def test_geometry_transforms():
from diofant import Tuple
c = Curve((x, x**2), (x, 0, 1))
pts = [Point(0, 0), Point(1/2, 1/4), Point(1, 1)]
cout = Curve((2*x - 4, 3*x**2 - 10), (x, 0, 1))
pts_out = [Point(-4, -10), Point(-3, -37/4), Point(-2, -7)]
assert c.scale(2, 3, (4, 5)) == cout
assert [c.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts
assert [cout.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts_out
assert Triangle(*pts).scale(2, 3, (4, 5)) == Triangle(*pts_out)
assert Ellipse((0, 0), 2, 3).scale(2, 3, (4, 5)) == \
Ellipse(Point(-4, -10), 4, 9)
assert Circle((0, 0), 2).scale(2, 3, (4, 5)) == \
Ellipse(Point(-4, -10), 4, 6)
assert Ellipse((0, 0), 2, 3).scale(3, 3, (4, 5)) == \
Ellipse(Point(-8, -10), 6, 9)
assert Circle((0, 0), 2).scale(3, 3, (4, 5)) == \
Circle(Point(-8, -10), 6)
assert Circle(Point(-8, -10), 6).scale(1/3, 1/3, (4, 5)) == \
Circle((0, 0), 2)
assert Curve((x + y, 3*x), (x, 0, 1)).subs(y, S.Half) == \
Curve((x + 1/2, 3*x), (x, 0, 1))
assert Curve((x, 3*x), (x, 0, 1)).translate(4, 5) == \
Curve((x + 4, 3*x + 5), (x, 0, 1))
assert Circle((0, 0), 2).translate(4, 5) == \
Circle((4, 5), 2)
assert Circle((0, 0), 2).scale(3, 3) == \
Circle((0, 0), 6)
assert Point(1, 1).scale(2, 3, (4, 5)) == \
Point(-2, -7)
assert Point(1, 1).translate(4, 5) == \
Point(5, 6)
assert scale(1, 2, (3, 4)).tolist() == \
[[1, 0, 0], [0, 2, 0], [0, -4, 1]]
assert RegularPolygon((0, 0), 1, 4).scale(2, 3, (4, 5)) == \
Polygon(Point(-2, -10), Point(-4, -7), Point(-6, -10), Point(-4, -13))
def test_transform():
p = Point(1, 1)
assert p.transform(rotate(pi / 2)) == Point(-1, 1)
assert p.transform(scale(3, 2)) == Point(3, 2)
assert p.transform(translate(1, 2)) == Point(2, 3)
