def test_invert_transform():
"""Test inversion of transformations."""
random_state = np.random.RandomState(0)
for _ in range(5):
R = matrix_from(a=random_axis_angle(random_state))
p = random_vector(random_state)
A2B = transform_from(R, p)
B2A = invert_transform(A2B)
A2B2 = np.linalg.inv(B2A)
assert_array_almost_equal(A2B, A2B2)
def test_vector_to_direction():
"""Test conversion from vector to direction in homogenous coordinates."""
v = np.array([1, 2, 3])
dA = vector_to_direction(v)
assert_array_almost_equal(dA, [1, 2, 3, 0])
random_state = np.random.RandomState(0)
R = matrix_from(a=random_axis_angle(random_state))
p = random_vector(random_state)
A2B = transform_from(R, p)
assert_transform(A2B)
_ = transform(A2B, dA)
def test_vector_to_point():
"""Test conversion from vector to homogenous coordinates."""
v = np.array([1, 2, 3])
pA = vector_to_point(v)
assert_array_almost_equal(pA, [1, 2, 3, 1])
random_state = np.random.RandomState(0)
R = matrix_from(a=random_axis_angle(random_state))
p = random_vector(random_state)
A2B = transform_from(R, p)
assert_transform(A2B)
pB = transform(A2B, pA)
==========================
Plot Transformed Cylinders
==========================
Plots surfaces of transformed cylindrical shells.
"""
print(__doc__)
import numpy as np
import matplotlib.pyplot as plt
from pytransform3d.transformations import transform_from, plot_transform
from pytransform3d.rotations import random_axis_angle, matrix_from_axis_angle
from pytransform3d.plot_utils import plot_cylinder, remove_frame
random_state = np.random.RandomState(42)
A2B = transform_from(R=matrix_from_axis_angle(random_axis_angle(random_state)),
p=random_state.randn(3))
ax = plot_cylinder(length=1.0,
radius=0.3,
thickness=0.1,
wireframe=False,
alpha=0.2)
plot_transform(ax=ax, A2B=np.eye(4), s=0.3, lw=3)
plot_cylinder(ax=ax,
length=1.0,
radius=0.3,
thickness=0.1,
A2B=A2B,
wireframe=False,
alpha=0.2)
plot_transform(ax=ax, A2B=A2B, s=0.3, lw=3)
"""
========
Plot Box
========
"""
print(__doc__)
import numpy as np
import pytransform3d.visualizer as pv
from pytransform3d.transformations import transform_from
from pytransform3d.rotations import random_axis_angle, matrix_from_axis_angle
random_state = np.random.RandomState(42)
fig = pv.figure()
A2B = transform_from(
R=matrix_from_axis_angle(random_axis_angle(random_state)),
p=np.zeros(3))
fig.plot_box(size=[0.2, 0.5, 1], A2B=A2B)
fig.plot_transform(A2B=A2B)
fig.view_init()
if "__file__" in globals():
fig.show()
else:
fig.save_image("__open3d_rendered_image.jpg")
"""
=====================================
Axis-Angle Representation of Rotation
=====================================
Any rotation can be represented with a single rotation about some axis.
Here we see a frame that is rotated in multiple steps around a rotation
axis.
"""
print(__doc__)
import numpy as np
import matplotlib.pyplot as plt
from pytransform3d.rotations import (random_axis_angle, matrix_from_axis_angle,
plot_basis, plot_axis_angle)
original = random_axis_angle(np.random.RandomState(5))
ax = plot_axis_angle(a=original)
for fraction in np.linspace(0, 1, 50):
a = original.copy()
a[-1] = fraction * original[-1]
R = matrix_from_axis_angle(a)
plot_basis(ax, R, alpha=0.2)
plt.subplots_adjust(left=0, right=1, bottom=0, top=1.1)
ax.view_init(azim=105, elev=12)
plt.show()
