从三个点找到圆心的算法是什么? [英] What is the algorithm for finding the center of a circle from three points?

问题描述

我在圆周上有三个点:

pt A = (A.x, A.y);
pt B = (B.x, B.y);
pt C = (C.x, C.y);

如何计算圆心?

在 Processing (Java) 中实现它.

Implementing it in Processing (Java).

我找到了答案并实施了一个可行的解决方案:

I found the answer and implemented a working solution:

 pt circleCenter(pt A, pt B, pt C) {

    float yDelta_a = B.y - A.y;
    float xDelta_a = B.x - A.x;
    float yDelta_b = C.y - B.y;
    float xDelta_b = C.x - B.x;
    pt center = P(0,0);

    float aSlope = yDelta_a/xDelta_a;
    float bSlope = yDelta_b/xDelta_b;  
    center.x = (aSlope*bSlope*(A.y - C.y) + bSlope*(A.x + B.x)
        - aSlope*(B.x+C.x) )/(2* (bSlope-aSlope) );
    center.y = -1*(center.x - (A.x+B.x)/2)/aSlope +  (A.y+B.y)/2;

    return center;
  }

推荐答案

这可能是一个相当深入的计算.这里有一个简单的分步说明:http://paulbourke.net/geometry/circlesphere/.一旦你有了圆的方程，你就可以简单地把它变成一个包含 H 和 K 的形式.点 (h,k) 将是圆心.

It can be a rather in depth calculation. There is a simple step-by-step here: http://paulbourke.net/geometry/circlesphere/. Once you have the equation of the circle, you can simply put it in a form involving H and K. The point (h,k) will be the center.

(在链接处向下滚动一点以获取方程式)

(scroll down a little ways at the link to get to the equations)

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