1## Copyright (C) 2021 David Legland
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27
28function line = radicalAxis(circle1, circle2)
29%RADICALAXIS Compute the radical axis (or radical line) of 2 circles.
30%
31%   L = radicalAxis(C1, C2)
32%   Computes the radical axis of 2 circles.
33%
34%   Example
35%   C1 = [10 10 5];
36%   C2 = [60 50 30];
37%   L = radicalAxis(C1, C2);
38%   hold on; axis equal;axis([0 100 0 100]);
39%   drawCircle(C1);drawCircle(C2);drawLine(L);
40%
41%   See also
42%   lines2d, circles2d, createCircle
43%
44%   Ref:
45%   http://mathworld.wolfram.com/RadicalLine.html
46%   http://en.wikipedia.org/wiki/Radical_axis
47%
48% ------
49% Author: David Legland
50% e-mail: david.legland@grignon.inra.fr
51% Created: 2007-05-15,    using Matlab 7.4.0.287 (R2007a)
52% Copyright 2007 INRA - BIA PV Nantes - MIAJ Jouy-en-Josas.
53%
54
55% extract circles parameters
56x1 = circle1(:,1);
57x2 = circle2(:,1);
58y1 = circle1(:,2);
59y2 = circle2(:,2);
60r1 = circle1(:,3);
61r2 = circle2(:,3);
62
63% distance between each couple of centers
64dist  = sqrt((x2-x1).^2 + (y2-y1).^2);
65
66% relative position of intersection point of
67% the radical line with the line joining circle centers
68d = (dist.^2 + r1.^2 - r2.^2) * .5 ./ dist;
69
70% compute angle of radical axis
71angle = lineAngle(createLine([x1 y1], [x2 y2]));
72cot = cos(angle);
73sit = sin(angle);
74
75% parameters of the line
76x0 = x1 + d*cot;
77y0 = y1 + d*sit;
78dx = -sit;
79dy = cot;
80
81% concatenate into one structure
82line = [x0 y0 dx dy];
83