使用 Python 测试折线是否相交

Question

是否有一个简单的解决方案来测试两条折线是否相交，而不使用任何库？

比如

PL1 = ((-1, -1), (1, -1), (1, 2)), PL2 = ((0, 1), (2, 1))

PL1.intersect(PL2)

我只能找到具有两个点的直线的解决方案。

Answer 1

如评论中所述，您可以在多边形的所有组成线之间应用传统的线交点算法（this for example）。例如：

def line_intersection(line1, line2):
    xdiff = (line1[0][0] - line1[1][0], line2[0][0] - line2[1][0])
    ydiff = (line1[0][1] - line1[1][1], line2[0][1] - line2[1][1])

    def det(a, b):
        return a[0] * b[1] - a[1] * b[0]

    div = det(xdiff, ydiff)
    if div == 0:
       return None

    d = (det(*line1), det(*line2))
    x = det(d, xdiff) / div
    y = det(d, ydiff) / div
    return x, y

def poly_intersection(poly1, poly2):

    for i, p1_first_point in enumerate(poly1[:-1]):
        p1_second_point = poly1[i + 1]

        for j, p2_first_point in enumerate(poly2[:-1]):
            p2_second_point = poly2[j + 1]

            if line_intersection((p1_first_point, p1_second_point), (p2_first_point, p2_second_point)):
                return True

    return False

PL1 = ((-1, -1), (1, -1), (1, 2))
PL2 = ((0, 1), (2, 1))

print poly_intersection(PL1, PL2)

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