def test_tangent(self):
q = QuadricCollection([Sphere(), Sphere(radius=2)])
p = PointCollection([Point(1, 0, 0), Point(2, 0, 0)])
assert all(q.contains(p))
assert q.tangent(at=p) == PlaneCollection([Plane(1, 0, 0, -1), Plane(1, 0, 0, -2)])
assert all(q.is_tangent(q.tangent(at=p)))
def test_intersect(self):
q = QuadricCollection([Circle(Point(0, 1), 1), Circle(Point(0, 2), 2)])
l = LineCollection(
[Line(Point(-1, 1), Point(1, 1)),
Line(Point(-1, 2), Point(1, 2))])
assert q.intersect(l) == [
PointCollection([Point(1, 1), Point(-2, 2)]),
PointCollection([Point(-1, 1), Point(2, 2)]),
]
q = QuadricCollection(
[Sphere(Point(0, 0, 1), 1),
Sphere(Point(0, 0, 2), 2)])
l = LineCollection([
Line(Point(-1, 0, 1), Point(1, 0, 1)),
Line(Point(-1, 0, 2), Point(1, 0, 2)),
])
m = Line(Point(-1, 0, 2), Point(1, 0, 2))
assert q.intersect(l) == [
PointCollection([Point(-1, 0, 1), Point(-2, 0, 2)]),
PointCollection([Point(1, 0, 1), Point(2, 0, 2)]),
]
assert q.intersect(m) == [
PointCollection([Point(0, 0, 2), Point(-2, 0, 2)]),
PointCollection([Point(0, 0, 2), Point(2, 0, 2)]),
]
def test_intersection(self):
s = Sphere(Point(0, 0, 2), 2)
l = Line(Point(-1, 0, 2), Point(1, 0, 2))
assert s.contains(Point(0, 0, 0))
assert s.intersect(l) == [Point(-2, 0, 2), Point(2, 0, 2)]
assert s.intersect(l-Point(0, 0, 2)) == [Point(0, 0, 0)]
s = Sphere(Point(0, 0, 0, 2), 2)
l = Line(Point(-1, 0, 0, 2), Point(1, 0, 0, 2))
assert s.contains(Point(0, 0, 0, 0))
assert s.intersect(l) == [Point(2, 0, 0, 2), Point(-2, 0, 0, 2)]
def test_s3(self):
s3 = Sphere(Point(1, 2, 3, 4), 5)
assert s3.center == Point(1, 2, 3, 4)
assert np.isclose(s3.radius, 5)
assert np.isclose(s3.volume, 1 / 2 * np.pi**2 * 5**4)
assert np.isclose(s3.area, 2 * np.pi**2 * 5**3)
def test_s2(self):
s2 = Sphere()
assert s2.center == Point(0, 0, 0)
assert np.isclose(s2.radius, 1)
assert np.isclose(s2.volume, 4 / 3 * np.pi)
assert np.isclose(s2.area, 4 * np.pi)
def test_intersect(self):
s = Sphere(Point(0, 0, 2), 2)
l = Line(Point(-1, 0, 2), Point(1, 0, 2))
assert s.contains(Point(0, 0, 0))
assert s.intersect(l) == [Point(-2, 0, 2), Point(2, 0, 2)]
assert s.intersect(l - Point(0, 0, 2)) == [Point(0, 0, 0)]
l = LineCollection([Line(Point(-1, 0, 2), Point(1, 0, 2)), Line(Point(0, 0, 0), Point(0, 0, 2))])
assert s.intersect(l) == [PointCollection([Point(-2, 0, 2), Point(0, 0, 0)]),
PointCollection([Point(2, 0, 2), Point(0, 0, 4)])]
s = Sphere(Point(0, 0, 0, 2), 2)
l = Line(Point(-1, 0, 0, 2), Point(1, 0, 0, 2))
assert s.contains(Point(0, 0, 0, 0))
assert s.intersect(l) == [Point(2, 0, 0, 2), Point(-2, 0, 0, 2)]
def test_contains(self):
s = QuadricCollection([Sphere(), Sphere(radius=2)])
p = Point(1, 0, 0)
assert np.all(s.contains(p) == [True, False])
def test_add(self):
s = Sphere()
p = Point(0, 0, 2)
assert s + p == Sphere(p)
assert s - p == Sphere(-p)
def test_transform(self):
s = Sphere(Point(0, 0, 2), 2)
t = translation(1, 1, -1)
assert t * s == Sphere(Point(1, 1, 1), 2)