1 %% Copyright (c) 2011, INRA
2 %% 2007-2011, David Legland <david.legland@grignon.inra.fr>
3 %% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
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35 %% @deftypefn {Function File} {@var{points} = } intersectCircles (@var{circle1}, @var{circle2})
36 %% Intersection points of two circles.
38 %% POINTS = intersectCircles(CIRCLE1, CIRCLE2)
39 %% Computes the intersetion point of the two circles CIRCLE1 and CIRCLE1.
40 %% Both circles are given with format: [XC YC R], with (XC,YC) being the
41 %% coordinates of the center and R being the radius.
42 %% POINTS is a 2-by-2 array, containing coordinate of an intersection
44 %% In the case of tangent circles, the intersection is returned twice. It
45 %% can be simplified by using the 'unique' function.
48 %% % intersection points of two distant circles
51 %% pts = intersectCircles(c1, c2)
56 %% % intersection points of two tangent circles
59 %% pts = intersectCircles(c1, c2)
63 %% pts2 = unique(pts, 'rows')
68 %% http://local.wasp.uwa.edu.au/~pbourke/geometry/2circle/
69 %% http://mathworld.wolfram.com/Circle-CircleIntersection.html
71 %% @seealso{circles2d, intersectLineCircle, radicalAxis}
74 function points = intersectCircles(circle1, circle2)
76 % adapt sizes of inputs
77 n1 = size(circle1, 1);
78 n2 = size(circle2, 1);
81 circle2 = repmat(circle2, n1, 1);
82 elseif n2 > 1 && n1 == 1
83 circle1 = repmat(circle1, n2, 1);
85 error('Both input should have same number of rows');
89 % extract center and radius of each circle
90 center1 = circle1(:, 1:2);
91 center2 = circle2(:, 1:2);
95 % allocate memory for result
97 points = NaN * ones(2*nPoints, 2);
99 % distance between circle centers
100 d12 = distancePoints(center1, center2, 'diag');
102 % get indices of circle couples with intersections
103 inds = d12 >= abs(r1 - r2) & d12 <= (r1 + r2);
109 % angle of line from center1 to center2
110 angle = angle2Points(center1(inds,:), center2(inds,:));
112 % position of intermediate point, located at the intersection of the
113 % radical axis with the line joining circle centers
114 d1m = d12(inds) / 2 + (r1(inds).^2 - r2(inds).^2) ./ (2 * d12(inds));
115 tmp = polarPoint(center1(inds, :), d1m, angle);
117 % distance between intermediate point and each intersection point
118 h = sqrt(r1(inds).^2 - d1m.^2);
120 % indices of valid intersections
121 inds2 = find(inds)*2;
124 % create intersection points
125 points(inds1, :) = polarPoint(tmp, h, angle - pi/2);
126 points(inds2, :) = polarPoint(tmp, h, angle + pi/2);