def test_reflect():
b = Symbol('b')
m = Symbol('m')
l = Line((0, b), slope=m)
p = Point(x, y)
r = p.reflect(l)
dp = l.perpendicular_segment(p).length
dr = l.perpendicular_segment(r).length
assert verify_numerically(dp, dr)
t = Triangle((0, 0), (1, 0), (2, 3))
assert t.area == -t.reflect(l).area
e = Ellipse((1, 0), 1, 2)
assert e.area == -e.reflect(Line((1, 0), slope=0)).area
assert e.area == -e.reflect(Line((1, 0), slope=oo)).area
pytest.raises(NotImplementedError, lambda: e.reflect(Line(
(1, 0), slope=m)))
assert Polygon((1, 0), (2, 0), (2, 2)).reflect(Line((3, 0), slope=oo)) \
== Triangle(Point(5, 0), Point(4, 0), Point(4, 2))
assert Polygon((1, 0), (2, 0), (2, 2)).reflect(Line((0, 3), slope=oo)) \
== Triangle(Point(-1, 0), Point(-2, 0), Point(-2, 2))
assert Polygon((1, 0), (2, 0), (2, 2)).reflect(Line((0, 3), slope=0)) \
== Triangle(Point(1, 6), Point(2, 6), Point(2, 4))
assert Polygon((1, 0), (2, 0), (2, 2)).reflect(Line((3, 0), slope=0)) \
== Triangle(Point(1, 0), Point(2, 0), Point(2, -2))
# test entity overrides
c = Circle((x, y), 3)
cr = c.reflect(l)
assert cr == Circle(r, -3)
assert c.area == -cr.area
pent = RegularPolygon((1, 2), 1, 5)
l = Line((0, pi), slope=sqrt(2))
rpent = pent.reflect(l)
assert rpent.center == pent.center.reflect(l)
assert [w.evalf(3) for w in rpent.vertices] == \
[Point2D(Float('-0.585815', dps=3),
Float('4.27051', dps=3)),
Point2D(Float('-1.69409', dps=3),
Float('4.66211', dps=3)),
Point2D(Float('-2.40918', dps=3),
Float('3.72949', dps=3)),
Point2D(Float('-1.74292', dps=3),
Float('2.76123', dps=3)),
Point2D(Float('-0.615967', dps=3),
Float('3.0957', dps=3))]
assert pent.area.equals(-rpent.area)
def test_Point2D():
p1 = Point2D(1, 5)
p2 = Point2D(4, 2.5)
p3 = Point2D(6.1, 3.5)
assert p1.distance(p2) == sqrt(61)/2
assert p2.distance(p3) == sqrt(541)/10
assert p1.bounds == (1, 5, 1, 5)
assert Point2D.is_concyclic() is False
pytest.raises(ValueError, lambda: Point2D(1, 1, 1))
pytest.raises(ValueError, lambda: Point2D(1, I))
def test_Point2D():
p1 = Point2D(1, 5)
p2 = Point2D(4, 2.5)
p3 = Point2D(6.1, 3.5)
assert p1.distance(p2) == sqrt(61) / 2
assert p2.distance(p3) == sqrt(541) / 10