Circe center coordinates and radius from coordinades ( A, B, C )

my problem is that i need to find circles center and radius from coordinates. (A,B,C)

So from this :

preferibly not with solve, but with "manual" calculations.

If manual is impossible, solve works too.

Hoping someone can help.

Thank you in advance. This is an amazing community.

Answer 1

[David Hill]

syms h k r x1 x2 x3 y1 y2 y3
eqn1=(x1-h)^2+(y1-k)^2==r^2;
eqn2=(x2-h)^2+(y2-k)^2==r^2;
eqn3=(x3-h)^2+(y3-k)^2==r^2;
[H,K,R]=solve([eqn1,eqn2,eqn3],[h,k,r]);

Answer 2

[Image Analyst]

See the FAQ:

https://matlab.fandom.com/wiki/FAQ#How_can_I_fit_a_circle_to_a_set_of_XY_data.3F

function [xCenter, yCenter, radius, a] = circlefit(x, y)
% circlefit(): Fits a circle through a set of points in the x - y plane.
% USAGE :
% [xCenter, yCenter, radius, a] = circlefit(X, Y)
% The output is the center point (xCenter, yCenter) and the radius of the fitted circle.
% "a" is an optional output vector describing the coefficients in the circle's equation:
%     x ^ 2 + y ^ 2 + a(1) * x + a(2) * y + a(3) = 0
% by Bucher Izhak 25 - Oct - 1991

numPoints = numel(x);
xx = x .* x;
yy = y .* y;
xy = x .* y;
A = [sum(x),  sum(y),  numPoints;
    sum(xy), sum(yy), sum(y);
    sum(xx), sum(xy), sum(x)];
B = [-sum(xx + yy) ;
    -sum(xx .* y + yy .* y);
    -sum(xx .* x + xy .* y)];
a = A \ B;
xCenter = -.5 * a(1);
yCenter = -.5 * a(2);
radius  =  sqrt((a(1) ^ 2 + a(2) ^ 2) / 4 - a(3));

To call

x = [1,4,5];
y = [1,4,2];
[xCenter, yCenter, radius, a] = circlefit(x, y)