Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / geometry-1.5.0 / graphs / delaunayGraph.m

diff --git a/octave_packages/geometry-1.5.0/graphs/delaunayGraph.m b/octave_packages/geometry-1.5.0/graphs/delaunayGraph.m
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+%% Copyright (C) 2011-2012 David Legland <david.legland@grignon.inra.fr>
+%% 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.
+%%
+%% 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {[@var{points} @var{edges}]= } delaunayGraph (@var{points})
+%% Graph associated to Delaunay triangulation of input points
+%%
+%% Compute the Delaunay triangulation of the set of input points, and
+%% convert to a set of edges. The output NODES is the same as the input
+%% POINTS.
+%%
+%% Example
+%% @example
+%%
+%% % Draw a planar graph correpspionding to Delaunay triangulation
+%% points = rand(30, 2) * 100;
+%% [nodes edges] = delaunayGraph(points);
+%% figure;
+%% drawGraph(nodes, edges);
+%%
+%% % Draw a 3Dgraph corresponding to Delaunay tetrahedrisation
+%% points = rand(20, 3) * 100;
+%% [nodes edges] = delaunayGraph(points);
+%% figure;
+%% drawGraph(nodes, edges);
+%% view(3);
+%%
+%% @end example
+%%
+%% @seealso{delaunay, delaunayn}
+%% @end deftypefn
+
+function [points edges] = delaunayGraph(points, varargin)
+  % compute triangulation
+  tri = delaunayn(points, varargin{:});
+
+  % number of simplices (triangles), and of vertices by simplex (3 in 2D)
+  nt = size(tri, 1);
+  nv = size(tri, 2);
+
+  % allocate memory
+  edges = zeros(nt * nv, 2);
+
+  % compute edges of each simplex
+  for i = 1:nv-1
+    edges((1:nt) + (i-1)*nt, :) = sort([tri(:, i) tri(:, i+1)], 2);
+  end
+  edges((1:nt) + (nv-1)*nt, :) = sort([tri(:, end) tri(:, 1)], 2);
+
+  % remove multiple edges
+  edges = unique(edges, 'rows');
+
+endfunction
+
+%!demo
+%! % Draw a planar graph correpspionding to Delaunay triangulation
+%! points = rand(30, 2) * 100;
+%! [nodes edges] = delaunayGraph(points);
+%! figure;
+%! drawGraph(nodes, edges);
+%! axis tight
+
+%!demo
+%! % WARNING 3d pltottig works correctly in Octave >= 3.6
+%! % Draw a 3Dgraph corresponding to Delaunay tetrahedrisation
+%! points = rand(20, 3) * 100;
+%! [nodes edges] = delaunayGraph(points);
+%! figure;
+%! drawGraph(nodes, edges);
+%! view(3);
+%! axis tight