def test_distance_2d(): p1 = Point(0, 0) p2 = Point(1, 1) half = S.Half s1 = Segment(Point(0, 0), Point(1, 1)) s2 = Segment(Point(half, half), Point(1, 0)) r = Ray(p1, p2) assert s1.distance(Point(0, 0)) == 0 assert s1.distance((0, 0)) == 0 assert s2.distance(Point(0, 0)) == 2**half / 2 assert s2.distance(Point(Rational(3) / 2, Rational(3) / 2)) == 2**half assert Line(p1, p2).distance(Point(-1, 1)) == sqrt(2) assert Line(p1, p2).distance(Point(1, -1)) == sqrt(2) assert Line(p1, p2).distance(Point(2, 2)) == 0 assert Line(p1, p2).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 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
def test_distance_2d(): p1 = Point(0, 0) p2 = Point(1, 1) half = Rational(1, 2) s1 = Segment(Point(0, 0), Point(1, 1)) s2 = Segment(Point(half, half), Point(1, 0)) r = Ray(p1, p2) assert s1.distance(Point(0, 0)) == 0 assert s1.distance((0, 0)) == 0 assert s2.distance(Point(0, 0)) == 2 ** half / 2 assert s2.distance(Point(Rational(3) / 2, Rational(3) / 2)) == 2 ** half assert Line(p1, p2).distance(Point(-1, 1)) == sqrt(2) assert Line(p1, p2).distance(Point(1, -1)) == sqrt(2) assert Line(p1, p2).distance(Point(2, 2)) == 0 assert Line(p1, p2).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 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
def test_line(): 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(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) == l1_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 p2_1 = Point(-2 * x1, 0) l2_1 = Line(p3, p5) assert l2.parallel_line(p1_1) == Line(p2_1, p1_1) assert l2_1.parallel_line(p1) == Line(p1, Point(0, 2)) 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.is_concurrent(l1) is False assert Line.is_concurrent(l1, l3) assert Line.is_concurrent(l1, l3, l3_1) assert Line.is_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, 1 + C.tan(4.05 * pi))) assert Ray((1, 1), angle=5) == Ray((1, 1), (2, 1 + C.tan(5))) raises(ValueError, lambda: Ray((1, 1), 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(p1, p2) 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 s1.perpendicular_bisector() == Line(Point(0, 1), Point(1, 0)) assert Segment((1, 1), (2, 3)).arbitrary_point() == Point(1 + t, 1 + 2 * t) # 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 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 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 # 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(): 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(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) == l1_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 p2_1 = Point(-2*x1, 0) l2_1 = Line(p3, p5) assert l2.parallel_line(p1_1) == Line(p2_1, p1_1) assert l2_1.parallel_line(p1) == Line(p1, Point(0, 2)) 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.is_concurrent(l1) is False assert Line.is_concurrent(l1, l3) assert Line.is_concurrent(l1, l3, l3_1) assert Line.is_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, 1 + C.tan(4.05*pi))) assert Ray((1, 1), angle=5) == Ray((1, 1), (2, 1 + C.tan(5))) raises(ValueError, lambda: Ray((1, 1), 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(p1, p2) 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 s1.perpendicular_bisector() == Line(Point(0, 1), Point(1, 0)) assert Segment((1, 1), (2, 3)).arbitrary_point() == Point(1 + t, 1 + 2*t) # 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 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 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 # 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]