I have three points on the circumference of a circle:
pt A = (A.x, A.y);
pt B = (B.x, B.y);
pt C = (C.x, C.y);
How do I calculate the center of the circle?
Implementing it in Processing (Java).
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;
}
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.
(scroll down a little ways at the link to get to the equations)