Hi there,

I'd like to register as an octave-forge developer. My sourceforge 
username is s5s. As a first contribution I've written a function which 
produces a simple closed path given a set of 2D coordinates (a path 
connecting all points). Below is a patch of the new file.

Simeon

Index: main/geometry/inst/polygons2d/closed_path.m
===================================================================
--- main/geometry/inst/polygons2d/closed_path.m    (revision 0)
+++ main/geometry/inst/polygons2d/closed_path.m    (revision 0)
@@ -0,0 +1,118 @@
+%% Copyright (C) 2012 Simeon Simeonov <simeon.simeono...@gmail.com>
+%% 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 program is free software: you can redistribute it and/or modify
+%% it under the terms of the GNU General Public License as published by
+%% the Free Software Foundation, either version 3 of the License, or
+%% (at your option) any later version.
+%%
+%% This program is distributed in the hope that it will be useful,
+%% but WITHOUT ANY WARRANTY; without even the implied warranty of
+%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+%% GNU General Public License for more details.
+
+%% You should have received a copy of the GNU General Public License
+%% along with this program.  If not, see <http://www.gnu.org/licenses/>.
+%%
+%% 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.
+%%
+%% 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 the copyright holders.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {@var{y} =} polygon (@var{x})
+%% Returns a simple closed path that passes through all the points in x.
+%% x is a vector containing 2D coordinates of the points.
+%%
+%% @end deftypefn
+
+%% Author: Simeon Simeonov <simeon.simeono...@gmail.com>
+
+function y = closed_path(x)
+
+if(size(x,1) > 1 && size(x,1) < size(x,2))
+    x = x';
+end
+
+N = size(x,1); % Number of points
+idx = zeros(N, 1); % ind contains the indices of the sorted coordinates
+
+a = find(x(:,2)==min(x(:,2)));
+
+if(size(a,1) > 1)
+    [~, i] = sort(x(a,1));
+    a = a(i(1));
+end
+
+x_1 = x(x(:,2)==x(a,2),:); % find all x with the same y coordinate
+
+if(x(a,1) == min(x(:,1)))
+    x_2 = x(x(:,1)==x(a,1),:); % find all x with the same x coordinate
+else
+   x_2 = x(a,:);
+end
+
+if(size(x_1,1) > 1 || size(x_2,1) > 1)
+    if(size(x_1,1) > 1)
+        x_1 = sort(x_1); % Sort by x coordinate
+        y(1,:) = x(a,:); % original starting point
+    end
+
+    if (size(x_2,1) > 1)
+        x_2 = sort(x_2, 'descend');
+    end
+
+    x_not = [x_1; x_2];
+    i = ismember(x,x_not,'rows');
+    x(i, :) = [];
+    x = [x_1(size(x_1,1),:); x];
+    x_1(size(x_1, 1),:) = [];
+    N = size(x,1);
+    a = 1;
+else
+    x_1 = [];
+    x_2 = x(a,:);
+end
+d = x - repmat(x(a,:), N, 1);
+th = d(:,2)./(d(:,1) + d(:,2));
+
+[~, idx0] = ismember(sort(th(th==0)), th);
+[~, idx1] = ismember(sort(th(th>0)), th);
+[~, idx2] = ismember(sort(th(th<0)), th);
+
+idx = [a; idx0; idx1; idx2];
+% I contains the indices of idx in a sorted order. [v i] = sort(idx) then
+% i==I.
+[~,I,J]= unique(idx);
+if(size(I,1) ~= size(J,1))
+    R = histc(J, 1:size(I,1)); % R(1) will always be 1?
+    idx_sorted = idx(I);
+    r = find(R>1);
+    for ri = r'
+        idx_repeated = idx_sorted(ri);
+        idx(idx==idx_repeated) = find(th==th(idx_sorted(ri)));
+    end
+end
+
+y = [x_1; x(idx,:); x_2;];
+
+endfunction


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