Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / geometry-1.5.0 / geom2d / intersectCircles.m

diff --git a/octave_packages/geometry-1.5.0/geom2d/intersectCircles.m b/octave_packages/geometry-1.5.0/geom2d/intersectCircles.m
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+%% Copyright (c) 2011, INRA
+%% 2007-2011, David Legland <david.legland@grignon.inra.fr>
+%% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%%
+%% All rights reserved.
+%% (simplified BSD License)
+%%
+%% 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 COPYRIGHT HOLDER 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 copyright holder.
+
+%% -*- 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
+