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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)) | |