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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 points = intersectCircles(circle1, circle2)
%INTERSECTCIRCLES Intersection points of two circles.
%
% POINTS = intersectCircles(CIRCLE1, CIRCLE2)
% Computes the intersetion point of the two circles CIRCLE1 and CIRCLE1.
% Both circles are given with format: [XC YC R], with (XC,YC) being the
% coordinates of the center and R being the radius.
% POINTS is a 2-by-2 array, containing coordinate of an intersection
% point on each row.
% In the case of tangent circles, the intersection is returned twice. It
% can be simplified by using the 'unique' function.
%
% Example
% % intersection points of two distant circles
% c1 = [0 0 10];
% c2 = [10 0 10];
% pts = intersectCircles(c1, c2)
% pts =
% 5 -8.6603
% 5 8.6603
%
% % intersection points of two tangent circles
% c1 = [0 0 10];
% c2 = [20 0 10];
% pts = intersectCircles(c1, c2)
% pts =
% 10 0
% 10 0
% pts2 = unique(pts, 'rows')
% pts2 =
% 10 0
%
% References
% http://local.wasp.uwa.edu.au/~pbourke/geometry/2circle/
% http://mathworld.wolfram.com/Circle-CircleIntersection.html
%
% See also
% circles2d, intersectLineCircle, radicalAxis
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2011-01-20, using Matlab 7.9.0.529 (R2009b)
% Copyright 2011-2023 INRA - Cepia Software Platform
% adapt sizes of inputs
n1 = size(circle1, 1);
n2 = size(circle2, 1);
if n1 ~= n2
if n1 > 1 && n2 == 1
circle2 = repmat(circle2, n1, 1);
elseif n2 > 1 && n1 == 1
circle1 = repmat(circle1, n2, 1);
else
error('Both input should have same number of rows');
end
end
% extract center and radius of each circle
center1 = circle1(:, 1:2);
center2 = circle2(:, 1:2);
r1 = circle1(:,3);
r2 = circle2(:,3);
% allocate memory for result
nPoints = length(r1);
points = NaN * ones(2*nPoints, 2);
% distance between circle centers
d12 = distancePoints(center1, center2, 'diag');
% get indices of circle couples with intersections
inds = d12 >= abs(r1 - r2) & d12 <= (r1 + r2);
if sum(inds) == 0
return;
end
% angle of line from center1 to center2
angle = angle2Points(center1(inds,:), center2(inds,:));
% position of intermediate point, located at the intersection of the
% radical axis with the line joining circle centers
d1m = d12(inds) / 2 + (r1(inds).^2 - r2(inds).^2) ./ (2 * d12(inds));
tmp = polarPoint(center1(inds, :), d1m, angle);
% distance between intermediate point and each intersection point
h = sqrt(r1(inds).^2 - d1m.^2);
% indices of valid intersections
inds2 = find(inds)*2;
inds1 = inds2 - 1;
% create intersection points
points(inds1, :) = polarPoint(tmp, h, angle - pi/2);
points(inds2, :) = polarPoint(tmp, h, angle + pi/2);
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