radicalAxis

RADICALAXIS Compute the radical axis (or radical line) of 2 circles.

   L = radicalAxis(C1, C2)
   Computes the radical axis of 2 circles.

   Example
   C1 = [10 10 5];
   C2 = [60 50 30];
   L = radicalAxis(C1, C2);
   hold on; axis equal;axis([0 100 0 100]); 
   drawCircle(C1);drawCircle(C2);drawLine(L);

   See also
   lines2d, circles2d, createCircle

   Ref:
   http://mathworld.wolfram.com/RadicalLine.html
   http://en.wikipedia.org/wiki/Radical_axis

 ------
 Author: David Legland
 e-mail: david.legland@grignon.inra.fr
 Created: 2007-05-15,    using Matlab 7.4.0.287 (R2007a)
 Copyright 2007 INRA - BIA PV Nantes - MIAJ Jouy-en-Josas.

0001 function line = radicalAxis(circle1, circle2)
0002 %RADICALAXIS Compute the radical axis (or radical line) of 2 circles.
0003 %
0004 %   L = radicalAxis(C1, C2)
0005 %   Computes the radical axis of 2 circles.
0006 %
0007 %   Example
0008 %   C1 = [10 10 5];
0009 %   C2 = [60 50 30];
0010 %   L = radicalAxis(C1, C2);
0011 %   hold on; axis equal;axis([0 100 0 100]);
0012 %   drawCircle(C1);drawCircle(C2);drawLine(L);
0013 %
0014 %   See also
0015 %   lines2d, circles2d, createCircle
0016 %
0017 %   Ref:
0018 %   http://mathworld.wolfram.com/RadicalLine.html
0019 %   http://en.wikipedia.org/wiki/Radical_axis
0020 %
0021 % ------
0022 % Author: David Legland
0023 % e-mail: david.legland@grignon.inra.fr
0024 % Created: 2007-05-15,    using Matlab 7.4.0.287 (R2007a)
0025 % Copyright 2007 INRA - BIA PV Nantes - MIAJ Jouy-en-Josas.
0026 %
0027 
0028 % extract circles parameters
0029 x1 = circle1(:,1);
0030 x2 = circle2(:,1);
0031 y1 = circle1(:,2);
0032 y2 = circle2(:,2);
0033 r1 = circle1(:,3);
0034 r2 = circle2(:,3);
0035 
0036 % distance between each couple of centers
0037 dist  = sqrt((x2-x1).^2 + (y2-y1).^2);
0038 
0039 % relative position of intersection point of
0040 % the radical line with the line joining circle centers
0041 d = (dist.^2 + r1.^2 - r2.^2) * .5 ./ dist;
0042 
0043 % compute angle of radical axis
0044 angle = lineAngle(createLine([x1 y1], [x2 y2]));
0045 cot = cos(angle);
0046 sit = sin(angle);
0047 
0048 % parameters of the line
0049 x0 = x1 + d*cot;
0050 y0 = y1 + d*sit;
0051 dx = -sit;
0052 dy = cot;
0053 
0054 % concatenate into one structure
0055 line = [x0 y0 dx dy];