def test_angle_bisectors():
a = Point(0, 0)
b = Point(1, 1)
c = Point(1, 0)
l = Line(a, b)
m = Line(a, c)
q, r = angle_bisectors(l, m)
assert is_perpendicular(q, r)
assert np.isclose(angle(l, q), angle(q, m))
p1 = Point(0, 0, 0)
p2 = Point(0, 1, 0)
p3 = Point(1, 0, 0)
l = Line(p1, p2)
m = Line(p1, p3)
q, r = angle_bisectors(l, m)
assert is_perpendicular(q, r)
assert np.isclose(angle(l, q), angle(q, m))
p1 = PointCollection([(0, 0), (0, 0)], homogenize=True)
p2 = PointCollection([(1, 1), (0, 1)], homogenize=True)
p3 = PointCollection([(1, 0), (1, 1)], homogenize=True)
l = LineCollection(p1, p2)
m = LineCollection(p1, p3)
q, r = angle_bisectors(l, m)
assert all(is_perpendicular(q, r))
assert np.allclose(angle(l, q), angle(q, m))
def test_perpendicular(self):
p1 = PointCollection([(1, 1, 0), (1, 1, 5)], homogenize=True)
p2 = PointCollection([(2, 1, 0), (2, 1, 5)], homogenize=True)
p3 = PointCollection([(0, 0, 0), (0, 0, 5)], homogenize=True)
l = LineCollection(p1, p2)
m = l.perpendicular(p1)
assert l.meet(m) == p1
assert all(is_perpendicular(l, m))
m = l.perpendicular(
p3 + PointCollection([(1, 1, 0), (0, 0, 0)], homogenize=True)
)
assert all(is_perpendicular(l, m))
e = PlaneCollection(l, p3)
m = e.perpendicular(p1)
assert e.meet(m) == p1
assert all(is_perpendicular(l, m))
m = e.perpendicular(p1 + PointCollection([m.direction[0], Point(0, 0, 0)]))
assert e.meet(m) == p1
assert all(is_perpendicular(l, m))
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_project(self):
p1 = PointCollection([(1, 1, 0), (1, 1, 5)], homogenize=True)
p2 = PointCollection([(2, 1, 0), (2, 1, 5)], homogenize=True)
p3 = PointCollection([(0, 0, 0), (0, 0, 5)], homogenize=True)
l = LineCollection(p1, p2)
assert l.project(p3) == PointCollection([(0, 1, 0), (0, 1, 5)], homogenize=True)
e = PlaneCollection([(0, 1, 0, -1), (0, 1, 0, -2)])
assert e.project(p3) == PointCollection([(0, 1, 0), (0, 2, 5)], homogenize=True)
def test_components(self):
l = Line(1, 2, 3)
m = Line(4, 5, 6)
g = Line(3, 2, 1)
h = Line(6, 5, 4)
q = QuadricCollection([Conic.from_lines(l, m), Conic.from_lines(g, h)])
assert q.components == [LineCollection([m, g]), LineCollection([l, h])]
e = Plane(1, 2, 3, 4)
f = Plane(4, 3, 2, 1)
g = Plane(5, 6, 7, 8)
h = Plane(8, 7, 6, 5)
q = QuadricCollection([Quadric.from_planes(e, f), Quadric.from_planes(g, h)])
assert q.components == [PlaneCollection([e, g]), PlaneCollection([f, h])]
def test_meet(self):
# three planes
a = PlaneCollection([Plane(1, 0, 0, 0), Plane(1, 0, 0, -1)])
b = PlaneCollection([Plane(0, 1, 0, 0), Plane(0, 1, 0, -1)])
c = PlaneCollection([Plane(0, 0, 1, 0), Plane(0, 0, 1, -1)])
assert meet(a, b, c) == PointCollection([Point(0, 0, 0), Point(1, 1, 1)])
# two planes
l = a.meet(b)
m = LineCollection(
[Line(Point(0, 0, 0), Point(0, 0, 1)), Line(Point(1, 1, 0), Point(1, 1, 1))]
)
assert l == m
# two lines in 2D
a = LineCollection([Line(0, 1, 0), Line(0, 1, -1)])
b = LineCollection([Line(1, 0, 0), Line(1, 0, -1)])
assert a.meet(b) == PointCollection([Point(0, 0), Point(1, 1)])
# two lines in 3D
a = LineCollection(
[Line(Point(0, 0, 0), Point(0, 0, 1)), Line(Point(1, 0, 0), Point(1, 0, 1))]
)
b = LineCollection(
[Line(Point(0, 0, 0), Point(0, 1, 0)), Line(Point(1, 0, 0), Point(1, 1, 0))]
)
assert a.meet(b) == PointCollection([Point(0, 0, 0), Point(1, 0, 0)])
# plane and line
a = LineCollection(
[Line(Point(0, 0, 0), Point(0, 0, 1)), Line(Point(1, 0, 0), Point(1, 0, 1))]
)
b = PlaneCollection([Plane(0, 0, 1, 0), Plane(0, 0, 1, -1)])
assert a.meet(b) == PointCollection([Point(0, 0, 0), Point(1, 0, 1)])
def test_angle():
a = Point(0, 0)
b = Point(1, 1)
c = Point(1, 0)
assert np.isclose(angle(a, b, c), np.pi / 4)
assert np.isclose(angle(a, c, b), -np.pi / 4)
e1 = Plane(1, 0, 0, 0)
e2 = Plane(0, 0, 1, 0)
assert np.isclose(abs(angle(e1, e2)), np.pi / 2)
p1 = Point(0, 0, 0)
p2 = Point(0, 1, 0)
p3 = Point(1, 0, 0)
assert np.isclose(abs(angle(p1, p2, p3)), np.pi / 2)
l = Line(p1, p2)
m = Line(p1, p3)
assert np.isclose(abs(angle(l, m)), np.pi / 2)
p1 = PointCollection([(0, 0), (0, 0)], homogenize=True)
p2 = PointCollection([(1, 1), (0, 1)], homogenize=True)
p3 = PointCollection([(1, 0), (1, 1)], homogenize=True)
assert np.allclose(angle(p1, p2, p3), np.pi / 4)
l = LineCollection(p1, p2)
m = LineCollection(p1, p3)
assert np.allclose(angle(l, m), np.pi / 4)
e1 = PlaneCollection([(0, 0, 1, 0), (1, 0, 0, 0)])
e2 = PlaneCollection([(1, 1, 1, 0), (0, 1, 0, 0)])
assert np.allclose(angle(e1, e2), [np.arccos(1 / np.sqrt(3)), np.pi / 2])
def test_is_perpendicular():
l = Line(0, 1, 0)
m = Line(1, 0, 0)
assert is_perpendicular(l, m)
p1 = Point(0, 0, 0)
p2 = Point(0, 1, 0)
p3 = Point(1, 0, 0)
l = Line(p1, p2)
m = Line(p1, p3)
assert is_perpendicular(l, m)
e1 = Plane(p1, p2, p3)
e2 = Plane(p1, p2, Point(0, 0, 1))
assert is_perpendicular(e1, e2)
l = LineCollection([(0, 1, 0), (0, 1, 0)])
m = LineCollection([(1, 0, 0), (1, -1, 0)])
assert list(is_perpendicular(l, m)) == [True, False]
e1 = PlaneCollection([(0, 0, 1, 0), (1, 0, 0, 0)])
e2 = PlaneCollection([(0, 1, 0, 0), (0, 0, 1, 0)])
assert all(is_perpendicular(e1, e2))
def test_intersection(self):
c = Circle(Point(0, 2), 2)
l = Line(Point(-1, 2), Point(1, 2))
assert c.contains(Point(0, 0))
assert c.intersect(l) == [Point(-2, 2), Point(2, 2)]
assert c.intersect(l - Point(0, 2)) == [Point(0, 0)]
l = LineCollection(
[Line(Point(-1, 2), Point(1, 2)),
Line(Point(0, 2), Point(0, 0))])
assert c.intersect(l) == [
PointCollection([Point(-2, 2), Point(0, 0)]),
PointCollection([Point(2, 2), Point(0, 4)])
]
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_intersect(self):
c = Circle(Point(0, 2), 2)
l = Line(Point(-1, 2), Point(1, 2))
assert c.contains(Point(0, 0))
assert c.intersect(l) == [Point(-2, 2), Point(2, 2)]
assert c.intersect(l - Point(0, 2)) == [Point(0, 0)]
l = LineCollection(
[Line(Point(-1, 2), Point(1, 2)),
Line(Point(0, 2), Point(0, 0))])
assert c.intersect(l) == [
PointCollection([Point(-2, 2), Point(0, 0)]),
PointCollection([Point(2, 2), Point(0, 4)]),
]
c1 = Circle(Point(0, 0), 5)
c2 = Circle(Point(8, 0), 5)
intersections = c1.intersect(c2)
assert Point(4, 3) in intersections
assert Point(4, -3) in intersections
def test_join(self):
# 2 points
a = PointCollection([Point(0, 0), Point(0, 1)])
b = PointCollection([Point(1, 0), Point(1, 1)])
assert a.join(b) == LineCollection([Line(0, 1, 0), Line(0, 1, -1)])
# 3 points
a = PointCollection([Point(0, 0, 0), Point(0, 0, 1)])
b = PointCollection([Point(1, 0, 0), Point(1, 0, 1)])
c = PointCollection([Point(0, 1, 0), Point(0, 1, 1)])
assert join(a, b, c) == PlaneCollection([Plane(0, 0, 1, 0), Plane(0, 0, 1, -1)])
# two lines
l = a.join(b)
m = a.join(c)
assert join(l, m) == PlaneCollection([Plane(0, 0, 1, 0), Plane(0, 0, 1, -1)])
# point and line
assert join(a, b.join(c)) == PlaneCollection(
[Plane(0, 0, 1, 0), Plane(0, 0, 1, -1)]
)
def test_intersect(self):
c = Circle(Point(0, 2), 2)
l = Line(Point(-1, 2), Point(1, 2))
assert c.contains(Point(0, 0))
assert c.intersect(l) == [Point(-2, 2), Point(2, 2)]
assert c.intersect(l - Point(0, 2)) == [Point(0, 0)]
l = LineCollection([Line(Point(-1, 2), Point(1, 2)), Line(Point(0, 2), Point(0, 0))])
assert c.intersect(l) == [PointCollection([Point(-2, 2), Point(0, 0)]),
PointCollection([Point(2, 2), Point(0, 4)])]
c1 = Circle(Point(0, 0), 5)
c2 = Circle(Point(8, 0), 5)
intersections = c1.intersect(c2)
assert Point(4, 3) in intersections
assert Point(4, -3) in intersections
c1 = Circle(Point(0, 0))
c2 = Circle(Point(0.5, 0))
i = c1.intersect(c2)
assert len(i) == 4
assert len([p for p in i if p.isreal]) == 2