python通过三个球的坐标和半径寻找交点坐标

wangzixiong0814

于 2024-09-17 12:02:03 发布

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文章标签： python 开发语言数学建模几何学

本文链接：https://blog.youkuaiyun.com/wangzixiong0814/article/details/142313110

感谢Marc Pony的代数推导：求三个球面交点的高效解法_3个球面相交点-优快云博客

def find_intersection(x1, y1, z1, x2, y2, z2, x3, y3, z3, r1, r2, r3):
    a11 = 2 * (x3 - x1)
    a12 = 2 * (y3 - y1)
    a13 = 2 * (z3 - z1)
    b1 = (r1) ** 2 - (r3) ** 2 - (x1) ** 2 + (x3) ** 2 - (y1) ** 2 + (y3) ** 2 - (z1) ** 2 + (z3) ** 2
    a21 = 2 * (x3 - x2)
    a22 = 2 * (y3 - y2)
    a23 = 2 * (z3 - z2)
    b2 = (r2) ** 2 - (r3) ** 2 - (x2) ** 2 + (x3) ** 2 - (y2) ** 2 + (y3) ** 2 - (z2) ** 2 + (z3) ** 2

    p1 = (a12 * a23 - a13 * a22) / (a11 * a22 - a12 * a21)
    q1 = (a22 * b1 - a12 * b2) / (a11 * a22 - a12 * a21)
    p2 = (a13 * a21 - a11 * a23) / (a11 * a22 - a12 * a21)
    q2 = (a11 * b2 - a21 * b1) / (a11 * a22 - a12 * a21)

    tempA = p1 ** 2 + p2 ** 2 + 1
    tempB = 2 * (p1 * q1 - z3 + p2 * q2 - p1 * x3 - p2 * y3)
    tempC = q1 ** 2 - 2 * q1 * x3 + q2 ** 2 - 2 * q2