def test_from_crossratio(self):
a = Point(0, 1)
b = Point(0, -1)
c = Point(1.5, 0.5)
d = Point(1.5, -0.5)
e = Point(-1.5, 0.5)
conic1 = Conic.from_points(a, b, c, d, e)
cr = crossratio(a, b, c, d, e)
conic2 = Conic.from_crossratio(cr, a, b, c, d)
assert conic1 == conic2
def test_from_foci(self):
f1 = Point(0, np.sqrt(5))
f2 = Point(0, -np.sqrt(5))
b = Point(0, 3)
conic = Conic.from_foci(f1, f2, b)
assert conic == Ellipse(Point(0, 0), 2, 3)
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_from_tangent(self):
a = Point(-1.5, 0.5)
b = Point(0, -1)
c = Point(1.5, 0.5)
d = Point(1.5, -0.5)
l = Line(0, 1, -1)
conic = Conic.from_tangent(l, a, b, c, d)
assert conic.contains(a)
assert conic.contains(b)
assert conic.contains(c)
assert conic.contains(d)
assert conic.is_tangent(l)
def test_from_points(self):
a = Point(0, 1)
b = Point(0, -1)
c = Point(1.5, 0.5)
d = Point(1.5, -0.5)
e = Point(-1.5, 0.5)
conic = Conic.from_points(a, b, c, d, e)
assert conic.contains(a)
assert conic.contains(b)
assert conic.contains(c)
assert conic.contains(d)
assert conic.contains(e)
def test_from_points(self):
a = Point(-1, 0)
b = Point(0, 3)
c = Point(1, 2)
d = Point(2, 1)
e = Point(0, -1)
conic = Conic.from_points(a, b, c, d, e)
assert conic.contains(a)
assert conic.contains(b)
assert conic.contains(c)
assert conic.contains(d)
assert conic.contains(e)
def test_intersect(self):
c = Circle(Point(0, 0), 1)
i = c.intersect(Line(0, 1, 0))
assert len(i) == 2
assert Point(1, 0) in i
assert Point(-1, 0) in i
c2 = Circle(Point(0, 2), 1)
assert Point(0, 1) in c.intersect(c2)
c3 = Conic.from_lines(Line(1, 0, 0), Line(0, 1, 0))
assert Point(1, 0) in c.intersect(c3)
assert Point(0, 1) in c.intersect(c3)
assert Point(-1, 0) in c.intersect(c3)
assert Point(0, -1) in c.intersect(c3)
def test_contains(self):
c = Conic([[1, 0, 0], [0, 1, 0], [0, 0, -1]])
assert c.contains(Point(1, 0))