result = quaternion.exp(source)
expected = np.array([0.84147098, 0, 0, 0.54030231])
np.testing.assert_almost_equal(result, expected)
# Tests from the boost::math::quaternion
source = np.array([4 * np.arctan(1), 0, 0, 0])
result = quaternion.exp(source) + [0, 0, 0, 1.0]
result = np.linalg.norm(result)
expected = 2 * np.finfo(result.dtype).eps
np.testing.assert_almost_equal(result, expected)
source = np.array([0, 4 * np.arctan(1), 0, 0])
result = quaternion.exp(source) + [0, 0, 0, 1.0]
result = np.linalg.norm(result)
expected = 2 * np.finfo(result.dtype).eps
np.testing.assert_almost_equal(result, expected)
source = np.array([0, 0, 4 * np.arctan(1), 0])
result = quaternion.exp(source) + [0, 0, 0, 1.0]
result = np.linalg.norm(result)
expected = 2 * np.finfo(result.dtype).eps
np.testing.assert_almost_equal(result, expected)
def octasphere(ndivisions: int):
"""Creates a unit sphere using octagon subdivision.
Creates a unit sphere using octagon subdivision. Modified slightly from the original code
by Philip Rideout (https://prideout.net/blog/octasphere).
"""
n = 2**ndivisions + 1
num_verts = n * (n + 1) // 2
verts = empty((num_verts, 3))
j = 0
for i in range(n):
theta = pi * 0.5 * i / (n - 1)
point_a = [0, sin(theta), cos(theta)]
point_b = [cos(theta), sin(theta), 0]
num_segments = n - 1 - i
j = compute_geodesic(verts, j, point_a, point_b, num_segments)
assert len(verts) == num_verts
num_faces = (n - 2) * (n - 1) + n - 1
faces = empty((num_faces, 3), dtype='int')
f, j0 = 0, 0
for col_index in range(n - 1):
col_height = n - 1 - col_index
j1 = j0 + 1
j2 = j0 + col_height + 1
j3 = j0 + col_height + 2
for row in range(col_height - 1):
faces[f + 0] = [j0 + row, j1 + row, j2 + row]
faces[f + 1] = [j2 + row, j1 + row, j3 + row]
f = f + 2
row = col_height - 1
faces[f] = [j0 + row, j1 + row, j2 + row]
f = f + 1
j0 = j2
euler_angles = array([
[0, 0, 0],
[0, 1, 0],
[0, 2, 0],
[0, 3, 0],
[1, 0, 0],
[1, 0, 1],
[1, 0, 2],
[1, 0, 3],
]) * pi * 0.5
quats = (quaternion.create_from_eulers(e) for e in euler_angles)
offset, combined_verts, combined_faces = 0, [], []
for quat in quats:
rotated_verts = [quaternion.apply_to_vector(quat, v) for v in verts]
rotated_faces = faces + offset
combined_verts.append(rotated_verts)
combined_faces.append(rotated_faces)
offset = offset + len(verts)
return vstack(combined_verts), vstack(combined_faces)
def test_create_from_eulers(self):
result = quaternion.create_from_eulers([1.0, 2.0, 3.0])
np.testing.assert_almost_equal(
result, [0.7549338, -0.2061492, 0.5015091, -0.3688714], decimal=5)
self.assertTrue(result.dtype == np.float)
def test_create_from_eulers_identity(self):
result = quaternion.create_from_eulers([0., 0., 0.])
np.testing.assert_equal(result, [0., 0., 0., 1.])
self.assertTrue(result.dtype == np.float)
def test_create_from_eulers(self):
result = quaternion.create_from_eulers([1.0, 2.0, 3.0])
np.testing.assert_almost_equal(result, [0.7549338, -0.2061492, 0.5015091, -0.3688714], decimal=5)
self.assertTrue(result.dtype == np.float)
def test_create_from_eulers_identity(self):
result = quaternion.create_from_eulers([0., 0., 0.])
np.testing.assert_equal(result, [0., 0., 0., 1.])
self.assertTrue(result.dtype == np.float)
