Question

我有三点坐标。请打电话给他们X1、Y1、X2、Y2、X3 Y3。

我需要计算X4,Y4,但我知道:

X1,Y1 is 350 units in distance from X4,Y4 X2,Y2 is 200 units in distance from X4,Y4 X3,Y3 is 50 units in distance from X4,Y4

Inow The Exact Values for X1,Y1, X2,Y2, and X3,Y3

我如何确定X4,Y4的确切地点?

Answer 1

(x - x1)^2 + (y - y1)^2 = r1^2  ------ p
(x - x2)^2 + (y - y2)^2 = r2^2  ------ q
(x - x3)^2 + (y - y3)^2 = r3^2  ------ r

这三个圈子的交汇点。

 p - q     ----- l 
 p - r     ----- n

http://en.wikipedia.org/wiki/Cramer%27s_rule”rel=“nofollow noreferer”>Cramer s Rule。

GET_POINT(x1,y1,r1,x2,y2,r2,x3,y3,r3):
    A = x1 - x2
    B = y1 - y2
    D = x1 - x3
    E = y1 - y3

    T = (r1*r1 - x1*x1 - y1*y1)
    C = (r2*r2 - x2*x2 - y2*y2) - T
    F = (r3*r3 - x3*x3 - y3*y3) - T

    A x + B y = C/2  // this is equation  l 
    D x + E y = F/2  // this is equation  n 

    // Cramer s Rule

    Mx = (C E  - B F) /2
    My = (A F  - D C) /2
    M  = AE - DB

    x = Mx/M
    y = My/M

    return (x,y)

Answer 2

你的职位只贴上“地理”。

解决贵问题的一个几何解决方案是将环绕(x1,y1)、(x2,y2)和(x3,y3)的圈子连接到(x4,y4)作为rad。 (x4,y4)是所有 the圈之间交织点。

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