1 %% Copyright (c) 2011, INRA
2 %% 2011, David Legland <david.legland@grignon.inra.fr>
3 %% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
5 %% All rights reserved.
6 %% (simplified BSD License)
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35 %% @deftypefn {Function File} {@var{points} = } intersectLineCircle (@var{line}, @var{circle})
36 %% Intersection point(s) of a line and a circle
38 %% INTERS = intersectLineCircle(LINE, CIRCLE);
39 %% Returns a 2-by-2 array, containing on each row the coordinates of an
40 %% intersection point. If the line and circle do not intersect, the result
41 %% is filled with NaN.
46 %% % create vertical line
50 %% pts = intersectLineCircle(l1, c1)
55 %% figure; clf; hold on;
56 %% axis([0 20 -10 10]);
59 %% drawPoint(pts, 'rx');
62 %% @seealso{lines2d, circles2d, intersectLines, intersectCircles}
65 function points = intersectLineCircle(line, circle)
71 center = circle(:, 1:2);
72 radius = circle(:, 3);
75 dp = line(:, 1:2) - center;
78 % coefficient of second order equation
79 a = sum(line(:, 3:4).^2, 2);
80 b = 2*sum(dp .* vl, 2);
81 c = sum(dp.^2, 2) - radius.^2;
84 delta = b .^ 2 - 4 * a .* c;
87 % find two roots of second order equation
88 u1 = (-b - sqrt(delta)) / 2 ./ a;
89 u2 = (-b + sqrt(delta)) / 2 ./ a;
91 % convert into 2D coordinate
92 points = [line(1:2) + u1 * line(3:4) ; line(1:2) + u2 * line(3:4)];
94 elseif abs(delta) < eps
95 % find unique root, and convert to 2D coord.
97 points = line(1:2) + u*line(3:4);
101 points = NaN * ones(2, 2);