Python geometry.Segment类代码示例

def main():

    O = Point(0, 0)
    p0 = Point(0, 10.1)
    p1 = Point(1.4, -9.6)
    m = p0.midpoint(p1)
    X = Line(O, Point(10, 0))
    Y = Line(O, Point(0, 10))

    ellipse = Ellipse(Point(0, 0), 5 , 10)
    sortie = Segment(Point(-0.01, 10), Point(0.01, 10))

    ray = Ray(m, p1)

    reflections = 0
    
    while not sortie.intersection(ray) and reflections < 5:
        targets = ellipse.intersection(ray)
        print " Targets: ", targets
        origin = next_origin(ray.p1, targets)
        tangents = ellipse.tangent_lines(origin)
        if len(tangents) > 1:
            print("Error computing intersection")
            break
        tangent = tangents.pop()
        alpha = next_angle(ray, tangent, (X, Y))
        reflections += 1
        ray = Ray(origin, angle=alpha)
        print "Reflections :", reflections

def test_perpendicular_bisector():
    s1 = Segment(Point(0, 0), Point(1, 1))
    aline = Line(Point(1 / 2, 1 / 2), Point(3 / 2, -1 / 2))
    on_line = Segment(Point(1 / 2, 1 / 2), Point(3 / 2, -1 / 2)).midpoint

    assert s1.perpendicular_bisector().equals(aline)
    assert s1.perpendicular_bisector(on_line) == Segment(s1.midpoint, on_line)
    assert s1.perpendicular_bisector(on_line + (1, 0)).equals(aline)

def test_is_similar():
    p1 = Point(2000, 2000)
    p2 = p1.scale(2, 2)

    r1 = Ray3D(Point3D(1, 1, 1), Point3D(1, 0, 0))
    r2 = Ray(Point(0, 0), Point(0, 1))

    s1 = Segment(Point(0, 0), p1)

    assert s1.is_similar(Segment(p1, p2))
    assert s1.is_similar(r2) is False
    assert r1.is_similar(Line3D(Point3D(1, 1, 1), Point3D(1, 0, 0))) is True
    assert r1.is_similar(Line3D(Point3D(0, 0, 0), Point3D(0, 1, 0))) is False

def adjust_out_of_bounds_points(vert1, vert2, boundaries):
	line_seg = None
	if vert1[0] < 0 or vert1[1] < 0 or vert2[0] < 0 or vert2[1] < 0 or vert1[0] > width or vert1[1] > height or vert2[0] > width or vert2[1] > height:
		line_seg = Segment(Point(vert1), Point(vert2))

		if vert1[0] < 0: 
			intrscts = line_seg.intersection(boundaries[3])
			if len(intrscts) == 0:
				return None, None
			intrsct = intrscts[0]
			vert1 = intrsct.x, intrsct.y

		if vert1[1] < 0: 
			intrscts = line_seg.intersection(boundaries[0])
			if len(intrscts) == 0:
				return None, None
			intrsct = intrscts[0]
			vert1 = intrsct.x, intrsct.y
		if vert2[0] < 0: 
			intrscts = line_seg.intersection(boundaries[3])
			if len(intrscts) == 0:
				return None, None
			intrsct = intrscts[0]
			vert2 = intrsct.x, intrsct.y
		if vert2[1] < 0: 
			intrscts = line_seg.intersection(boundaries[0])
			if len(intrscts) == 0:
				return None, None
			intrsct = intrscts[0]
			vert2 = intrsct.x, intrsct.y
		if vert1[0] > width: 
			intrscts = line_seg.intersection(boundaries[1])
			if len(intrscts) == 0:
				return None, None
			intrsct = intrscts[0]
			vert1 = intrsct.x, intrsct.y
		if vert1[1] > height: 
			intrscts = line_seg.intersection(boundaries[2])
			if len(intrscts) == 0:
				return None, None
			intrsct = intrscts[0]
			vert1 = intrsct.x, intrsct.y
		if vert2[0] > width: 
			intrscts = line_seg.intersection(boundaries[1])
			if len(intrscts) == 0:
				return None, None
			intrsct = intrscts[0]
			vert2 = intrsct.x, intrsct.y
		if vert2[1] > height:
			intrscts = line_seg.intersection(boundaries[2])
			if len(intrscts) == 0:
				return None, None
			intrsct = intrscts[0]
			vert2 = intrsct.x, intrsct.y
	return vert1, vert2

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

#.........这里部分代码省略.........
    # 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))
    # XXX don't know why this fails without str
    assert str(Ray((1, 1), angle=4.2 * pi)) == str(Ray(Point(1, 1), Point(2, 1 + C.tan(0.2 * 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(1 / (1 - t), 1 / (1 - t))

    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

def test_line():
    p1 = Point(0, 0)
    p2 = Point(1, 1)
    p3 = Point(x1, x1)
    p4 = Point(y1, y1)
    p5 = Point(x1, 1 + x1)

    l1 = Line(p1, p2)
    l2 = Line(p3, p4)
    l3 = Line(p3, p5)

    # Basic stuff
    assert Line(p1, p2) == Line(p2, p1)
    assert l1 == l2
    assert l1 != l3
    assert l1.slope == 1
    assert l3.slope == oo
    assert p1 in l1 # is p1 on the line l1?
    assert p1 not in l3

    assert simplify(l1.equation()) in (x-y, y-x)
    assert simplify(l3.equation()) in (x-x1, x1-x)

    assert l2.arbitrary_point() in l2
    for ind in xrange(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) == False

    # 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) == 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, l3)
    assert Line.is_concurrent(l1, l3, l3_1)
    assert Line.is_concurrent(l1, l1_1, l3) == False

    # Projection
    assert l2.projection(p4) == p4
    assert l1.projection(p1_1) == p1
    assert l3.projection(p2) == Point(x1, 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)
    r1 = Ray(p1, Point(-1, 5))
    r2 = Ray(p1, Point(-1, 1))
    r3 = Ray(p3, p5)
    assert l1.projection(r1) == Ray(p1, p2)
    assert l1.projection(r2) == p1
    assert r3 != r1

    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))

    # 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)

    # 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))
    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))
#.........这里部分代码省略.........

#.........这里部分代码省略.........
    assert intersection(l1, l1.parallel_line(p5)) == []

    # Concurrency
    l3_1 = Line(Point(5, x1), Point(-Rational(3, 5), x1))
    assert Line.is_concurrent(l1, l3)
    assert Line.is_concurrent(l1, l3, l3_1)
    assert Line.is_concurrent(l1, l1_1, l3) == False

    # Projection
    assert l2.projection(p4) == p4
    assert l1.projection(p1_1) == p1
    assert l3.projection(p2) == Point(x1, 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))
    # XXX don't know why this fails without str
    assert str(Ray((1, 1), angle=4.2 * pi)) == str(Ray(Point(1, 1), Point(2, 1 + C.tan(0.2 * pi))))
    assert Ray((1, 1), angle=5) == Ray((1, 1), (2, 1 + C.tan(5)))
    raises(ValueError, "Ray((1, 1), 1)")

    r1 = Ray(p1, Point(-1, 5))
    r2 = Ray(p1, Point(-1, 1))
    r3 = Ray(p3, p5)
    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(1 / (1 - t), 1 / (1 - t))

    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)

    # 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
    assert (Point(2 * a, 0) in s) is False  # XXX should be None?

    # 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)

    # 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))
    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) == []

def test_intersection_2d():
    p1 = Point(0, 0)
    p2 = Point(1, 1)
    p3 = Point(x1, x1)
    p4 = Point(y1, y1)

    l1 = Line(p1, p2)
    l3 = Line(Point(0, 0), Point(3, 4))

    r1 = Ray(Point(1, 1), Point(2, 2))
    r2 = Ray(Point(0, 0), Point(3, 4))
    r4 = Ray(p1, p2)
    r6 = Ray(Point(0, 1), Point(1, 2))
    r7 = Ray(Point(0.5, 0.5), Point(1, 1))

    s1 = Segment(p1, p2)
    s2 = Segment(Point(0.25, 0.25), Point(0.5, 0.5))
    s3 = Segment(Point(0, 0), Point(3, 4))

    assert intersection(l1, p1) == [p1]
    assert intersection(l1, Point(x1, 1 + x1)) == []
    assert intersection(l1, Line(p3, p4)) in [[l1], [Line(p3, p4)]]
    assert intersection(l1, l1.parallel_line(Point(x1, 1 + x1))) == []
    assert intersection(l3, l3) == [l3]
    assert intersection(l3, r2) == [r2]
    assert intersection(l3, s3) == [s3]
    assert intersection(s3, l3) == [s3]
    assert intersection(Segment(Point(-10, 10), Point(10, 10)), Segment(Point(-5, -5), Point(-5, 5))) == []
    assert intersection(r2, l3) == [r2]
    assert intersection(r1, Ray(Point(2, 2), Point(0, 0))) == [Segment(Point(1, 1), Point(2, 2))]
    assert intersection(r1, Ray(Point(1, 1), Point(-1, -1))) == [Point(1, 1)]
    assert intersection(r1, Segment(Point(0, 0), Point(2, 2))) == [Segment(Point(1, 1), Point(2, 2))]

    assert r4.intersection(s2) == [s2]
    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))]
    assert r4.intersection(Ray(p2, p1)) == [s1]
    assert Ray(p2, p1).intersection(r6) == []
    assert r4.intersection(r7) == r7.intersection(r4) == [r7]
    assert Ray3D((0, 0), (3, 0)).intersection(Ray3D((1, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))]
    assert Ray3D((1, 0), (3, 0)).intersection(Ray3D((0, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))]
    assert Ray(Point(0, 0), Point(0, 4)).intersection(Ray(Point(0, 1), Point(0, -1))) == \
           [Segment(Point(0, 0), Point(0, 1))]

    assert Segment3D((0, 0), (3, 0)).intersection(
        Segment3D((1, 0), (2, 0))) == [Segment3D((1, 0), (2, 0))]
    assert Segment3D((1, 0), (2, 0)).intersection(
        Segment3D((0, 0), (3, 0))) == [Segment3D((1, 0), (2, 0))]
    assert Segment3D((0, 0), (3, 0)).intersection(
        Segment3D((3, 0), (4, 0))) == [Point3D((3, 0))]
    assert Segment3D((0, 0), (3, 0)).intersection(
        Segment3D((2, 0), (5, 0))) == [Segment3D((3, 0), (2, 0))]
    assert Segment3D((0, 0), (3, 0)).intersection(
        Segment3D((-2, 0), (1, 0))) == [Segment3D((0, 0), (1, 0))]
    assert Segment3D((0, 0), (3, 0)).intersection(
        Segment3D((-2, 0), (0, 0))) == [Point3D(0, 0)]
    assert s1.intersection(Segment(Point(1, 1), Point(2, 2))) == [Point(1, 1)]
    assert s1.intersection(Segment(Point(0.5, 0.5), Point(1.5, 1.5))) == [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 s1.intersection(Line(Point(1, 0), Point(2, 1))) == []
    assert s1.intersection(s2) == [s2]
    assert s2.intersection(s1) == [s2]

def test_contains_nonreal_symbols():
    u, v, w, z = symbols('u, v, w, z')
    l = Segment(Point(u, w), Point(v, z))
    p = Point(2*u/3 + v/3, 2*w/3 + z/3)
    assert l.contains(p)

def test_basic_properties_2d():
    p1 = Point(0, 0)
    p2 = Point(1, 1)
    p10 = Point(2000, 2000)
    p_r3 = Ray(p1, p2).random_point()
    p_r4 = Ray(p2, p1).random_point()

    l1 = Line(p1, p2)
    l3 = Line(Point(x1, x1), Point(x1, 1 + x1))
    l4 = Line(p1, Point(1, 0))

    r1 = Ray(p1, Point(0, 1))
    r2 = Ray(Point(0, 1), p1)

    s1 = Segment(p1, p10)
    p_s1 = s1.random_point()

    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))
    assert Line(p1, p2).scale(2, 1) == Line(p1, Point(2, 1))
    assert Line(p1, p2) == Line(p1, p2)
    assert Line(p1, p2) != Line(p2, p1)
    assert l1 != Line(Point(x1, x1), Point(y1, y1))
    assert l1 != l3
    assert Line(p1, p10) != Line(p10, p1)
    assert Line(p1, p10) != p1
    assert p1 in l1  # is p1 on the line l1?
    assert p1 not in l3
    assert s1 in Line(p1, p10)
    assert Ray(Point(0, 0), Point(0, 1)) in Ray(Point(0, 0), Point(0, 2))
    assert Ray(Point(0, 0), Point(0, 2)) in Ray(Point(0, 0), Point(0, 1))
    assert (r1 in s1) is False
    assert Segment(p1, p2) in s1
    assert Ray(Point(x1, x1), Point(x1, 1 + x1)) != Ray(p1, Point(-1, 5))
    assert Segment(p1, p2).midpoint == Point(Rational(1, 2), Rational(1, 2))
    assert Segment(p1, Point(-x1, x1)).length == sqrt(2 * (x1 ** 2))

    assert l1.slope == 1
    assert l3.slope == oo
    assert l4.slope == 0
    assert Line(p1, Point(0, 1)).slope == oo
    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), Segment(p1, Point(0, 1)).random_point()).slope == Segment(p1, Point(0, 1)).slope

    assert l4.coefficients == (0, 1, 0)
    assert Line((-x, x), (-x + 1, x - 1)).coefficients == (1, 1, 0)
    assert Line(p1, Point(0, 1)).coefficients == (1, 0, 0)
    # 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))

    for ind in range(0, 5):
        assert l3.random_point() in l3

    assert p_r3.x >= p1.x and p_r3.y >= p1.y
    assert p_r4.x <= p2.x and p_r4.y <= p2.y
    assert p1.x <= p_s1.x <= p10.x and p1.y <= p_s1.y <= p10.y
    assert hash(s1) == hash(Segment(p10, p1))

    assert s1.plot_interval() == [t, 0, 1]
    assert Line(p1, p10).plot_interval() == [t, -5, 5]
    assert Ray((0, 0), angle=pi / 4).plot_interval() == [t, 0, 10]

def generate_polygons(points_dict, segments, points, point_to_segment_dict):
	
	polygons = []
	segments_to_polygons = {}
	i = 1

	for p in points:
		point = Point(p)
		#draw_point(point, WHITE)
		polygon_vertices = []
		closest_segment = None
		for seg in segments:
			if closest_segment == None or abs(seg.distance(point)) < abs(closest_segment.distance(point)):
				closest_segment = seg
		
		polygon_vertices.extend(closest_segment.points)
		current_vertex = closest_segment.points[0] 
		previous_vertex = closest_segment.points[1]
		
		polygon_complete = False 
		segs = [closest_segment]
		
		while not polygon_complete:
			#time.sleep(2)
			#draw_point(current_vertex, WHITE)
			#draw_point(previous_vertex, ORANGE)

			vertex_list = points_dict[current_vertex]
			temp_seg_list = []
			#for v in vertex_list:
			#	segs = point_to_segment_dict[v]
			#	temp_seg_list.extend(segs)
			closest_vertex = None 
			best_seg = None
			#draw_segment(closest_segment, ORANGE)
			
			for vertex in vertex_list:
				if vertex != previous_vertex:
					
					temp_seg = Segment(current_vertex, vertex)
					temp_seg_mid = temp_seg.midpoint
					point_to_temp_mid = Segment(temp_seg_mid, point)
					#draw_segment(point_to_temp_mid, WHITE)
					
					relevant_segs = []
					relevant_segs.extend(segs)
					relevant_segs.extend(temp_seg_list)

					
					closest = True
					for seg in segments:
						closer_points = point_to_temp_mid.intersection(seg)
						if len(closer_points) > 0:
							if not temp_seg.distance(closer_points[0]) < 0.001:
								closest = False
								
								#draw_point(closer_points[0], BLUE)
								#draw_segment(temp_seg, BLUE)
						
					if closest:
						closest_vertex = vertex
						best_seg = temp_seg
						break

			print closest_vertex
			if closest_vertex in polygon_vertices:
				polygon_complete = True

			segs.append(best_seg)
			polygon_vertices.append(closest_vertex)
			previous_vertex = current_vertex
			current_vertex = closest_vertex

		print(str(i))
		i += 1
		#for seg in segs:
			#draw_segment(seg, WHITE)

		polygon = GraphNode(point, polygon_vertices)

		#c = polygon.centroid
		#p = (c.x, c.y)
		#pygame.draw.circle(screen, ORANGE, p, 2, 1)

		pygame.display.flip()

		polygons.append(polygon)

		for seg in segs:
			if not seg in segments_to_polygons:
				segments_to_polygons[seg] = []
			segments_to_polygons[seg].append(polygon)

	return polygons, segments_to_polygons

#.........这里部分代码省略.........
    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]

def test_intersection_2d():
    p1 = Point(0, 0)
    p2 = Point(1, 1)
    p3 = Point(x1, x1)
    p4 = Point(y1, y1)

    l1 = Line(p1, p2)
    l3 = Line(Point(0, 0), Point(3, 4))

    r1 = Ray(Point(1, 1), Point(2, 2))
    r2 = Ray(Point(0, 0), Point(3, 4))
    r4 = Ray(p1, p2)
    r6 = Ray(Point(0, 1), Point(1, 2))
    r7 = Ray(Point(0.5, 0.5), Point(1, 1))

    s1 = Segment(p1, p2)
    s2 = Segment(Point(0.25, 0.25), Point(0.5, 0.5))
    s3 = Segment(Point(0, 0), Point(3, 4))

    assert intersection(l1, p1) == [p1]
    assert intersection(l1, Point(x1, 1 + x1)) == []
    assert intersection(l1, Line(p3, p4)) in [[l1], [Line(p3, p4)]]
    assert intersection(l1, l1.parallel_line(Point(x1, 1 + x1))) == []
    assert intersection(l3, l3) == [l3]
    assert intersection(l3, r2) == [r2]
    assert intersection(l3, s3) == [s3]
    assert intersection(s3, l3) == [s3]
    assert intersection(Segment(Point(-10, 10), Point(10, 10)), Segment(Point(-5, -5), Point(-5, 5))) == []
    assert intersection(r2, l3) == [r2]
    assert intersection(r1, Ray(Point(2, 2), Point(0, 0))) == [Segment(Point(1, 1), Point(2, 2))]
    assert intersection(r1, Ray(Point(1, 1), Point(-1, -1))) == [Point(1, 1)]
    assert intersection(r1, Segment(Point(0, 0), Point(2, 2))) == [Segment(Point(1, 1), Point(2, 2))]

    assert r4.intersection(s2) == [s2]
    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))]
    assert r4.intersection(Ray(p2, p1)) == [s1]
    assert Ray(p2, p1).intersection(r6) == []
    assert r4.intersection(r7) == r7.intersection(r4) == [r7]
    assert Ray3D((0, 0), (3, 0)).intersection(Ray3D((1, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))]
    assert Ray3D((1, 0), (3, 0)).intersection(Ray3D((0, 0), (3, 0))) == [Ray3D((1, 0), (3, 0))]
    assert Ray(Point(0, 0), Point(0, 4)).intersection(Ray(Point(0, 1), Point(0, -1))) == \
           [Segment(Point(0, 0), Point(0, 1))]

    assert Segment3D((0, 0), (3, 0)).intersection(
        Segment3D((1, 0), (2, 0))) == [Segment3D((1, 0), (2, 0))]
    assert Segment3D((1, 0), (2, 0)).intersection(
        Segment3D((0, 0), (3, 0))) == [Segment3D((1, 0), (2, 0))]
    assert Segment3D((0, 0), (3, 0)).intersection(
        Segment3D((3, 0), (4, 0))) == [Point3D((3, 0))]
    assert Segment3D((0, 0), (3, 0)).intersection(
        Segment3D((2, 0), (5, 0))) == [Segment3D((2, 0), (3, 0))]
    assert Segment3D((0, 0), (3, 0)).intersection(
        Segment3D((-2, 0), (1, 0))) == [Segment3D((0, 0), (1, 0))]
    assert Segment3D((0, 0), (3, 0)).intersection(
        Segment3D((-2, 0), (0, 0))) == [Point3D(0, 0)]
    assert s1.intersection(Segment(Point(1, 1), Point(2, 2))) == [Point(1, 1)]
    assert s1.intersection(Segment(Point(0.5, 0.5), Point(1.5, 1.5))) == [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 s1.intersection(Line(Point(1, 0), Point(2, 1))) == []
    assert s1.intersection(s2) == [s2]
    assert s2.intersection(s1) == [s2]

    assert asa(120, 8, 52) == \
           Triangle(
               Point(0, 0),
               Point(8, 0),
               Point(-4 * cos(19 * pi / 90) / sin(2 * pi / 45),
                     4 * sqrt(3) * cos(19 * pi / 90) / sin(2 * pi / 45)))
    assert Line((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)]
    assert Line((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)]
    assert Ray((0, 0), (1, 1)).intersection(Ray((1, 0), (1, 2))) == [Point(1, 1)]
    assert Ray((0, 0), (1, 1)).intersection(Segment((1, 0), (1, 2))) == [Point(1, 1)]
    assert Ray((0, 0), (10, 10)).contains(Segment((1, 1), (2, 2))) is True
    assert Segment((1, 1), (2, 2)) in Line((0, 0), (10, 10))

    # 16628 - this should be fast
    p0 = Point2D(S(249)/5, S(497999)/10000)
    p1 = Point2D((-58977084786*sqrt(405639795226) + 2030690077184193 +
        20112207807*sqrt(630547164901) + 99600*sqrt(255775022850776494562626))
        /(2000*sqrt(255775022850776494562626) + 1991998000*sqrt(405639795226)
        + 1991998000*sqrt(630547164901) + 1622561172902000),
        (-498000*sqrt(255775022850776494562626) - 995999*sqrt(630547164901) +
        90004251917891999 +
        496005510002*sqrt(405639795226))/(10000*sqrt(255775022850776494562626)
        + 9959990000*sqrt(405639795226) + 9959990000*sqrt(630547164901) +
        8112805864510000))
    p2 = Point2D(S(497)/10, -S(497)/10)
    p3 = Point2D(-S(497)/10, -S(497)/10)
    l = Line(p0, p1)
    s = Segment(p2, p3)
    n = (-52673223862*sqrt(405639795226) - 15764156209307469 -
        9803028531*sqrt(630547164901) +
        33200*sqrt(255775022850776494562626))
    d = sqrt(405639795226) + 315274080450 + 498000*sqrt(
        630547164901) + sqrt(255775022850776494562626)
    assert intersection(l, s) == [
        Point2D(n/d*S(3)/2000, -S(497)/10)]

    def __init__(self, point1, point2, point3, *args, **kwargs):
        super(DimensionItem, self).__init__(*args, **kwargs)

        # Create segment between the two points
        segment = Segment(point1, point2)

        # Get a line parallel to segment that passes through the third point
        parallel_line = segment.parallel_line(point3)

        # Get perpendicular segments from the points to the new parallel line
        perpendicular_line_p1 = parallel_line.perpendicular_segment(point1)
        perpendicular_line_p2 = parallel_line.perpendicular_segment(point2)

        # Order of XX.points from sympy changes if point3 is above or below
        # the segment, remove original point so we are left with new one
        perpendicular_line_p1_points = list(perpendicular_line_p1.points)
        perpendicular_line_p1_points.remove(point1)
        perpendicular_line_p2_points = list(perpendicular_line_p2.points)
        perpendicular_line_p2_points.remove(point2)

        # TODO: Refactor, code repeated 3 times
        self.path = QtGui.QPainterPath(QtCore.QPointF(point1.x, point1.y))
        self.path.lineTo(perpendicular_line_p1_points[0].x, perpendicular_line_p1_points[0].y)
        self.path.lineTo(perpendicular_line_p2_points[0].x, perpendicular_line_p2_points[0].y)
        self.path.lineTo(point2.x, point2.y)

        self.path_item = DimensionSceneItem(self.path)
        self.add_scene_item(self.path_item)

        new_segment = Segment(perpendicular_line_p1_points[0], perpendicular_line_p2_points[0])
        midpoint = new_segment.midpoint

        segment_midpoint = segment.midpoint

        # TODO: Customizable precision
        self.text_item = TextSceneItem('{0:.2f}'.format(float(segment.length.evalf())))
        self.text_item.setTransform(self.text_item.sceneTransform().scale(1, -1))
        self.add_scene_item(self.text_item)

        bounding_rect = self.text_item.boundingRect()
        offset_x = 0
        offset_y = 0

        # Quadrant 1, 4, Horizontal Right
        if midpoint.x > segment_midpoint.x:
            offset_x = bounding_rect.width() / 2

        # Quadrant 2, 3, Horizontal Left
        if midpoint.x < segment_midpoint.x:
            offset_x = -bounding_rect.width() / 2

        # Quadrant 1, 2, Vertical Top
        if midpoint.y > segment_midpoint.y:
            offset_y = bounding_rect.height() / 2

        # Quadrant 3, 4, Vertical Bottom
        if midpoint.y < segment_midpoint.y:
            offset_y = -bounding_rect.height() / 2

        self.text_item.setPos(midpoint.x + offset_x, midpoint.y + offset_y)

        # Point used to allow alligning dimension labels
        point_item = HiddenPointItem(midpoint)
        self.add_child_item(point_item)