/usr/share/octave/packages/geometry-1.7.0/geom2d/radicalAxis.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{line} = } radicalAxis (@var{circle1}, @var{circle2})
## 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);
##
## Ref:
## http://mathworld.wolfram.com/RadicalLine.html
## http://en.wikipedia.org/wiki/Radical_axis
##
## @seealso{lines2d, circles2d, createCircle}
##
## @end deftypefn
function line = radicalAxis(circle1, circle2)
# extract circles parameters
x1 = circle1(:,1);
x2 = circle2(:,1);
y1 = circle1(:,2);
y2 = circle2(:,2);
r1 = circle1(:,3);
r2 = circle2(:,3);
# distance between each couple of centers
dist = sqrt((x2-x1).^2 + (y2-y1).^2);
# relative position of intersection point of
# the radical line with the line joining circle centers
d = (dist.^2 + r1.^2 - r2.^2) * .5 ./ dist;
# compute angle of radical axis
angle = lineAngle(createLine([x1 y1], [x2 y2]));
cot = cos(angle);
sit = sin(angle);
# parameters of the line
x0 = x1 + d*cot;
y0 = y1 + d*sit;
dx = -sit;
dy = cot;
# concatenate into one structure
line = [x0 y0 dx dy];
endfunction
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