def test_cp1():
p = Point(1 + 0j)
q = Point(0 + 1j)
m = Transformation([[np.e**(np.pi / 2 * 1j), 0], [0, 1]])
assert m * p == q
c = crossratio(p, q, m * q, m * m * q)
assert np.isclose(np.real(c), c)
def test_pow(self):
t = translation(1, 2)
assert t**0 == Transformation(np.eye(3))
assert t**1 == t
assert t**2 == translation(2, 4)
assert t**3 == translation(3, 6)
assert t**(-2) == translation(-2, -4)
def test_from_points(self):
p1 = Point(0, 0)
p2 = Point(1, 0)
p3 = Point(0, 1)
p4 = Point(3, 5)
l = Line(p1, p3)
M = Transformation.from_points((p1, p1 + Point(1, 1)), (p2, p2 + Point(1, 1)), (p3, p3 + Point(1, 1)), (p4, p4 + Point(1, 1)))
assert M*p3 == Point(1, 2)
assert (M*l).contains(M*p1)
assert (M*l).contains(M*p3)
def test_from_points_and_conics(self):
c1 = Circle()
p1 = Point(0, -1)
p2 = Point(0, 1)
p3 = Point(1, 0)
c2 = Circle(Point(0, 2), 2)
q1 = Point(0, 0)
q2 = Point(0, 4)
q3 = Point(2, 2)
t = Transformation.from_points_and_conics([p1, p2, p3], [q1, q2, q3],
c1, c2)
assert t * p1 == q1
assert t * p2 == q2
assert t * p2 == q2
assert t.apply(c1) == c2
def test_inverse(self):
E = Transformation(np.eye(4))
M = rotation(np.pi, axis=Point(0, 1, 0))
assert M.inverse() * M == E
