--- /dev/null
+%% Copyright (c) 2011, INRA
+%% 2004-2011, 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{dist} = } minDistancePoints (@var{pts})
+%% @deftypefnx {Function File} {@var{dist} = } minDistancePoints (@var{pts1},@var{pts2})
+%% @deftypefnx {Function File} {@var{dist} = } minDistancePoints (@dots{},@var{norm})
+%% @deftypefnx {Function File} {[@var{dist} @var{i} @var{j}] = } minDistancePoints (@var{pts1}, @var{pts2}, @dots{})
+%% @deftypefnx {Function File} {[@var{dist} @var{j}] = } minDistancePoints (@var{pts1}, @var{pts2}, @dots{})
+%% Minimal distance between several points.
+%%
+%% Returns the minimum distance between all couple of points in @var{pts}. @var{pts} is
+%% an array of [NxND] values, N being the number of points and ND the
+%% dimension of the points.
+%%
+%% Computes for each point in @var{pts1} the minimal distance to every point of
+%% @var{pts2}. @var{pts1} and @var{pts2} are [NxD] arrays, where N is the number of points,
+%% and D is the dimension. Dimension must be the same for both arrays, but
+%% number of points can be different.
+%% The result is an array the same length as @var{pts1}.
+%%
+%% When @var{norm} is provided, it uses a user-specified norm. @var{norm}=2 means euclidean norm (the default),
+%% @var{norm}=1 is the Manhattan (or "taxi-driver") distance.
+%% Increasing @var{norm} growing up reduces the minimal distance, with a limit
+%% to the biggest coordinate difference among dimensions.
+%%
+%%
+%% Returns indices @var{i} and @var{j} of the 2 points which are the closest. @var{dist}
+%% verifies relation:
+%% @var{dist} = distancePoints(@var{pts}(@var{i},:), @var{pts}(@var{j},:));
+%%
+%% If only 2 output arguments are given, it returns the indices of points which are the closest. @var{j} has the
+%% same size as @var{dist}. for each I It verifies the relation :
+%% @var{dist}(I) = distancePoints(@var{pts1}(I,:), @var{pts2}(@var{J},:));
+%%
+%%
+%% Examples:
+%%
+%% @example
+%% % minimal distance between random planar points
+%% points = rand(20,2)*100;
+%% minDist = minDistancePoints(points);
+%%
+%% % minimal distance between random space points
+%% points = rand(30,3)*100;
+%% [minDist ind1 ind2] = minDistancePoints(points);
+%% minDist
+%% distancePoints(points(ind1, :), points(ind2, :))
+%% % results should be the same
+%%
+%% % minimal distance between 2 sets of points
+%% points1 = rand(30,2)*100;
+%% points2 = rand(30,2)*100;
+%% [minDists inds] = minDistancePoints(points1, points2);
+%% minDists(10)
+%% distancePoints(points1(10, :), points2(inds(10), :))
+%% % results should be the same
+%% @end example
+%%
+%% @seealso{points2d, distancePoints}
+%% @end deftypefn
+
+function varargout = minDistancePoints(p1, varargin)
+
+ %% Initialisations
+
+ % default norm (euclidean)
+ n = 2;
+
+ % flag for processing of all points
+ allPoints = false;
+
+ % process input variables
+ if isempty(varargin)
+ % specify only one array of points, not the norm
+ p2 = p1;
+
+ elseif length(varargin)==1
+ var = varargin{1};
+ if length(var)>1
+ % specify two arrays of points
+ p2 = var;
+ allPoints = true;
+ else
+ % specify array of points and the norm
+ n = var;
+ p2 = p1;
+ end
+
+ else
+ % specify two array of points and the norm
+ p2 = varargin{1};
+ n = varargin{2};
+ allPoints = true;
+ end
+
+
+ % number of points in each array
+ n1 = size(p1, 1);
+ n2 = size(p2, 1);
+
+ % dimension of points
+ d = size(p1, 2);
+
+
+ %% Computation of distances
+
+ % allocate memory
+ dist = zeros(n1, n2);
+
+ % different behaviour depending on the norm used
+ if n==2
+ % Compute euclidian distance. this is the default case
+ % Compute difference of coordinate for each pair of point ([n1*n2] array)
+ % and for each dimension. -> dist is a [n1*n2] array.
+ % in 2D: dist = dx.*dx + dy.*dy;
+ for i=1:d
+ dist = dist + (repmat(p1(:,i), [1 n2])-repmat(p2(:,i)', [n1 1])).^2;
+ end
+
+ % compute minimal distance:
+ if ~allPoints
+ % either on all couple of points
+ mat = repmat((1:n1)', [1 n1]);
+ ind = mat < mat';
+ [minSqDist ind] = min(dist(ind));
+ else
+ % or for each point of P1
+ [minSqDist ind] = min(dist, [], 2);
+ end
+
+ % convert squared distance to distance
+ minDist = sqrt(minSqDist);
+ elseif n==inf
+ % infinite norm corresponds to maximum absolute value of differences
+ % in 2D: dist = max(abs(dx) + max(abs(dy));
+ for i=1:d
+ dist = max(dist, abs(p1(:,i)-p2(:,i)));
+ end
+ else
+ % compute distance using the specified norm.
+ % in 2D: dist = power(abs(dx), n) + power(abs(dy), n);
+ for i=1:d
+ dist = dist + power((abs(repmat(p1(:,i), [1 n2])-repmat(p2(:,i)', [n1 1]))), n);
+ end
+
+ % compute minimal distance
+ if ~allPoints
+ % either on all couple of points
+ mat = repmat((1:n1)', [1 n1]);
+ ind = mat < mat';
+ [minSqDist ind] = min(dist(ind));
+ else
+ % or for each point of P1
+ [minSqDist ind] = min(dist, [], 2);
+ end
+
+ % convert squared distance to distance
+ minDist = power(minSqDist, 1/n);
+ end
+
+
+
+ if ~allPoints
+ % convert index in array to row ad column subindices.
+ % This uses the fact that index are sorted in a triangular matrix,
+ % with the last index of each column being a so-called triangular
+ % number
+ ind2 = ceil((-1+sqrt(8*ind+1))/2);
+ ind1 = ind - ind2*(ind2-1)/2;
+ ind2 = ind2 + 1;
+ end
+
+
+ %% format output parameters
+
+ % format output depending on number of asked parameters
+ if nargout<=1
+ varargout{1} = minDist;
+ elseif nargout==2
+ % If two arrays are asked, 'ind' is an array of indices, one for each
+ % point in var{pts}1, corresponding to the result in minDist
+ varargout{1} = minDist;
+ varargout{2} = ind;
+ elseif nargout==3
+ % If only one array is asked, minDist is a scalar, ind1 and ind2 are 2
+ % indices corresponding to the closest points.
+ varargout{1} = minDist;
+ varargout{2} = ind1;
+ varargout{3} = ind2;
+ end
+
+endfunction
+
+%!test
+%! pts = [50 10;40 60;30 30;20 0;10 60;10 30;0 10];
+%! assert (minDistancePoints(pts), 20);
+
+%!test
+%! pts = [10 10;25 5;20 20;30 20;10 30];
+%! [dist ind1 ind2] = minDistancePoints(pts);
+%! assert (10, dist, 1e-6);
+%! assert (3, ind1, 1e-6);
+%! assert (4, ind2, 1e-6);
+
+%!test
+%! pts = [0 80;10 60;20 40;30 20;40 0;0 0;100 0;0 100;0 -10;-10 -20];
+%! assert (minDistancePoints([40 50], pts), 10*sqrt(5), 1e-6);
+%! assert (minDistancePoints([25 30], pts), 5*sqrt(5), 1e-6);
+%! assert (minDistancePoints([30 40], pts), 10, 1e-6);
+%! assert (minDistancePoints([20 40], pts), 0, 1e-6);
+
+%!test
+%! pts1 = [40 50;25 30;40 20];
+%! pts2 = [0 80;10 60;20 40;30 20;40 0;0 0;100 0;0 100;0 -10;-10 -20];
+%! res = [10*sqrt(5);5*sqrt(5);10];
+%! assert (minDistancePoints(pts1, pts2), res, 1e-6);
+
+%!test
+%! pts = [50 10;40 60;40 30;20 0;10 60;10 30;0 10];
+%! assert (minDistancePoints(pts, 1), 30, 1e-6);
+%! assert (minDistancePoints(pts, 100), 20, 1e-6);
+
+%!test
+%! pts = [0 80;10 60;20 40;30 20;40 0;0 0;100 0;0 100;0 -10;-10 -20];
+%! assert (minDistancePoints([40 50], pts, 2), 10*sqrt(5), 1e-6);
+%! assert (minDistancePoints([25 30], pts, 2), 5*sqrt(5), 1e-6);
+%! assert (minDistancePoints([30 40], pts, 2), 10, 1e-6);
+%! assert (minDistancePoints([20 40], pts, 2), 0, 1e-6);
+%! assert (minDistancePoints([40 50], pts, 1), 30, 1e-6);
+%! assert (minDistancePoints([25 30], pts, 1), 15, 1e-6);
+%! assert (minDistancePoints([30 40], pts, 1), 10, 1e-6);
+%! assert (minDistancePoints([20 40], pts, 1), 0, 1e-6);
+
+%!test
+%! pts1 = [40 50;25 30;40 20];
+%! pts2 = [0 80;10 60;20 40;30 20;40 0;0 0;100 0;0 100;0 -10;-10 -20];
+%! res1 = [10*sqrt(5);5*sqrt(5);10];
+%! assert (minDistancePoints(pts1, pts2, 2), res1, 1e-6);
+%! res2 = [30;15;10];
+%! assert (minDistancePoints(pts1, pts2, 1), res2);
+
+%!test
+%! pts1 = [40 50;20 30;40 20];
+%! pts2 = [0 80;10 60;20 40;30 20;40 0;0 0;100 0;0 100;0 -10;-10 -20];
+%! dists0 = [10*sqrt(5);10;10];
+%! inds1 = [3;3;4];
+%! [minDists inds] = minDistancePoints(pts1, pts2);
+%! assert (dists0, minDists);
+%! assert (inds1, inds);
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