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## Copyright (C) 2004-2011 David Legland <david.legland@grignon.inra.fr>
## 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
## 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.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{points} = } intersectLineCircle (@var{line}, @var{circle})
## Intersection point(s) of a line and a circle
##
## INTERS = intersectLineCircle(LINE, CIRCLE);
## Returns a 2-by-2 array, containing on each row the coordinates of an
## intersection point. If the line and circle do not intersect, the result
## is filled with 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;
##
## @seealso{lines2d, circles2d, intersectLines, intersectCircles}
## @end deftypefn
function points = intersectLineCircle(line, circle)
# local precision
eps = 1e-14;
# center parameters
center = circle(:, 1:2);
radius = circle(:, 3);
# line parameters
dp = line(:, 1:2) - center;
vl = line(:, 3:4);
# coefficient 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;
if delta > eps
# find two roots of second order equation
u1 = (-b - sqrt(delta)) / 2 ./ a;
u2 = (-b + sqrt(delta)) / 2 ./ a;
# convert into 2D coordinate
points = [line(1:2) + u1 * line(3:4) ; line(1:2) + u2 * line(3:4)];
elseif abs(delta) < eps
# find unique root, and convert to 2D coord.
u = -b / 2 ./ a;
points = line(1:2) + u*line(3:4);
else
# fill with NaN
points = NaN * ones(2, 2);
return;
end
endfunction
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