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| from sympy.core.numbers import Rational | |
| from sympy.core.singleton import S | |
| from sympy.geometry import Circle, Line, Point, Polygon, Segment | |
| from sympy.sets import FiniteSet, Union, Intersection, EmptySet | |
| def test_booleans(): | |
| """ test basic unions and intersections """ | |
| half = S.Half | |
| p1, p2, p3, p4 = map(Point, [(0, 0), (1, 0), (5, 1), (0, 1)]) | |
| p5, p6, p7 = map(Point, [(3, 2), (1, -1), (0, 2)]) | |
| l1 = Line(Point(0,0), Point(1,1)) | |
| l2 = Line(Point(half, half), Point(5,5)) | |
| l3 = Line(p2, p3) | |
| l4 = Line(p3, p4) | |
| poly1 = Polygon(p1, p2, p3, p4) | |
| poly2 = Polygon(p5, p6, p7) | |
| poly3 = Polygon(p1, p2, p5) | |
| assert Union(l1, l2).equals(l1) | |
| assert Intersection(l1, l2).equals(l1) | |
| assert Intersection(l1, l4) == FiniteSet(Point(1,1)) | |
| assert Intersection(Union(l1, l4), l3) == FiniteSet(Point(Rational(-1, 3), Rational(-1, 3)), Point(5, 1)) | |
| assert Intersection(l1, FiniteSet(Point(7,-7))) == EmptySet | |
| assert Intersection(Circle(Point(0,0), 3), Line(p1,p2)) == FiniteSet(Point(-3,0), Point(3,0)) | |
| assert Intersection(l1, FiniteSet(p1)) == FiniteSet(p1) | |
| assert Union(l1, FiniteSet(p1)) == l1 | |
| fs = FiniteSet(Point(Rational(1, 3), 1), Point(Rational(2, 3), 0), Point(Rational(9, 5), Rational(1, 5)), Point(Rational(7, 3), 1)) | |
| # test the intersection of polygons | |
| assert Intersection(poly1, poly2) == fs | |
| # make sure if we union polygons with subsets, the subsets go away | |
| assert Union(poly1, poly2, fs) == Union(poly1, poly2) | |
| # make sure that if we union with a FiniteSet that isn't a subset, | |
| # that the points in the intersection stop being listed | |
| assert Union(poly1, FiniteSet(Point(0,0), Point(3,5))) == Union(poly1, FiniteSet(Point(3,5))) | |
| # intersect two polygons that share an edge | |
| assert Intersection(poly1, poly3) == Union(FiniteSet(Point(Rational(3, 2), 1), Point(2, 1)), Segment(Point(0, 0), Point(1, 0))) | |