本文介绍了确定的点的坐标基于其已知的差异从三个其他点的处理方法,对大家解决问题具有一定的参考价值,需要的朋友们下面随着小编来一起学习吧!

问题描述

我有三个点的平面上的坐标。让我们称他们为X1,Y1,X2,Y2,Y3 X3

我需要计算X4,Y4但我知道的是:

X1,Y1为350台,距离X4,Y4X2,Y2是200个单位在从X4,Y4距离X3,Y3是50个单位的距离X4,Y4

我知道确切的值对于X1,Y1,X2,Y2,和X3,Y3

如何确定X4的确切位置,Y4?

解决方案

 (X  -  X1)^ 2 +(Y  -  Y1)^ 2 = R1 ^ 2 ----- -  P
(X  -  X 2)^ 2 +(Y  -  Y2)^ 2 = R2 ^ 2 ------ q
(X  -  X 3)^ 2 +(Y  -  Y3)^ 2 = R3 ^ 2 ------ř
 

解决了这3个圆的交点。

 对 -  q -----升
 对 -   -  [R -----ñ
 

使用解方程(L)和(n) 克莱姆法则

 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的
    F =(R3 * R3  -  X3 * X3  -  Y3 * Y3) -  T的

    一λ+ B Y = C / 2 //这是方程式L
    深x + E Y = F / 2 //这是等式'N'

    //克莱姆法则

    MX =(权证 -  B F)/ 2
    我=(A F  -  D C)/ 2
    M = AE  -  DB

    X =的Mx / M
    Y =我/ M

    回报(X,Y)
 

I have the coordinates of three points on a plane. Let's call them X1,Y1, X2,Y2, X3 Y3.

I need to calculate X4,Y4 but all I know is:

X1,Y1 is 350 units in distance from X4,Y4X2,Y2 is 200 units in distance from X4,Y4X3,Y3 is 50 units in distance from X4,Y4

I Know The Exact Values For X1,Y1, X2,Y2, and X3,Y3

How can I determine the exact location of X4,Y4?

解决方案
(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

Solve for intersection point of these 3 circles.

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

Solve equation (l) and (n) using 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)

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10-15 03:29