def test_translate_inertia(translation):
shape = PlatonicFamily.get_shape("Cube")
# Choose a volume > 1 to test the volume scaling, but don't choose one
# that's too large because the uncentered polyhedral calculation has
# massive error without fixing that.
shape.volume = 2
shape.center = (0, 0, 0)
translated_shape = ConvexPolyhedron(shape.vertices + translation)
translated_inertia = translate_inertia_tensor(translation,
shape.inertia_tensor,
shape.volume)
mc_tensor = compute_inertia_mc(translated_shape.vertices, 1e4)
assert np.allclose(
translated_inertia,
translated_shape._compute_inertia_tensor(False),
atol=2e-1,
rtol=2e-1,
)
assert np.allclose(mc_tensor,
translated_shape._compute_inertia_tensor(False),
atol=2e-1,
rtol=2e-1)
assert np.allclose(mc_tensor, translated_inertia, atol=1e-2, rtol=1e-2)
assert np.allclose(mc_tensor,
translated_shape.inertia_tensor,
atol=1e-2,
rtol=1e-2)
def test_rotate_inertia(points):
# Use the input as noise rather than the base points to avoid precision and
# degenerate cases provided by hypothesis.
tet = PlatonicFamily.get_shape("Tetrahedron")
vertices = tet.vertices + points
rotation = rowan.random.rand()
shape = ConvexPolyhedron(vertices)
rotated_shape = ConvexPolyhedron(rowan.rotate(rotation, vertices))
mat = rowan.to_matrix(rotation)
rotated_inertia = rotate_order2_tensor(mat, shape.inertia_tensor)
assert np.allclose(rotated_inertia, rotated_shape.inertia_tensor)
def test_curvature():
"""Regression test against values computed with older method."""
# The shapes in the PlatonicFamily are normalized to unit volume.
known_shapes = {
"Cube": 0.75,
"Dodecahedron": 0.6703242780091758,
"Icosahedron": 0.6715997848012972,
"Octahedron": 0.75518565565632,
"Tetrahedron": 0.9303430847680867,
}
for name, curvature in known_shapes.items():
poly = PlatonicFamily.get_shape(name)
if name == "Dodecahedron":
poly.merge_faces(rtol=1)
assert np.isclose(poly.mean_curvature, curvature)
def test_dihedrals():
known_shapes = {
"Tetrahedron": np.arccos(1 / 3),
"Cube": np.pi / 2,
"Octahedron": np.pi - np.arccos(1 / 3),
"Dodecahedron": np.pi - np.arctan(2),
"Icosahedron": np.pi - np.arccos(np.sqrt(5) / 3),
}
for name, dihedral in known_shapes.items():
poly = PlatonicFamily.get_shape(name)
# The dodecahedron needs a more expansive merge to get all the
# faces joined.
if name == "Dodecahedron":
poly.merge_faces(rtol=1)
for i in range(poly.num_faces):
for j in poly.neighbors[i]:
assert np.isclose(poly.get_dihedral(i, j), dihedral)
def test_rotate_inertia(tetrahedron):
# Use the input as noise rather than the base points to avoid precision and
# degenerate cases provided by hypothesis.
tet = PlatonicFamily.get_shape("Tetrahedron")
@given(
arrays(np.float64, (4, 3),
elements=floats(-10, 10, width=64),
unique=True),
Random3DRotationStrategy,
)
def testfun(points, rotation):
vertices = tet.vertices + points
shape = ConvexPolyhedron(vertices)
rotated_shape = ConvexPolyhedron(rowan.rotate(rotation, vertices))
mat = rowan.to_matrix(rotation)
rotated_inertia = rotate_order2_tensor(mat, shape.inertia_tensor)
assert np.allclose(rotated_inertia, rotated_shape.inertia_tensor)
testfun()
def platonic_solids():
for shape_name in PlatonicFamily.data:
yield PlatonicFamily.get_shape(shape_name)
def tetrahedron():
tet = PlatonicFamily.get_shape("Tetrahedron")
tet.volume = 1
return tet
def platonic_solids():
"""Generate platonic solids."""
for shape_name in PlatonicFamily.data:
yield PlatonicFamily.get_shape(shape_name)
c1.center, c2.center, *args, **kwargs)
def platonic_solids():
"""Generate platonic solids."""
for shape_name in PlatonicFamily.data:
yield PlatonicFamily.get_shape(shape_name)
# A convenient mark decorator that also includes names for the polyhedra.
# Assumes that the argument name is "poly".
_platonic_shape_names = PlatonicFamily.data.keys()
named_platonic_mark = pytest.mark.parametrize(
argnames="poly",
argvalues=[
PlatonicFamily.get_shape(name) for name in _platonic_shape_names
],
ids=_platonic_shape_names,
)
def regular_polygons(n=10):
"""Generate regular polygons."""
for i in range(3, n + 1):
yield RegularNGonFamily.get_shape(i)
def _test_get_set_minimal_bounding_sphere_radius(shape, centered=False):
"""Test getting and setting the minimal bounding circle radius.
This function will work for any shape in two or three dimensions based on