def test_translate_inertia(translation):
shape = PlatonicFamily()("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_insphere_from_center_convex_hulls(points, test_points):
hull = ConvexHull(points)
poly = ConvexPolyhedron(points[hull.vertices])
insphere = poly.insphere_from_center
assert poly.is_inside(insphere.center)
test_points *= insphere.radius * 3
points_in_sphere = insphere.is_inside(test_points)
points_in_poly = poly.is_inside(test_points)
assert np.all(points_in_sphere <= points_in_poly)
assert insphere.volume < poly.volume
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()("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_diagonalize_inertia(points):
"""Test that we can orient a polyhedron along its principal axes."""
hull = ConvexHull(points)
poly = ConvexPolyhedron(points[hull.vertices])
try:
it = poly.inertia_tensor
except ValueError:
# Triangulation can fail, this is a limitation of polytri and not something we
# can address without implementing a more robust algorithm.
return
if not np.allclose(np.diag(np.diag(it)), it):
poly.diagonalize_inertia()
it = poly.inertia_tensor
assert np.allclose(np.diag(np.diag(it)), it)
def test_volume_damasceno_shapes(shape):
if shape["name"] in ("RESERVED", "Sphere"):
return
vertices = shape["vertices"]
poly = ConvexPolyhedron(vertices)
hull = ConvexHull(vertices)
assert np.isclose(poly.volume, hull.volume)
def test_circumsphere_from_center():
"""Validate circumsphere by testing the polyhedron.
This checks that all points outside this circumsphere are also outside the
polyhedron. Note that this is a necessary but not sufficient condition for
correctness.
"""
# Building convex polyhedra is the slowest part of this test, so rather
# than testing all the shapes from this particular dataset every time we
# instead test a random subset each time the test runs. To further speed
# the tests, we build all convex polyhedra ahead of time. Each set of
# random points is tested against a different random polyhedron.
import random
family = family_from_doi("10.1126/science.1220869")[0]
shapes = [
ConvexPolyhedron(s["vertices"])
for s in random.sample(
[s for s in family.data.values() if len(s["vertices"])],
len(family.data) // 5,
)
]
# Use a nested function to avoid warnings from hypothesis. While the shape
# does get modified inside the testfun, it's simply being recentered each
# time, which is not destructive since it can be overwritten in subsequent
# calls.
# See https://github.com/HypothesisWorks/hypothesis/issues/377
@given(
center=arrays(
np.float64, (3,), elements=floats(-10, 10, width=64), unique=True
),
points=arrays(
np.float64, (50, 3), elements=floats(-1, 1, width=64), unique=True
),
shape_index=integers(0, len(shapes) - 1),
)
def testfun(center, points, shape_index):
poly = shapes[shape_index]
poly.center = center
sphere = poly.circumsphere_from_center
scaled_points = points * sphere.radius + sphere.center
points_outside = np.logical_not(sphere.is_inside(scaled_points))
# Verify that all points outside the circumsphere are also outside the
# polyhedron.
assert not np.any(np.logical_and(points_outside, poly.is_inside(scaled_points)))
testfun()
def test_moment_inertia_damasceno_shapes(shape):
# These shapes pass the test for a sufficiently high number of samples, but
# the number is too high to be worth running them regularly.
bad_shapes = [
"Augmented Truncated Dodecahedron",
"Deltoidal Hexecontahedron",
"Disdyakis Triacontahedron",
"Truncated Dodecahedron",
"Truncated Icosidodecahedron",
"Metabiaugmented Truncated Dodecahedron",
"Pentagonal Hexecontahedron",
"Paragyrate Diminished Rhombicosidodecahedron",
"Square Cupola",
"Triaugmented Truncated Dodecahedron",
"Parabiaugmented Truncated Dodecahedron",
]
if shape["name"] in ["RESERVED", "Sphere"] + bad_shapes:
return
np.random.seed(0)
poly = ConvexPolyhedron(shape["vertices"])
num_samples = 1000
accept = False
# Loop over different sampling rates to minimize the test runtime.
while num_samples < 1e8:
try:
coxeter_result = poly.inertia_tensor
mc_result = compute_inertia_mc(shape["vertices"], num_samples)
assert np.allclose(coxeter_result, mc_result, atol=1e-1)
accept = True
break
except AssertionError:
num_samples *= 10
continue
if not accept:
raise AssertionError(
"The test failed for shape {}.\nMC Result: "
"\n{}\ncoxeter result: \n{}".format(
shape["name"], mc_result, coxeter_result
)
)
def test_convex_surface_area(points):
"""Check the surface areas of various convex sets."""
hull = ConvexHull(points)
poly = ConvexPolyhedron(points[hull.vertices])
assert np.isclose(hull.area, poly.surface_area)
def test_convex_volume(points):
"""Check the volumes of various convex sets."""
hull = ConvexHull(points)
poly = ConvexPolyhedron(hull.points[hull.vertices])
assert np.isclose(hull.volume, poly.volume)