Python Segment.perpendicular_bisector方法代码示例

# 需要导入模块: from sympy.geometry import Segment [as 别名]
# 或者: from sympy.geometry.Segment import perpendicular_bisector [as 别名]
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)

# 需要导入模块: from sympy.geometry import Segment [as 别名]
# 或者: from sympy.geometry.Segment import perpendicular_bisector [as 别名]

#.........这里部分代码省略.........
    # 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

    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))

# 需要导入模块: from sympy.geometry import Segment [as 别名]
# 或者: from sympy.geometry.Segment import perpendicular_bisector [as 别名]
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.........

# 需要导入模块: from sympy.geometry import Segment [as 别名]
# 或者: from sympy.geometry.Segment import perpendicular_bisector [as 别名]

#.........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) == []

# 需要导入模块: from sympy.geometry import Segment [as 别名]
# 或者: from sympy.geometry.Segment import perpendicular_bisector [as 别名]

#.........这里部分代码省略.........
    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)