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| from sympy.core.numbers import (Rational, pi) | |
| from sympy.core.singleton import S | |
| from sympy.core.symbol import (Dummy, symbols) | |
| from sympy.functions.elementary.miscellaneous import sqrt | |
| from sympy.functions.elementary.trigonometric import (asin, cos, sin) | |
| from sympy.geometry import Line, Point, Ray, Segment, Point3D, Line3D, Ray3D, Segment3D, Plane, Circle | |
| from sympy.geometry.util import are_coplanar | |
| from sympy.testing.pytest import raises | |
| def test_plane(): | |
| x, y, z, u, v = symbols('x y z u v', real=True) | |
| p1 = Point3D(0, 0, 0) | |
| p2 = Point3D(1, 1, 1) | |
| p3 = Point3D(1, 2, 3) | |
| pl3 = Plane(p1, p2, p3) | |
| pl4 = Plane(p1, normal_vector=(1, 1, 1)) | |
| pl4b = Plane(p1, p2) | |
| pl5 = Plane(p3, normal_vector=(1, 2, 3)) | |
| pl6 = Plane(Point3D(2, 3, 7), normal_vector=(2, 2, 2)) | |
| pl7 = Plane(Point3D(1, -5, -6), normal_vector=(1, -2, 1)) | |
| pl8 = Plane(p1, normal_vector=(0, 0, 1)) | |
| pl9 = Plane(p1, normal_vector=(0, 12, 0)) | |
| pl10 = Plane(p1, normal_vector=(-2, 0, 0)) | |
| pl11 = Plane(p2, normal_vector=(0, 0, 1)) | |
| l1 = Line3D(Point3D(5, 0, 0), Point3D(1, -1, 1)) | |
| l2 = Line3D(Point3D(0, -2, 0), Point3D(3, 1, 1)) | |
| l3 = Line3D(Point3D(0, -1, 0), Point3D(5, -1, 9)) | |
| raises(ValueError, lambda: Plane(p1, p1, p1)) | |
| assert Plane(p1, p2, p3) != Plane(p1, p3, p2) | |
| assert Plane(p1, p2, p3).is_coplanar(Plane(p1, p3, p2)) | |
| assert Plane(p1, p2, p3).is_coplanar(p1) | |
| assert Plane(p1, p2, p3).is_coplanar(Circle(p1, 1)) is False | |
| assert Plane(p1, normal_vector=(0, 0, 1)).is_coplanar(Circle(p1, 1)) | |
| assert pl3 == Plane(Point3D(0, 0, 0), normal_vector=(1, -2, 1)) | |
| assert pl3 != pl4 | |
| assert pl4 == pl4b | |
| assert pl5 == Plane(Point3D(1, 2, 3), normal_vector=(1, 2, 3)) | |
| assert pl5.equation(x, y, z) == x + 2*y + 3*z - 14 | |
| assert pl3.equation(x, y, z) == x - 2*y + z | |
| assert pl3.p1 == p1 | |
| assert pl4.p1 == p1 | |
| assert pl5.p1 == p3 | |
| assert pl4.normal_vector == (1, 1, 1) | |
| assert pl5.normal_vector == (1, 2, 3) | |
| assert p1 in pl3 | |
| assert p1 in pl4 | |
| assert p3 in pl5 | |
| assert pl3.projection(Point(0, 0)) == p1 | |
| p = pl3.projection(Point3D(1, 1, 0)) | |
| assert p == Point3D(Rational(7, 6), Rational(2, 3), Rational(1, 6)) | |
| assert p in pl3 | |
| l = pl3.projection_line(Line(Point(0, 0), Point(1, 1))) | |
| assert l == Line3D(Point3D(0, 0, 0), Point3D(Rational(7, 6), Rational(2, 3), Rational(1, 6))) | |
| assert l in pl3 | |
| # get a segment that does not intersect the plane which is also | |
| # parallel to pl3's normal veector | |
| t = Dummy() | |
| r = pl3.random_point() | |
| a = pl3.perpendicular_line(r).arbitrary_point(t) | |
| s = Segment3D(a.subs(t, 1), a.subs(t, 2)) | |
| assert s.p1 not in pl3 and s.p2 not in pl3 | |
| assert pl3.projection_line(s).equals(r) | |
| assert pl3.projection_line(Segment(Point(1, 0), Point(1, 1))) == \ | |
| Segment3D(Point3D(Rational(5, 6), Rational(1, 3), Rational(-1, 6)), Point3D(Rational(7, 6), Rational(2, 3), Rational(1, 6))) | |
| assert pl6.projection_line(Ray(Point(1, 0), Point(1, 1))) == \ | |
| Ray3D(Point3D(Rational(14, 3), Rational(11, 3), Rational(11, 3)), Point3D(Rational(13, 3), Rational(13, 3), Rational(10, 3))) | |
| assert pl3.perpendicular_line(r.args) == pl3.perpendicular_line(r) | |
| assert pl3.is_parallel(pl6) is False | |
| assert pl4.is_parallel(pl6) | |
| assert pl3.is_parallel(Line(p1, p2)) | |
| assert pl6.is_parallel(l1) is False | |
| assert pl3.is_perpendicular(pl6) | |
| assert pl4.is_perpendicular(pl7) | |
| assert pl6.is_perpendicular(pl7) | |
| assert pl6.is_perpendicular(pl4) is False | |
| assert pl6.is_perpendicular(l1) is False | |
| assert pl6.is_perpendicular(Line((0, 0, 0), (1, 1, 1))) | |
| assert pl6.is_perpendicular((1, 1)) is False | |
| assert pl6.distance(pl6.arbitrary_point(u, v)) == 0 | |
| assert pl7.distance(pl7.arbitrary_point(u, v)) == 0 | |
| assert pl6.distance(pl6.arbitrary_point(t)) == 0 | |
| assert pl7.distance(pl7.arbitrary_point(t)) == 0 | |
| assert pl6.p1.distance(pl6.arbitrary_point(t)).simplify() == 1 | |
| assert pl7.p1.distance(pl7.arbitrary_point(t)).simplify() == 1 | |
| assert pl3.arbitrary_point(t) == Point3D(-sqrt(30)*sin(t)/30 + \ | |
| 2*sqrt(5)*cos(t)/5, sqrt(30)*sin(t)/15 + sqrt(5)*cos(t)/5, sqrt(30)*sin(t)/6) | |
| assert pl3.arbitrary_point(u, v) == Point3D(2*u - v, u + 2*v, 5*v) | |
| assert pl7.distance(Point3D(1, 3, 5)) == 5*sqrt(6)/6 | |
| assert pl6.distance(Point3D(0, 0, 0)) == 4*sqrt(3) | |
| assert pl6.distance(pl6.p1) == 0 | |
| assert pl7.distance(pl6) == 0 | |
| assert pl7.distance(l1) == 0 | |
| assert pl6.distance(Segment3D(Point3D(2, 3, 1), Point3D(1, 3, 4))) == \ | |
| pl6.distance(Point3D(1, 3, 4)) == 4*sqrt(3)/3 | |
| assert pl6.distance(Segment3D(Point3D(1, 3, 4), Point3D(0, 3, 7))) == \ | |
| pl6.distance(Point3D(0, 3, 7)) == 2*sqrt(3)/3 | |
| assert pl6.distance(Segment3D(Point3D(0, 3, 7), Point3D(-1, 3, 10))) == 0 | |
| assert pl6.distance(Segment3D(Point3D(-1, 3, 10), Point3D(-2, 3, 13))) == 0 | |
| assert pl6.distance(Segment3D(Point3D(-2, 3, 13), Point3D(-3, 3, 16))) == \ | |
| pl6.distance(Point3D(-2, 3, 13)) == 2*sqrt(3)/3 | |
| assert pl6.distance(Plane(Point3D(5, 5, 5), normal_vector=(8, 8, 8))) == sqrt(3) | |
| assert pl6.distance(Ray3D(Point3D(1, 3, 4), direction_ratio=[1, 0, -3])) == 4*sqrt(3)/3 | |
| assert pl6.distance(Ray3D(Point3D(2, 3, 1), direction_ratio=[-1, 0, 3])) == 0 | |
| assert pl6.angle_between(pl3) == pi/2 | |
| assert pl6.angle_between(pl6) == 0 | |
| assert pl6.angle_between(pl4) == 0 | |
| assert pl7.angle_between(Line3D(Point3D(2, 3, 5), Point3D(2, 4, 6))) == \ | |
| -asin(sqrt(3)/6) | |
| assert pl6.angle_between(Ray3D(Point3D(2, 4, 1), Point3D(6, 5, 3))) == \ | |
| asin(sqrt(7)/3) | |
| assert pl7.angle_between(Segment3D(Point3D(5, 6, 1), Point3D(1, 2, 4))) == \ | |
| asin(7*sqrt(246)/246) | |
| assert are_coplanar(l1, l2, l3) is False | |
| assert are_coplanar(l1) is False | |
| assert are_coplanar(Point3D(2, 7, 2), Point3D(0, 0, 2), | |
| Point3D(1, 1, 2), Point3D(1, 2, 2)) | |
| assert are_coplanar(Plane(p1, p2, p3), Plane(p1, p3, p2)) | |
| assert Plane.are_concurrent(pl3, pl4, pl5) is False | |
| assert Plane.are_concurrent(pl6) is False | |
| raises(ValueError, lambda: Plane.are_concurrent(Point3D(0, 0, 0))) | |
| raises(ValueError, lambda: Plane((1, 2, 3), normal_vector=(0, 0, 0))) | |
| assert pl3.parallel_plane(Point3D(1, 2, 5)) == Plane(Point3D(1, 2, 5), \ | |
| normal_vector=(1, -2, 1)) | |
| # perpendicular_plane | |
| p = Plane((0, 0, 0), (1, 0, 0)) | |
| # default | |
| assert p.perpendicular_plane() == Plane(Point3D(0, 0, 0), (0, 1, 0)) | |
| # 1 pt | |
| assert p.perpendicular_plane(Point3D(1, 0, 1)) == \ | |
| Plane(Point3D(1, 0, 1), (0, 1, 0)) | |
| # pts as tuples | |
| assert p.perpendicular_plane((1, 0, 1), (1, 1, 1)) == \ | |
| Plane(Point3D(1, 0, 1), (0, 0, -1)) | |
| # more than two planes | |
| raises(ValueError, lambda: p.perpendicular_plane((1, 0, 1), (1, 1, 1), (1, 1, 0))) | |
| a, b = Point3D(0, 0, 0), Point3D(0, 1, 0) | |
| Z = (0, 0, 1) | |
| p = Plane(a, normal_vector=Z) | |
| # case 4 | |
| assert p.perpendicular_plane(a, b) == Plane(a, (1, 0, 0)) | |
| n = Point3D(*Z) | |
| # case 1 | |
| assert p.perpendicular_plane(a, n) == Plane(a, (-1, 0, 0)) | |
| # case 2 | |
| assert Plane(a, normal_vector=b.args).perpendicular_plane(a, a + b) == \ | |
| Plane(Point3D(0, 0, 0), (1, 0, 0)) | |
| # case 1&3 | |
| assert Plane(b, normal_vector=Z).perpendicular_plane(b, b + n) == \ | |
| Plane(Point3D(0, 1, 0), (-1, 0, 0)) | |
| # case 2&3 | |
| assert Plane(b, normal_vector=b.args).perpendicular_plane(n, n + b) == \ | |
| Plane(Point3D(0, 0, 1), (1, 0, 0)) | |
| p = Plane(a, normal_vector=(0, 0, 1)) | |
| assert p.perpendicular_plane() == Plane(a, normal_vector=(1, 0, 0)) | |
| assert pl6.intersection(pl6) == [pl6] | |
| assert pl4.intersection(pl4.p1) == [pl4.p1] | |
| assert pl3.intersection(pl6) == [ | |
| Line3D(Point3D(8, 4, 0), Point3D(2, 4, 6))] | |
| assert pl3.intersection(Line3D(Point3D(1,2,4), Point3D(4,4,2))) == [ | |
| Point3D(2, Rational(8, 3), Rational(10, 3))] | |
| assert pl3.intersection(Plane(Point3D(6, 0, 0), normal_vector=(2, -5, 3)) | |
| ) == [Line3D(Point3D(-24, -12, 0), Point3D(-25, -13, -1))] | |
| assert pl6.intersection(Ray3D(Point3D(2, 3, 1), Point3D(1, 3, 4))) == [ | |
| Point3D(-1, 3, 10)] | |
| assert pl6.intersection(Segment3D(Point3D(2, 3, 1), Point3D(1, 3, 4))) == [] | |
| assert pl7.intersection(Line(Point(2, 3), Point(4, 2))) == [ | |
| Point3D(Rational(13, 2), Rational(3, 4), 0)] | |
| r = Ray(Point(2, 3), Point(4, 2)) | |
| assert Plane((1,2,0), normal_vector=(0,0,1)).intersection(r) == [ | |
| Ray3D(Point(2, 3), Point(4, 2))] | |
| assert pl9.intersection(pl8) == [Line3D(Point3D(0, 0, 0), Point3D(12, 0, 0))] | |
| assert pl10.intersection(pl11) == [Line3D(Point3D(0, 0, 1), Point3D(0, 2, 1))] | |
| assert pl4.intersection(pl8) == [Line3D(Point3D(0, 0, 0), Point3D(1, -1, 0))] | |
| assert pl11.intersection(pl8) == [] | |
| assert pl9.intersection(pl11) == [Line3D(Point3D(0, 0, 1), Point3D(12, 0, 1))] | |
| assert pl9.intersection(pl4) == [Line3D(Point3D(0, 0, 0), Point3D(12, 0, -12))] | |
| assert pl3.random_point() in pl3 | |
| assert pl3.random_point(seed=1) in pl3 | |
| # test geometrical entity using equals | |
| assert pl4.intersection(pl4.p1)[0].equals(pl4.p1) | |
| assert pl3.intersection(pl6)[0].equals(Line3D(Point3D(8, 4, 0), Point3D(2, 4, 6))) | |
| pl8 = Plane((1, 2, 0), normal_vector=(0, 0, 1)) | |
| assert pl8.intersection(Line3D(p1, (1, 12, 0)))[0].equals(Line((0, 0, 0), (0.1, 1.2, 0))) | |
| assert pl8.intersection(Ray3D(p1, (1, 12, 0)))[0].equals(Ray((0, 0, 0), (1, 12, 0))) | |
| assert pl8.intersection(Segment3D(p1, (21, 1, 0)))[0].equals(Segment3D(p1, (21, 1, 0))) | |
| assert pl8.intersection(Plane(p1, normal_vector=(0, 0, 112)))[0].equals(pl8) | |
| assert pl8.intersection(Plane(p1, normal_vector=(0, 12, 0)))[0].equals( | |
| Line3D(p1, direction_ratio=(112 * pi, 0, 0))) | |
| assert pl8.intersection(Plane(p1, normal_vector=(11, 0, 1)))[0].equals( | |
| Line3D(p1, direction_ratio=(0, -11, 0))) | |
| assert pl8.intersection(Plane(p1, normal_vector=(1, 0, 11)))[0].equals( | |
| Line3D(p1, direction_ratio=(0, 11, 0))) | |
| assert pl8.intersection(Plane(p1, normal_vector=(-1, -1, -11)))[0].equals( | |
| Line3D(p1, direction_ratio=(1, -1, 0))) | |
| assert pl3.random_point() in pl3 | |
| assert len(pl8.intersection(Ray3D(Point3D(0, 2, 3), Point3D(1, 0, 3)))) == 0 | |
| # check if two plane are equals | |
| assert pl6.intersection(pl6)[0].equals(pl6) | |
| assert pl8.equals(Plane(p1, normal_vector=(0, 12, 0))) is False | |
| assert pl8.equals(pl8) | |
| assert pl8.equals(Plane(p1, normal_vector=(0, 0, -12))) | |
| assert pl8.equals(Plane(p1, normal_vector=(0, 0, -12*sqrt(3)))) | |
| assert pl8.equals(p1) is False | |
| # issue 8570 | |
| l2 = Line3D(Point3D(Rational(50000004459633, 5000000000000), | |
| Rational(-891926590718643, 1000000000000000), | |
| Rational(231800966893633, 100000000000000)), | |
| Point3D(Rational(50000004459633, 50000000000000), | |
| Rational(-222981647679771, 250000000000000), | |
| Rational(231800966893633, 100000000000000))) | |
| p2 = Plane(Point3D(Rational(402775636372767, 100000000000000), | |
| Rational(-97224357654973, 100000000000000), | |
| Rational(216793600814789, 100000000000000)), | |
| (-S('9.00000087501922'), -S('4.81170658872543e-13'), | |
| S('0.0'))) | |
| assert str([i.n(2) for i in p2.intersection(l2)]) == \ | |
| '[Point3D(4.0, -0.89, 2.3)]' | |
| def test_dimension_normalization(): | |
| A = Plane(Point3D(1, 1, 2), normal_vector=(1, 1, 1)) | |
| b = Point(1, 1) | |
| assert A.projection(b) == Point(Rational(5, 3), Rational(5, 3), Rational(2, 3)) | |
| a, b = Point(0, 0), Point3D(0, 1) | |
| Z = (0, 0, 1) | |
| p = Plane(a, normal_vector=Z) | |
| assert p.perpendicular_plane(a, b) == Plane(Point3D(0, 0, 0), (1, 0, 0)) | |
| assert Plane((1, 2, 1), (2, 1, 0), (3, 1, 2) | |
| ).intersection((2, 1)) == [Point(2, 1, 0)] | |
| def test_parameter_value(): | |
| t, u, v = symbols("t, u v") | |
| p1, p2, p3 = Point(0, 0, 0), Point(0, 0, 1), Point(0, 1, 0) | |
| p = Plane(p1, p2, p3) | |
| assert p.parameter_value((0, -3, 2), t) == {t: asin(2*sqrt(13)/13)} | |
| assert p.parameter_value((0, -3, 2), u, v) == {u: 3, v: 2} | |
| assert p.parameter_value(p1, t) == p1 | |
| raises(ValueError, lambda: p.parameter_value((1, 0, 0), t)) | |
| raises(ValueError, lambda: p.parameter_value(Line(Point(0, 0), Point(1, 1)), t)) | |
| raises(ValueError, lambda: p.parameter_value((0, -3, 2), t, 1)) | |