def test_best_fit(points, sphere_expected):
points = Points(points)
sphere_fit = Sphere.best_fit(points)
assert sphere_fit.point.is_close(sphere_expected.point, abs_tol=1e-9)
assert math.isclose(sphere_fit.radius, sphere_expected.radius)
def spheres(draw):
"""
Return a strategy which generates Circle objects.
Returns
-------
LazyStrategy
Hypothesis strategy.
Examples
--------
>>> from hypothesis import find
>>> from tests.property.strategies import spheres
>>> sphere = find(spheres(), lambda x: x.radius >= 1)
>>> round(sphere.radius)
1
"""
return Sphere(draw(arrays_fixed(3)), draw(radii))
(Circle([0, 0], 5), [0, -2], [0, -5]),
(Circle([0, 1], 5), [0, -2], [0, -4]),
(Circle([0, 0], 1), [1, 1], math.sqrt(2) / 2 * np.ones(2)),
(Circle([0, 0], 2), [1, 1], math.sqrt(2) * np.ones(2)),
],
)
def test_project_point_circle(circle, point, point_expected):
point_projected = circle.project_point(point)
assert point_projected.is_close(point_expected)
@pytest.mark.parametrize(
"sphere, point, point_expected",
[
(Sphere([0, 0, 0], 1), [1, 0, 0], [1, 0, 0]),
(Sphere([0, 0, 0], 2), [1, 0, 0], [2, 0, 0]),
(Sphere([0, 0, 0], 0.1), [1, 0, 0], [0.1, 0, 0]),
(Sphere([-1, 0, 0], 1), [1, 0, 0], [0, 0, 0]),
(Sphere([0, 0, 0], 1), [1, 1, 1], math.sqrt(3) / 3 * np.ones(3)),
(Sphere([0, 0, 0], 3), [1, 1, 1], math.sqrt(3) * np.ones(3)),
],
)
def test_project_point_sphere(sphere, point, point_expected):
point_projected = sphere.project_point(point)
assert point_projected.is_close(point_expected)
@pytest.mark.parametrize(
"circle_or_sphere, point",
"""
Sphere-Line Intersection
========================
"""
from skspatial.objects import Sphere, Line
from skspatial.plotting import plot_3d
sphere = Sphere([0, 0, 0], 1)
line = Line([0, 0, 0], [1, 1, 1])
point_a, point_b = sphere.intersect_line(line)
plot_3d(
line.plotter(t_1=-1, c='k'),
sphere.plotter(alpha=0.2),
point_a.plotter(c='r', s=100),
point_b.plotter(c='r', s=100),
)
(Circle([0, 0], 1), Line([0, -2], [1, 0])),
(Circle([0, 0], 1), Line([2, 0], [0, 1])),
(Circle([0, 0], 1), Line([3, 0], [1, 1])),
(Circle([1.5, 0], 1), Line([0, 0], [1, 0])),
],
)
def test_intersect_circle_line_failure(circle, line):
with pytest.raises(Exception):
circle.intersect_line(line)
@pytest.mark.parametrize(
"sphere, line, point_a_expected, point_b_expected",
[
(Sphere([0, 0, 0], 1), Line([0, 0, 0], [1, 0, 0]), [-1, 0, 0
], [1, 0, 0]),
(
Sphere([0, 0, 0], 1),
Line([0, 0, 0], [1, 1, 0]),
-math.sqrt(2) / 2 * np.array([1, 1, 0]),
math.sqrt(2) / 2 * np.array([1, 1, 0]),
),
(
Sphere([0, 0, 0], 1),
Line([0, 0, 0], [1, 1, 1]),
-math.sqrt(3) / 3 * np.ones(3),
math.sqrt(3) / 3 * np.ones(3),
),
(Sphere([1, 0, 0], 1), Line([0, 0, 0], [1, 0, 0]), [0, 0, 0
], [2, 0, 0]),
@pytest.mark.parametrize(
("obj_spatial", "repr_expected"),
[
(Point([0]), "Point([0])"),
(Point([0, 0]), "Point([0, 0])"),
(Point([0.5, 0]), "Point([0.5, 0. ])"),
(Point([-11, 0]), "Point([-11, 0])"),
(Vector([-11, 0]), "Vector([-11, 0])"),
(Vector([-11.0, 0.0]), "Vector([-11., 0.])"),
(Vector([0, 0]), "Vector([0, 0])"),
(Vector([0.5, 0]), "Vector([0.5, 0. ])"),
(Points([[1.5, 2], [5, 3]]), "Points([[1.5, 2. ],\n [5. , 3. ]])"),
(Line([0, 0], [1, 0]), "Line(point=Point([0, 0]), direction=Vector([1, 0]))"),
(Line([-1, 2, 3], [5, 4, 2]), "Line(point=Point([-1, 2, 3]), direction=Vector([5, 4, 2]))"),
(Line(np.zeros(2), [1, 0]), "Line(point=Point([0., 0.]), direction=Vector([1, 0]))"),
(Plane([0, 0], [1, 0]), "Plane(point=Point([0, 0]), normal=Vector([1, 0]))"),
(Plane([-1, 2, 3], [5, 4, 2]), "Plane(point=Point([-1, 2, 3]), normal=Vector([5, 4, 2]))"),
(Circle([0, 0], 1), "Circle(point=Point([0, 0]), radius=1)"),
(Circle([0, 0], 2.5), "Circle(point=Point([0, 0]), radius=2.5)"),
(Sphere([0, 0, 0], 1), "Sphere(point=Point([0, 0, 0]), radius=1)"),
(
Triangle([0, 0], [0, 1], [1, 0]),
"Triangle(point_a=Point([0, 0]), point_b=Point([0, 1]), point_c=Point([1, 0]))",
),
(Cylinder([0, 0, 0], [0, 0, 1], 1), "Cylinder(point=Point([0, 0, 0]), vector=Vector([0, 0, 1]), radius=1)"),
],
)
def test_repr(obj_spatial, repr_expected):
assert repr(obj_spatial) == repr_expected
[0, 1, 1]]),
(Plane([0, 0, 0], [1, 1, 0]), [[-1, 1, -1], [1, -1, -1], [-1, 1, 1],
[1, -1, 1]]),
],
)
def test_plane_points(plane, points_expected):
points = plane.to_points()
assert points.is_close(points_expected)
@pytest.mark.parametrize(
"sphere, n_angles, points_expected",
[
(Sphere([0, 0, 0], 1), 1, [[0, 0, 1]]),
(Sphere([0, 0, 0], 1), 2, [[0, 0, -1], [0, 0, 1]]),
(Sphere([0, 0, 0], 1), 3, [[0, -1, 0], [0, 0, -1], [0, 0, 1],
[0, 1, 0]]),
(Sphere([0, 0, 0], 2), 3, [[0, -2, 0], [0, 0, -2], [0, 0, 2],
[0, 2, 0]]),
(Sphere([1, 0, 0], 1), 3, [[1, -1, 0], [1, 0, -1], [1, 0, 1],
[1, 1, 0]]),
(Sphere([1, 1, 1], 1), 3, [[1, 0, 1], [1, 1, 0], [1, 1, 2], [1, 2, 1]
]),
],
)
def test_sphere_points(sphere, n_angles, points_expected):
array_rounded = sphere.to_points(n_angles).round(3)
points_unique = Points(array_rounded).unique()
(Circle([0, 0], 1), [0, 0], False),
(Circle([0, 0], 1), [1, 1], False),
(Circle([0, 0], 2), [1, 0], False),
(Circle([1, 0], 1), [1, 0], False),
(Circle([0, 0], math.sqrt(2)), [1, 1], True),
],
)
def test_circle_contains_point(circle, point, bool_expected):
assert circle.contains_point(point) == bool_expected
@pytest.mark.parametrize(
"sphere, point, bool_expected",
[
(Sphere([0, 0, 0], 1), [1, 0, 0], True),
(Sphere([0, 0, 0], 1), [0, 1, 0], True),
(Sphere([0, 0, 0], 1), [0, 0, 1], True),
(Sphere([0, 0, 0], 1), [-1, 0, 0], True),
(Sphere([0, 0, 0], 1), [0, -1, 0], True),
(Sphere([0, 0, 0], 1), [0, 0, -1], True),
(Sphere([0, 0, 0], 1), [1, 1, 0], False),
(Sphere([1, 0, 0], 1), [1, 0, 0], False),
(Sphere([1, 0, 0], 1), [2, 0, 0], True),
(Sphere([0, 0, 0], 2), [0, 2, 0], True),
(Sphere([0, 0, 0], math.sqrt(3)), [1, 1, 1], True),
],
)
def test_sphere_contains_point(sphere, point, bool_expected):
assert sphere.contains_point(point) == bool_expected
def test_surface_area_volume(radius, surface_area_expected, volume_expected):
sphere = Sphere([0, 0, 0], radius)
assert math.isclose(sphere.surface_area(), surface_area_expected)
assert math.isclose(sphere.volume(), volume_expected)
def test_failure(point, radius, message_expected):
with pytest.raises(ValueError, match=message_expected):
Sphere(point, radius)
def test_best_fit_failure(points, message_expected):
with pytest.raises(ValueError, match=message_expected):
Sphere.best_fit(points)
(4.5, 81 * np.pi, 121.5 * np.pi),
(10, 400 * np.pi, 4000 / 3 * np.pi),
],
)
def test_surface_area_volume(radius, surface_area_expected, volume_expected):
sphere = Sphere([0, 0, 0], radius)
assert math.isclose(sphere.surface_area(), surface_area_expected)
assert math.isclose(sphere.volume(), volume_expected)
@pytest.mark.parametrize(
("sphere", "point", "dist_expected"),
[
(Sphere([0, 0, 0], 1), [0, 0, 0], 1),
(Sphere([0, 0, 0], 1), [1, 0, 0], 0),
(Sphere([0, 0, 0], 1), [0, -1, 0], 0),
(Sphere([0, 0, 0], 2), [0, 0, 0], 2),
(Sphere([0, 0, 0], 1), [1, 1, 1], math.sqrt(3) - 1),
(Sphere([0, 0, 0], 2), [1, 1, 1], 2 - math.sqrt(3)),
(Sphere([1, 0, 0], 2), [0, 0, 0], 1),
],
)
def test_distance_point(sphere, point, dist_expected):
assert math.isclose(sphere.distance_point(point), dist_expected)
@pytest.mark.parametrize(
("sphere", "point", "bool_expected"),
def test_failure(point, radius):
with pytest.raises(Exception):
Sphere(point, radius)
(Circle([0, 0], 1), [0, -1], 0),
(Circle([0, 0], 1), [2, 0], 1),
(Circle([0, 0], 1), [1, 1], math.sqrt(2) - 1),
(Circle([1, 1], 1), [0, 0], math.sqrt(2) - 1),
(Circle([0, 0], 2), [0, 5], 3),
],
)
def test_distance_circle_point(circle, point, dist_expected):
assert math.isclose(circle.distance_point(point), dist_expected)
@pytest.mark.parametrize(
"sphere, point, dist_expected",
[
(Sphere([0, 0, 0], 1), [0, 0, 0], 1),
(Sphere([0, 0, 0], 1), [1, 0, 0], 0),
(Sphere([0, 0, 0], 1), [0, -1, 0], 0),
(Sphere([0, 0, 0], 2), [0, 0, 0], 2),
(Sphere([0, 0, 0], 1), [1, 1, 1], math.sqrt(3) - 1),
(Sphere([0, 0, 0], 2), [1, 1, 1], 2 - math.sqrt(3)),
(Sphere([1, 0, 0], 2), [0, 0, 0], 1),
],
)
def test_distance_plane_point(sphere, point, dist_expected):
assert math.isclose(sphere.distance_point(point), dist_expected)
@pytest.mark.parametrize(
"array_a, array_b, array_c, area_expected",