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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 = intersectLineCircle(line, circle)
%INTERSECTLINECIRCLE Intersection point(s) of a line and a circle.
%
% INTERS = intersectLineCircle(LINE, CIRCLE);
% Returns a 2-by-2-by-N array, containing on each row the coordinates of
% an intersection point for each line-circle pair, i.e. INTERS(:,:,k)
% contains the intersections between LINE(k,:) and CIRCLE(k,:).
%
% If a line-circle pair does not intersect, the corresponding results are
% set to NaN.
%
% Example
% % base point
% center = [10 0];
% % create vertical line
% l1 = [center 0 1];
% % circle
% c1 = [center 5];
% pts = intersectLineCircle(l1, c1)
% pts =
% 10 -5
% 10 5
% % draw the result
% figure; clf; hold on;
% axis([0 20 -10 10]);
% drawLine(l1);
% drawCircle(c1);
% drawPoint(pts, 'rx');
% axis equal;
%
% See also
% lines2d, circles2d, intersectLines, intersectCircles
%
% References
% http://local.wasp.uwa.edu.au/~pbourke/geometry/sphereline/
% http://mathworld.wolfram.com/Circle-LineIntersection.html
%
% ------
% Authors: David Legland, JuanPi Carbajal
% E-mail: david.legland@inrae.fr, ajuanpi+dev@gmail.com
% Created: 2011-01-14, using Matlab 7.9.0.529 (R2009b)
% Copyright 2011-2023 INRA - Cepia Software Platform
% check size of inputs
nLines = size(line, 1);
nCircles = size(circle, 1);
if nLines ~= nCircles
error ('matGeom:geom3d:invalidArguments', ...
'Requires same number of lines and circles');
end
% center parameters
center = circle(:, 1:2);
radius = circle(:, 3);
% line parameters
dp = line(:, 1:2) - center;
vl = line(:, 3:4);
% coefficients of second order equation
a = sum(line(:, 3:4).^2, 2);
b = 2 * sum(dp .* vl, 2);
c = sum(dp.^2, 2) - radius.^2;
% discriminant
delta = b .^ 2 - 4 * a .* c;
points = nan(2, 2, nCircles);
valid = delta >= 0;
if any(valid)
% compute roots (as a N-by-N-by-2 array)
u = bsxfun(@plus, -b(valid), bsxfun(@times, [-1 1], sqrt(delta(valid))));
u = bsxfun(@rdivide, u, a(valid)) / 2;
if sum(valid) == 1
points = [...
line(1:2) + u(:,1) .* line(3:4); ...
line(1:2) + u(:,2) .* line(3:4)];
else
tmp = [...
line(valid, 1:2) + u(:,1) .* line(valid, 3:4) ...
line(valid, 1:2) + u(:,2) .* line(valid, 3:4)].';
points(:, :, valid) = permute(reshape(tmp, [2, 2, nCircles]), [2 1 3]);
end
end
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