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from sympy.core.numbers import pi
from sympy.functions.elementary.trigonometric import (cos, sin)
from sympy.vector.coordsysrect import CoordSys3D
from sympy.vector.parametricregion import ParametricRegion, parametric_region_list
from sympy.geometry import Point, Segment, Curve, Ellipse, Line, Parabola, Polygon
from sympy.testing.pytest import raises
from sympy.abc import a, b, r, t, x, y, z, theta, phi
C = CoordSys3D('C')
def test_ParametricRegion():
point = ParametricRegion((3, 4))
assert point.definition == (3, 4)
assert point.parameters == ()
assert point.limits == {}
assert point.dimensions == 0
# line x = y
line_xy = ParametricRegion((y, y), (y, 1, 5))
assert line_xy .definition == (y, y)
assert line_xy.parameters == (y,)
assert line_xy.dimensions == 1
# line y = z
line_yz = ParametricRegion((x,t,t), x, (t, 1, 2))
assert line_yz.definition == (x,t,t)
assert line_yz.parameters == (x, t)
assert line_yz.limits == {t: (1, 2)}
assert line_yz.dimensions == 1
p1 = ParametricRegion((9*a, -16*b), (a, 0, 2), (b, -1, 5))
assert p1.definition == (9*a, -16*b)
assert p1.parameters == (a, b)
assert p1.limits == {a: (0, 2), b: (-1, 5)}
assert p1.dimensions == 2
p2 = ParametricRegion((t, t**3), t)
assert p2.parameters == (t,)
assert p2.limits == {}
assert p2.dimensions == 0
circle = ParametricRegion((r*cos(theta), r*sin(theta)), r, (theta, 0, 2*pi))
assert circle.definition == (r*cos(theta), r*sin(theta))
assert circle.dimensions == 1
halfdisc = ParametricRegion((r*cos(theta), r*sin(theta)), (r, -2, 2), (theta, 0, pi))
assert halfdisc.definition == (r*cos(theta), r*sin(theta))
assert halfdisc.parameters == (r, theta)
assert halfdisc.limits == {r: (-2, 2), theta: (0, pi)}
assert halfdisc.dimensions == 2
ellipse = ParametricRegion((a*cos(t), b*sin(t)), (t, 0, 8))
assert ellipse.parameters == (t,)
assert ellipse.limits == {t: (0, 8)}
assert ellipse.dimensions == 1
cylinder = ParametricRegion((r*cos(theta), r*sin(theta), z), (r, 0, 1), (theta, 0, 2*pi), (z, 0, 4))
assert cylinder.parameters == (r, theta, z)
assert cylinder.dimensions == 3
sphere = ParametricRegion((r*sin(phi)*cos(theta),r*sin(phi)*sin(theta), r*cos(phi)),
r, (theta, 0, 2*pi), (phi, 0, pi))
assert sphere.definition == (r*sin(phi)*cos(theta),r*sin(phi)*sin(theta), r*cos(phi))
assert sphere.parameters == (r, theta, phi)
assert sphere.dimensions == 2
raises(ValueError, lambda: ParametricRegion((a*t**2, 2*a*t), (a, -2)))
raises(ValueError, lambda: ParametricRegion((a, b), (a**2, sin(b)), (a, 2, 4, 6)))
def test_parametric_region_list():
point = Point(-5, 12)
assert parametric_region_list(point) == [ParametricRegion((-5, 12))]
e = Ellipse(Point(2, 8), 2, 6)
assert parametric_region_list(e, t) == [ParametricRegion((2*cos(t) + 2, 6*sin(t) + 8), (t, 0, 2*pi))]
c = Curve((t, t**3), (t, 5, 3))
assert parametric_region_list(c) == [ParametricRegion((t, t**3), (t, 5, 3))]
s = Segment(Point(2, 11, -6), Point(0, 2, 5))
assert parametric_region_list(s, t) == [ParametricRegion((2 - 2*t, 11 - 9*t, 11*t - 6), (t, 0, 1))]
s1 = Segment(Point(0, 0), (1, 0))
assert parametric_region_list(s1, t) == [ParametricRegion((t, 0), (t, 0, 1))]
s2 = Segment(Point(1, 2, 3), Point(1, 2, 5))
assert parametric_region_list(s2, t) == [ParametricRegion((1, 2, 2*t + 3), (t, 0, 1))]
s3 = Segment(Point(12, 56), Point(12, 56))
assert parametric_region_list(s3) == [ParametricRegion((12, 56))]
poly = Polygon((1,3), (-3, 8), (2, 4))
assert parametric_region_list(poly, t) == [ParametricRegion((1 - 4*t, 5*t + 3), (t, 0, 1)), ParametricRegion((5*t - 3, 8 - 4*t), (t, 0, 1)), ParametricRegion((2 - t, 4 - t), (t, 0, 1))]
p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7,8)))
raises(ValueError, lambda: parametric_region_list(p1))
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