/usr/share/octave/packages/geometry-1.7.0/geom2d/intersectCircles.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
## notice, this list of conditions and the following disclaimer in the
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##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{points} = } intersectCircles (@var{circle1}, @var{circle2})
## 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
##
## @seealso{circles2d, intersectLineCircle, radicalAxis}
## @end deftypefn
function points = intersectCircles(circle1, circle2)
# 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);
endfunction
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