def test_contains(): p1 = Point(0, 0) r = Ray(p1, Point(4, 4)) r1 = Ray3D(p1, Point3D(0, 0, -1)) r2 = Ray3D(p1, Point3D(0, 1, 0)) r3 = Ray3D(p1, Point3D(0, 0, 1)) l = Line(Point(0, 1), Point(3, 4)) # Segment contains assert Point(0, (a + b) / 2) in Segment((0, a), (0, b)) assert Point((a + b) / 2, 0) in Segment((a, 0), (b, 0)) assert Point3D(0, 1, 0) in Segment3D((0, 1, 0), (0, 1, 0)) assert Point3D(1, 0, 0) in Segment3D((1, 0, 0), (1, 0, 0)) assert Segment3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).contains([]) is True assert Segment3D(Point3D(0, 0, 0), Point3D(1, 0, 0)).contains( Segment3D(Point3D(2, 2, 2), Point3D(3, 2, 2))) is False # Line contains assert l.contains(Point(0, 1)) is True assert l.contains((0, 1)) is True assert l.contains((0, 0)) is False # Ray contains assert r.contains(p1) is True assert r.contains((1, 1)) is True assert r.contains((1, 3)) is False assert r.contains(Segment((1, 1), (2, 2))) is True assert r.contains(Segment((1, 2), (2, 5))) is False assert r.contains(Ray((2, 2), (3, 3))) is True assert r.contains(Ray((2, 2), (3, 5))) is False assert r1.contains(Segment3D(p1, Point3D(0, 0, -10))) is True assert r1.contains(Segment3D(Point3D(1, 1, 1), Point3D(2, 2, 2))) is False assert r2.contains(Point3D(0, 0, 0)) is True assert r3.contains(Point3D(0, 0, 0)) is True assert Ray3D(Point3D(1, 1, 1), Point3D(1, 0, 0)).contains([]) is False assert Line3D((0, 0, 0), (x, y, z)).contains((2 * x, 2 * y, 2 * z)) with warnings.catch_warnings(record=True) as w: assert Line3D(p1, Point3D(0, 1, 0)).contains(Point(1.0, 1.0)) is False assert len(w) == 1 with warnings.catch_warnings(record=True) as w: assert r3.contains(Point(1.0, 1.0)) is False assert len(w) == 1
def test_line_geom(): x = Symbol('x', real=True) y = Symbol('y', real=True) x1 = Symbol('x1', real=True) y1 = Symbol('y1', real=True) half = Rational(1, 2) p1 = Point(0, 0) p2 = Point(1, 1) p3 = Point(x1, x1) p4 = Point(y1, y1) p5 = Point(x1, 1 + x1) p6 = Point(1, 0) p7 = Point(0, 1) p8 = Point(2, 0) p9 = Point(2, 1) l1 = Line(p1, p2) l2 = Line(p3, p4) l3 = Line(p3, p5) l4 = Line(p1, p6) l5 = Line(p1, p7) l6 = Line(p8, p9) l7 = Line(p2, p9) raises(ValueError, lambda: Line(Point(0, 0), Point(0, 0))) # Basic stuff assert Line((1, 1), slope=1) == Line((1, 1), (2, 2)) assert Line((1, 1), slope=oo) == Line((1, 1), (1, 2)) assert Line((1, 1), slope=-oo) == Line((1, 1), (1, 2)) raises(TypeError, lambda: Line((1, 1), 1)) assert Line(p1, p2) == Line(p1, p2) assert Line(p1, p2) != Line(p2, p1) assert l1 != l2 assert l1 != l3 assert l1.slope == 1 assert l1.length == oo assert l3.slope == oo assert l4.slope == 0 assert l4.coefficients == (0, 1, 0) assert l4.equation(x=x, y=y) == y assert l5.slope == oo assert l5.coefficients == (1, 0, 0) assert l5.equation() == x assert l6.equation() == x - 2 assert l7.equation() == y - 1 assert p1 in l1 # is p1 on the line l1? assert p1 not in l3 assert Line((-x, x), (-x + 1, x - 1)).coefficients == (1, 1, 0) assert simplify(l1.equation()) in (x - y, y - x) assert simplify(l3.equation()) in (x - x1, x1 - x) assert Line(p1, p2).scale(2, 1) == Line(p1, p9) assert l2.arbitrary_point() in l2 for ind in range(0, 5): assert l3.random_point() in l3 # Orthogonality p1_1 = Point(-x1, x1) l1_1 = Line(p1, p1_1) assert l1.perpendicular_line(p1.args).equals( Line(Point(0, 0), Point(1, -1))) assert l1.perpendicular_line(p1).equals(Line(Point(0, 0), Point(1, -1))) assert Line.is_perpendicular(l1, l1_1) assert Line.is_perpendicular(l1, l2) is False p = l1.random_point() assert l1.perpendicular_segment(p) == p # Parallelity l2_1 = Line(p3, p5) assert l2.parallel_line(p1_1).equals( Line(Point(-x1, x1), Point(-y1, 2 * x1 - y1))) assert l2_1.parallel_line(p1.args).equals(Line(Point(0, 0), Point(0, -1))) assert l2_1.parallel_line(p1).equals(Line(Point(0, 0), Point(0, -1))) assert Line.is_parallel(l1, l2) assert Line.is_parallel(l2, l3) is False assert Line.is_parallel(l2, l2.parallel_line(p1_1)) assert Line.is_parallel(l2_1, l2_1.parallel_line(p1)) # Intersection assert intersection(l1, p1) == [p1] assert intersection(l1, p5) == [] assert intersection(l1, l2) in [[l1], [l2]] assert intersection(l1, l1.parallel_line(p5)) == [] # Concurrency l3_1 = Line(Point(5, x1), Point(-Rational(3, 5), x1)) assert Line.are_concurrent(l1) is False assert Line.are_concurrent(l1, l3) assert Line.are_concurrent(l1, l1, l1, l3) assert Line.are_concurrent(l1, l3, l3_1) assert Line.are_concurrent(l1, l1_1, l3) is False # Projection assert l2.projection(p4) == p4 assert l1.projection(p1_1) == p1 assert l3.projection(p2) == Point(x1, 1) raises( GeometryError, lambda: Line(Point(0, 0), Point(1, 0)).projection( Circle(Point(0, 0), 1))) # Finding angles l1_1 = Line(p1, Point(5, 0)) assert feq(Line.angle_between(l1, l1_1).evalf(), pi.evalf() / 4) a = Point(1, 2, 3, 4) b = a.orthogonal_direction o = a.origin assert Line(a, o).angle_between(Line(b, o)) == pi / 2 # Testing Rays and Segments (very similar to Lines) assert Ray((1, 1), angle=pi / 4) == Ray((1, 1), (2, 2)) assert Ray((1, 1), angle=pi / 2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=-pi / 2) == Ray((1, 1), (1, 0)) assert Ray((1, 1), angle=-3 * pi / 2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=5 * pi / 2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=5.0 * pi / 2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=pi) == Ray((1, 1), (0, 1)) assert Ray((1, 1), angle=3.0 * pi) == Ray((1, 1), (0, 1)) assert Ray((1, 1), angle=4.0 * pi) == Ray((1, 1), (2, 1)) assert Ray((1, 1), angle=0) == Ray((1, 1), (2, 1)) assert Ray((1, 1), angle=4.05 * pi) == Ray( Point(1, 1), Point( 2, -sqrt(5) * sqrt(2 * sqrt(5) + 10) / 4 - sqrt(2 * sqrt(5) + 10) / 4 + 2 + sqrt(5))) assert Ray((1, 1), angle=4.02 * pi) == Ray(Point(1, 1), Point(2, 1 + tan(4.02 * pi))) assert Ray((1, 1), angle=5) == Ray((1, 1), (2, 1 + tan(5))) raises(TypeError, lambda: Ray((1, 1), 1)) # issue 7963 r = Ray((0, 0), angle=x) assert r.subs(x, 3 * pi / 4) == Ray((0, 0), (-1, 1)) assert r.subs(x, 5 * pi / 4) == Ray((0, 0), (-1, -1)) assert r.subs(x, -pi / 4) == Ray((0, 0), (1, -1)) assert r.subs(x, pi / 2) == Ray((0, 0), (0, 1)) assert r.subs(x, -pi / 2) == Ray((0, 0), (0, -1)) r1 = Ray(p1, Point(-1, 5)) r2 = Ray(p1, Point(-1, 1)) r3 = Ray(p3, p5) r4 = Ray(p1, p2) r5 = Ray(p2, p1) r6 = Ray(Point(0, 1), Point(1, 2)) r7 = Ray(Point(0.5, 0.5), Point(1, 1)) assert l1.projection(r1) == Ray(Point(0, 0), Point(2, 2)) assert l1.projection(r2) == p1 assert r3 != r1 t = Symbol('t', real=True) assert Ray((1, 1), angle=pi/4).arbitrary_point() == \ Point(t + 1, t + 1) r8 = Ray(Point(0, 0), Point(0, 4)) r9 = Ray(Point(0, 1), Point(0, -1)) assert r8.intersection(r9) == [Segment(Point(0, 0), Point(0, 1))] s1 = Segment(p1, p2) s2 = Segment(p1, p1_1) assert s1.midpoint == Point(Rational(1, 2), Rational(1, 2)) assert s2.length == sqrt(2 * (x1**2)) assert Segment((1, 1), (2, 3)).arbitrary_point() == Point(1 + t, 1 + 2 * t) aline = Line(Point(1 / 2, 1 / 2), Point(3 / 2, -1 / 2)) assert s1.perpendicular_bisector().equals(aline) on_line = Segment(Point(1 / 2, 1 / 2), Point(3 / 2, -1 / 2)).midpoint assert s1.perpendicular_bisector(on_line) == Segment(s1.midpoint, on_line) assert s1.perpendicular_bisector(on_line + (1, 0)).equals(aline) # intersections assert s1.intersection(Line(p6, p9)) == [] s3 = Segment(Point(0.25, 0.25), Point(0.5, 0.5)) assert s1.intersection(s3) == [s3] assert s3.intersection(s1) == [s3] assert r4.intersection(s3) == [s3] assert r4.intersection(Segment(Point(2, 3), Point(3, 4))) == [] assert r4.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == \ [Segment(p1, Point(0.5, 0.5))] s3 = Segment(Point(1, 1), Point(2, 2)) assert s1.intersection(s3) == [Point(1, 1)] s3 = Segment(Point(0.5, 0.5), Point(1.5, 1.5)) assert s1.intersection(s3) == [Segment(Point(0.5, 0.5), p2)] assert s1.intersection(Segment(Point(4, 4), Point(5, 5))) == [] assert s1.intersection(Segment(Point(-1, -1), p1)) == [p1] assert s1.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == \ [Segment(p1, Point(0.5, 0.5))] assert r4.intersection(r5) == [s1] assert r5.intersection(r6) == [] assert r4.intersection(r7) == r7.intersection(r4) == [r7] # Segment contains a, b = symbols('a,b', real=True) s = Segment((0, a), (0, b)) assert Point(0, (a + b) / 2) in s s = Segment((a, 0), (b, 0)) assert Point((a + b) / 2, 0) in s raises(Undecidable, lambda: Point(2 * a, 0) in s) # Testing distance from a Segment to an object s1 = Segment(Point(0, 0), Point(1, 1)) s2 = Segment(Point(half, half), Point(1, 0)) pt1 = Point(0, 0) pt2 = Point(Rational(3) / 2, Rational(3) / 2) assert s1.distance(pt1) == 0 assert s1.distance((0, 0)) == 0 assert s2.distance(pt1) == 2**(half) / 2 assert s2.distance(pt2) == 2**(half) # Line to point p1, p2 = Point(0, 0), Point(1, 1) s = Line(p1, p2) assert s.distance(Point(-1, 1)) == sqrt(2) assert s.distance(Point(1, -1)) == sqrt(2) assert s.distance(Point(2, 2)) == 0 assert s.distance((-1, 1)) == sqrt(2) assert Line((0, 0), (0, 1)).distance(p1) == 0 assert Line((0, 0), (0, 1)).distance(p2) == 1 assert Line((0, 0), (1, 0)).distance(p1) == 0 assert Line((0, 0), (1, 0)).distance(p2) == 1 m = symbols('m', real=True) l = Line((0, 5), slope=m) p = Point(2, 3) assert (l.distance(p) - 2 * abs(m + 1) / sqrt(m**2 + 1)).equals(0) # Ray to point r = Ray(p1, p2) assert r.distance(Point(-1, -1)) == sqrt(2) assert r.distance(Point(1, 1)) == 0 assert r.distance(Point(-1, 1)) == sqrt(2) assert Ray((1, 1), (2, 2)).distance(Point(1.5, 3)) == 3 * sqrt(2) / 4 assert r.distance((1, 1)) == 0 #Line contains p1, p2 = Point(0, 1), Point(3, 4) l = Line(p1, p2) assert l.contains(p1) is True assert l.contains((0, 1)) is True assert l.contains((0, 0)) is False #Ray contains p1, p2 = Point(0, 0), Point(4, 4) r = Ray(p1, p2) assert r.contains(p1) is True assert r.contains((1, 1)) is True assert r.contains((1, 3)) is False s = Segment((1, 1), (2, 2)) assert r.contains(s) is True s = Segment((1, 2), (2, 5)) assert r.contains(s) is False r1 = Ray((2, 2), (3, 3)) assert r.contains(r1) is True r1 = Ray((2, 2), (3, 5)) assert r.contains(r1) is False # Special cases of projection and intersection r1 = Ray(Point(1, 1), Point(2, 2)) r2 = Ray(Point(2, 2), Point(0, 0)) r3 = Ray(Point(1, 1), Point(-1, -1)) r4 = Ray(Point(0, 4), Point(-1, -5)) r5 = Ray(Point(2, 2), Point(3, 3)) assert intersection(r1, r2) == [Segment(Point(1, 1), Point(2, 2))] assert intersection(r1, r3) == [Point(1, 1)] assert r1.projection(r3) == Point(1, 1) assert r1.projection(r4) == Segment(Point(1, 1), Point(2, 2)) r5 = Ray(Point(0, 0), Point(0, 1)) r6 = Ray(Point(0, 0), Point(0, 2)) assert r5 in r6 assert r6 in r5 s1 = Segment(Point(0, 0), Point(2, 2)) s2 = Segment(Point(-1, 5), Point(-5, -10)) s3 = Segment(Point(0, 4), Point(-2, 2)) assert intersection(r1, s1) == [Segment(Point(1, 1), Point(2, 2))] assert r1.projection(s2) == Segment(Point(1, 1), Point(2, 2)) assert s3.projection(r1) == Segment(Point(0, 4), Point(-1, 3)) l1 = Line(Point(0, 0), Point(3, 4)) r1 = Ray(Point(0, 0), Point(3, 4)) s1 = Segment(Point(0, 0), Point(3, 4)) assert intersection(l1, l1) == [l1] assert intersection(l1, r1) == [r1] assert intersection(l1, s1) == [s1] assert intersection(r1, l1) == [r1] assert intersection(s1, l1) == [s1] entity1 = Segment(Point(-10, 10), Point(10, 10)) entity2 = Segment(Point(-5, -5), Point(-5, 5)) assert intersection(entity1, entity2) == [] r1 = Ray(p1, Point(0, 1)) r2 = Ray(Point(0, 1), p1) r3 = Ray(p1, p2) r4 = Ray(p2, p1) s1 = Segment(p1, Point(0, 1)) assert Line(r1.source, r1.random_point()).slope == r1.slope assert Line(r2.source, r2.random_point()).slope == r2.slope assert Segment(Point(0, -1), s1.random_point()).slope == s1.slope p_r3 = r3.random_point() p_r4 = r4.random_point() assert p_r3.x >= p1.x and p_r3.y >= p1.y assert p_r4.x <= p2.x and p_r4.y <= p2.y p10 = Point(2000, 2000) s1 = Segment(p1, p10) p_s1 = s1.random_point() assert p1.x <= p_s1.x and p_s1.x <= p10.x and \ p1.y <= p_s1.y and p_s1.y <= p10.y s2 = Segment(p10, p1) assert hash(s1) == hash(s2) p11 = p10.scale(2, 2) assert s1.is_similar(Segment(p10, p11)) assert s1.is_similar(r1) is False assert (r1 in s1) is False assert Segment(p1, p2) in s1 assert s1.plot_interval() == [t, 0, 1] assert s1 in Line(p1, p10) assert Line(p1, p10) != Line(p10, p1) assert Line(p1, p10) != p1 assert Line(p1, p10).plot_interval() == [t, -5, 5] assert Ray((0, 0), angle=pi/4).plot_interval() == \ [t, 0, 10]
def test_line_geom(): x = Symbol('x', real=True) y = Symbol('y', real=True) x1 = Symbol('x1', real=True) y1 = Symbol('y1', real=True) half = Rational(1, 2) p1 = Point(0, 0) p2 = Point(1, 1) p3 = Point(x1, x1) p4 = Point(y1, y1) p5 = Point(x1, 1 + x1) p6 = Point(1, 0) p7 = Point(0, 1) p8 = Point(2, 0) p9 = Point(2, 1) l1 = Line(p1, p2) l2 = Line(p3, p4) l3 = Line(p3, p5) l4 = Line(p1, p6) l5 = Line(p1, p7) l6 = Line(p8, p9) l7 = Line(p2, p9) raises(ValueError, lambda: Line(Point(0, 0), Point(0, 0))) # Basic stuff assert Line((1, 1), slope=1) == Line((1, 1), (2, 2)) assert Line((1, 1), slope=oo) == Line((1, 1), (1, 2)) assert Line((1, 1), slope=-oo) == Line((1, 1), (1, 2)) raises(ValueError, lambda: Line((1, 1), 1)) assert Line(p1, p2) == Line(p1, p2) assert Line(p1, p2) != Line(p2, p1) assert l1 != l2 assert l1 != l3 assert l1.slope == 1 assert l1.length == oo assert l3.slope == oo assert l4.slope == 0 assert l4.coefficients == (0, 1, 0) assert l4.equation(x=x, y=y) == y assert l5.slope == oo assert l5.coefficients == (1, 0, 0) assert l5.equation() == x assert l6.equation() == x - 2 assert l7.equation() == y - 1 assert p1 in l1 # is p1 on the line l1? assert p1 not in l3 assert Line((-x, x), (-x + 1, x - 1)).coefficients == (1, 1, 0) assert simplify(l1.equation()) in (x - y, y - x) assert simplify(l3.equation()) in (x - x1, x1 - x) assert Line(p1, p2).scale(2, 1) == Line(p1, p9) assert l2.arbitrary_point() in l2 for ind in range(0, 5): assert l3.random_point() in l3 # Orthogonality p1_1 = Point(-x1, x1) l1_1 = Line(p1, p1_1) assert l1.perpendicular_line(p1.args) == Line(Point(0, 0), Point(1, -1)) assert l1.perpendicular_line(p1) == Line(Point(0, 0), Point(1, -1)) assert Line.is_perpendicular(l1, l1_1) assert Line.is_perpendicular(l1, l2) is False p = l1.random_point() assert l1.perpendicular_segment(p) == p # Parallelity l2_1 = Line(p3, p5) assert l2.parallel_line(p1_1) == Line(Point(-x1, x1), Point(-y1, 2*x1 - y1)) assert l2_1.parallel_line(p1.args) == Line(Point(0, 0), Point(0, -1)) assert l2_1.parallel_line(p1) == Line(Point(0, 0), Point(0, -1)) assert Line.is_parallel(l1, l2) assert Line.is_parallel(l2, l3) is False assert Line.is_parallel(l2, l2.parallel_line(p1_1)) assert Line.is_parallel(l2_1, l2_1.parallel_line(p1)) # Intersection assert intersection(l1, p1) == [p1] assert intersection(l1, p5) == [] assert intersection(l1, l2) in [[l1], [l2]] assert intersection(l1, l1.parallel_line(p5)) == [] # Concurrency l3_1 = Line(Point(5, x1), Point(-Rational(3, 5), x1)) assert Line.are_concurrent(l1) is False assert Line.are_concurrent(l1, l3) assert Line.are_concurrent(l1, l1, l1, l3) assert Line.are_concurrent(l1, l3, l3_1) assert Line.are_concurrent(l1, l1_1, l3) is False # Projection assert l2.projection(p4) == p4 assert l1.projection(p1_1) == p1 assert l3.projection(p2) == Point(x1, 1) raises(GeometryError, lambda: Line(Point(0, 0), Point(1, 0)) .projection(Circle(Point(0, 0), 1))) # Finding angles l1_1 = Line(p1, Point(5, 0)) assert feq(Line.angle_between(l1, l1_1).evalf(), pi.evalf()/4) # Testing Rays and Segments (very similar to Lines) assert Ray((1, 1), angle=pi/4) == Ray((1, 1), (2, 2)) assert Ray((1, 1), angle=pi/2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=-pi/2) == Ray((1, 1), (1, 0)) assert Ray((1, 1), angle=-3*pi/2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=5*pi/2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=5.0*pi/2) == Ray((1, 1), (1, 2)) assert Ray((1, 1), angle=pi) == Ray((1, 1), (0, 1)) assert Ray((1, 1), angle=3.0*pi) == Ray((1, 1), (0, 1)) assert Ray((1, 1), angle=4.0*pi) == Ray((1, 1), (2, 1)) assert Ray((1, 1), angle=0) == Ray((1, 1), (2, 1)) assert Ray((1, 1), angle=4.05*pi) == Ray(Point(1, 1), Point(2, -sqrt(5)*sqrt(2*sqrt(5) + 10)/4 - sqrt(2*sqrt(5) + 10)/4 + 2 + sqrt(5))) assert Ray((1, 1), angle=4.02*pi) == Ray(Point(1, 1), Point(2, 1 + tan(4.02*pi))) assert Ray((1, 1), angle=5) == Ray((1, 1), (2, 1 + tan(5))) raises(ValueError, lambda: Ray((1, 1), 1)) # issue 7963 r = Ray((0, 0), angle=x) assert r.subs(x, 3*pi/4) == Ray((0, 0), (-1, 1)) assert r.subs(x, 5*pi/4) == Ray((0, 0), (-1, -1)) assert r.subs(x, -pi/4) == Ray((0, 0), (1, -1)) assert r.subs(x, pi/2) == Ray((0, 0), (0, 1)) assert r.subs(x, -pi/2) == Ray((0, 0), (0, -1)) r1 = Ray(p1, Point(-1, 5)) r2 = Ray(p1, Point(-1, 1)) r3 = Ray(p3, p5) r4 = Ray(p1, p2) r5 = Ray(p2, p1) r6 = Ray(Point(0, 1), Point(1, 2)) r7 = Ray(Point(0.5, 0.5), Point(1, 1)) assert l1.projection(r1) == Ray(Point(0, 0), Point(2, 2)) assert l1.projection(r2) == p1 assert r3 != r1 t = Symbol('t', real=True) assert Ray((1, 1), angle=pi/4).arbitrary_point() == \ Point(t + 1, t + 1) r8 = Ray(Point(0, 0), Point(0, 4)) r9 = Ray(Point(0, 1), Point(0, -1)) assert r8.intersection(r9) == [Segment(Point(0, 0), Point(0, 1))] s1 = Segment(p1, p2) s2 = Segment(p1, p1_1) assert s1.midpoint == Point(Rational(1, 2), Rational(1, 2)) assert s2.length == sqrt( 2*(x1**2) ) assert Segment((1, 1), (2, 3)).arbitrary_point() == Point(1 + t, 1 + 2*t) assert s1.perpendicular_bisector() == \ Line(Point(1/2, 1/2), Point(3/2, -1/2)) # intersections assert s1.intersection(Line(p6, p9)) == [] s3 = Segment(Point(0.25, 0.25), Point(0.5, 0.5)) assert s1.intersection(s3) == [s1] assert s3.intersection(s1) == [s3] assert r4.intersection(s3) == [s3] assert r4.intersection(Segment(Point(2, 3), Point(3, 4))) == [] assert r4.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == \ [Segment(p1, Point(0.5, 0.5))] s3 = Segment(Point(1, 1), Point(2, 2)) assert s1.intersection(s3) == [Point(1, 1)] s3 = Segment(Point(0.5, 0.5), Point(1.5, 1.5)) assert s1.intersection(s3) == [Segment(Point(0.5, 0.5), p2)] assert s1.intersection(Segment(Point(4, 4), Point(5, 5))) == [] assert s1.intersection(Segment(Point(-1, -1), p1)) == [p1] assert s1.intersection(Segment(Point(-1, -1), Point(0.5, 0.5))) == \ [Segment(p1, Point(0.5, 0.5))] assert r4.intersection(r5) == [s1] assert r5.intersection(r6) == [] assert r4.intersection(r7) == r7.intersection(r4) == [r7] # Segment contains a, b = symbols('a,b') s = Segment((0, a), (0, b)) assert Point(0, (a + b)/2) in s s = Segment((a, 0), (b, 0)) assert Point((a + b)/2, 0) in s raises(Undecidable, lambda: Point(2*a, 0) in s) # Testing distance from a Segment to an object s1 = Segment(Point(0, 0), Point(1, 1)) s2 = Segment(Point(half, half), Point(1, 0)) pt1 = Point(0, 0) pt2 = Point(Rational(3)/2, Rational(3)/2) assert s1.distance(pt1) == 0 assert s1.distance((0, 0)) == 0 assert s2.distance(pt1) == 2**(half)/2 assert s2.distance(pt2) == 2**(half) # Line to point p1, p2 = Point(0, 0), Point(1, 1) s = Line(p1, p2) assert s.distance(Point(-1, 1)) == sqrt(2) assert s.distance(Point(1, -1)) == sqrt(2) assert s.distance(Point(2, 2)) == 0 assert s.distance((-1, 1)) == sqrt(2) assert Line((0, 0), (0, 1)).distance(p1) == 0 assert Line((0, 0), (0, 1)).distance(p2) == 1 assert Line((0, 0), (1, 0)).distance(p1) == 0 assert Line((0, 0), (1, 0)).distance(p2) == 1 m = symbols('m') l = Line((0, 5), slope=m) p = Point(2, 3) assert l.distance(p) == 2*abs(m + 1)/sqrt(m**2 + 1) # Ray to point r = Ray(p1, p2) assert r.distance(Point(-1, -1)) == sqrt(2) assert r.distance(Point(1, 1)) == 0 assert r.distance(Point(-1, 1)) == sqrt(2) assert Ray((1, 1), (2, 2)).distance(Point(1.5, 3)) == 3*sqrt(2)/4 assert r.distance((1, 1)) == 0 #Line contains p1, p2 = Point(0, 1), Point(3, 4) l = Line(p1, p2) assert l.contains(p1) is True assert l.contains((0, 1)) is True assert l.contains((0, 0)) is False #Ray contains p1, p2 = Point(0, 0), Point(4, 4) r = Ray(p1, p2) assert r.contains(p1) is True assert r.contains((1, 1)) is True assert r.contains((1, 3)) is False s = Segment((1, 1), (2, 2)) assert r.contains(s) is True s = Segment((1, 2), (2, 5)) assert r.contains(s) is False r1 = Ray((2, 2), (3, 3)) assert r.contains(r1) is True r1 = Ray((2, 2), (3, 5)) assert r.contains(r1) is False # Special cases of projection and intersection r1 = Ray(Point(1, 1), Point(2, 2)) r2 = Ray(Point(2, 2), Point(0, 0)) r3 = Ray(Point(1, 1), Point(-1, -1)) r4 = Ray(Point(0, 4), Point(-1, -5)) r5 = Ray(Point(2, 2), Point(3, 3)) assert intersection(r1, r2) == [Segment(Point(1, 1), Point(2, 2))] assert intersection(r1, r3) == [Point(1, 1)] assert r1.projection(r3) == Point(1, 1) assert r1.projection(r4) == Segment(Point(1, 1), Point(2, 2)) r5 = Ray(Point(0, 0), Point(0, 1)) r6 = Ray(Point(0, 0), Point(0, 2)) assert r5 in r6 assert r6 in r5 s1 = Segment(Point(0, 0), Point(2, 2)) s2 = Segment(Point(-1, 5), Point(-5, -10)) s3 = Segment(Point(0, 4), Point(-2, 2)) assert intersection(r1, s1) == [Segment(Point(1, 1), Point(2, 2))] assert r1.projection(s2) == Segment(Point(1, 1), Point(2, 2)) assert s3.projection(r1) == Segment(Point(0, 4), Point(-1, 3)) l1 = Line(Point(0, 0), Point(3, 4)) r1 = Ray(Point(0, 0), Point(3, 4)) s1 = Segment(Point(0, 0), Point(3, 4)) assert intersection(l1, l1) == [l1] assert intersection(l1, r1) == [r1] assert intersection(l1, s1) == [s1] assert intersection(r1, l1) == [r1] assert intersection(s1, l1) == [s1] entity1 = Segment(Point(-10, 10), Point(10, 10)) entity2 = Segment(Point(-5, -5), Point(-5, 5)) assert intersection(entity1, entity2) == [] r1 = Ray(p1, Point(0, 1)) r2 = Ray(Point(0, 1), p1) r3 = Ray(p1, p2) r4 = Ray(p2, p1) s1 = Segment(p1, Point(0, 1)) assert Line(r1.source, r1.random_point()).slope == r1.slope assert Line(r2.source, r2.random_point()).slope == r2.slope assert Segment(Point(0, -1), s1.random_point()).slope == s1.slope p_r3 = r3.random_point() p_r4 = r4.random_point() assert p_r3.x >= p1.x and p_r3.y >= p1.y assert p_r4.x <= p2.x and p_r4.y <= p2.y p10 = Point(2000, 2000) s1 = Segment(p1, p10) p_s1 = s1.random_point() assert p1.x <= p_s1.x and p_s1.x <= p10.x and \ p1.y <= p_s1.y and p_s1.y <= p10.y s2 = Segment(p10, p1) assert hash(s1) == hash(s2) p11 = p10.scale(2, 2) assert s1.is_similar(Segment(p10, p11)) assert s1.is_similar(r1) is False assert (r1 in s1) is False assert Segment(p1, p2) in s1 assert s1.plot_interval() == [t, 0, 1] assert s1 in Line(p1, p10) assert Line(p1, p10) != Line(p10, p1) assert Line(p1, p10) != p1 assert Line(p1, p10).plot_interval() == [t, -5, 5] assert Ray((0, 0), angle=pi/4).plot_interval() == \ [t, 0, 10]