How to generate a circle through three points #144

Let the three given points be a, b, c. Use x and y subscripts represent x and y coordinates, so that the x and y co-ordinates of a are a_x and a_y.

The coordinates of the center p = (p_x, p_y) of the circle determined by a, b, and c are:

A = bx - ax
B = by - ay
C = cx - ax
D = cy - ay
E = A × (ax + bx) + B × (ay + by)
F = C × (ax + cx) + D × (ay + cy)
G = 2 × (A × (cy - by) - B × (cx - bx))
px = (D × E - B × F) ÷ G
py = (A × F - C × E) ÷ G

If G is zero then the three points are collinear and no finite-radius circle through them exists. Otherwise, the radius of the circle is:

Original resource:	The Delphi Pool
Author:	Joseph O'Rourke
Added:	2009/11/06
Last updated:	2009/11/06