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## Copyright (C) 2024 David Legland
## 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
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function line = radicalAxis(circle1, circle2)
%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@inrae.fr
% Created: 2007-05-15, using Matlab 7.4.0.287 (R2007a)
% Copyright 2007-2023 INRA - BIA PV Nantes - MIAJ Jouy-en-Josas
% 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];
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