def tilted(self, new_point, coplanar_point):
"""
Create a new plane, tilted so it passes through `new_point`. Also
specify a `coplanar_point` which the old and new planes should have
in common.
Args:
new_point (np.arraylike): A point on the desired plane, with shape
`(3,)`.
coplanar_point (np.arraylike): The `(3,)` point which the old and
new planes have in common.
Returns:
Plane: The adjusted plane.
"""
vg.shape.check(locals(), "new_point", (3, ))
vg.shape.check(locals(), "coplanar_point", (3, ))
vector_along_old_plane = self.project_point(new_point) - coplanar_point
vector_along_new_plane = new_point - coplanar_point
axis_of_rotation = vg.perpendicular(vector_along_old_plane,
self.normal)
angle_between_vectors = vg.signed_angle(
vector_along_old_plane,
vector_along_new_plane,
look=axis_of_rotation,
units="rad",
)
new_normal = vg.rotate(
self.normal,
around_axis=axis_of_rotation,
angle=angle_between_vectors,
units="rad",
)
return Plane(point_on_plane=coplanar_point, unit_normal=new_normal)
def test_project_point_to_line_stacked_both():
p1 = np.array([5.0, 5.0, 4.0])
p2 = np.array([10.0, 10.0, 6.0])
along_line = p2 - p1
common_kwargs = dict(
reference_points_of_lines=np.array([p1, p1, p1]),
vectors_along_lines=np.array([along_line, along_line, along_line]),
)
other_point_on_line = np.array([0.0, 0.0, 2.0])
example_perpendicular_displacement = [
k * vg.perpendicular(vg.normalize(along_line), vg.basis.x)
for k in [0.1, 0.5, -2.0]
]
example_points = np.vstack([p1, p2, other_point_on_line])
expected_projected_points = np.vstack([p1, p2, other_point_on_line])
np.testing.assert_array_almost_equal(
project_point_to_line(points=example_points, **common_kwargs),
expected_projected_points,
)
np.testing.assert_array_almost_equal(
project_point_to_line(points=example_points +
example_perpendicular_displacement,
**common_kwargs),
expected_projected_points,
)
def test_project_point_to_line():
p1 = np.array([5.0, 5.0, 4.0])
p2 = np.array([10.0, 10.0, 6.0])
along_line = p2 - p1
common_kwargs = dict(reference_points_of_lines=p1,
vectors_along_lines=along_line)
np.testing.assert_array_almost_equal(
project_point_to_line(points=p1, **common_kwargs), p1)
np.testing.assert_array_almost_equal(
project_point_to_line(points=p2, **common_kwargs), p2)
other_point_on_line = np.array([0.0, 0.0, 2.0])
np.testing.assert_array_almost_equal(
project_point_to_line(points=other_point_on_line, **common_kwargs),
other_point_on_line,
)
example_perpendicular_displacement = [
k * vg.perpendicular(vg.normalize(along_line), vg.basis.x)
for k in [0.1, 0.5, -2.0]
]
for point_on_line in [p1, p2, other_point_on_line]:
for displacement in example_perpendicular_displacement:
np.testing.assert_array_almost_equal(
project_point_to_line(points=point_on_line + displacement,
**common_kwargs),
point_on_line,
)
def test_project():
p1 = np.array([5.0, 5.0, 4.0])
p2 = np.array([10.0, 10.0, 6.0])
line = Line.from_points(p1, p2)
np.testing.assert_array_almost_equal(line.project(p1), p1)
np.testing.assert_array_almost_equal(line.project(p2), p2)
other_point_on_line = np.array([0.0, 0.0, 2.0])
np.testing.assert_array_almost_equal(line.project(other_point_on_line),
other_point_on_line)
example_perpendicular_displacement = [
k * vg.perpendicular(line.along, vg.basis.x) for k in [0.1, 0.5, -2.0]
]
for p in [p1, p2, other_point_on_line]:
for displacement in example_perpendicular_displacement:
np.testing.assert_array_almost_equal(
line.project(p + displacement), p)
def test_project_stacked():
p1 = np.array([5.0, 5.0, 4.0])
p2 = np.array([10.0, 10.0, 6.0])
line = Line.from_points(p1, p2)
other_point_on_line = np.array([0.0, 0.0, 2.0])
example_perpendicular_displacement = [
k * vg.perpendicular(line.along, vg.basis.x) for k in [0.1, 0.5, -2.0]
]
example_points = np.vstack([p1, p2, other_point_on_line])
expected_projected_points = np.vstack([p1, p2, other_point_on_line])
np.testing.assert_array_almost_equal(line.project(example_points),
expected_projected_points)
np.testing.assert_array_almost_equal(
line.project(example_points + example_perpendicular_displacement),
expected_projected_points,
)