--- a/main/geometry/NEWS	Sun Apr 15 11:00:12 2012 +0000
+++ b/main/geometry/NEWS	Sun Apr 15 11:23:54 2012 +0000
@@ -9,6 +9,11 @@
  - curve2polyline.m: Converts a polynomial curve into a polyline by the adaptive
                      sampling method.
 
+* Changed functions
+ - distancePointEdge.m: Now the function computes the distance between all points
+                        and all edges. A third optional argument provides
+                        backward compatibility.
+
 * Known issues
  - simplifypolygon.m returns empty polygons when points are repeated, i.e when
   the polygon is not correctly formed.

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main/geometry/inst/polygons2d/simplifypolyline.m	Sun Apr 15 11:23:54 2012 +0000
@@ -0,0 +1,129 @@
+%% Copyright (c) 2012 Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%%
+%%    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
+%%    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/>.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {[@var{pline2} @var{idx}] = } simplifypolyline (@var{pline})
+%% @deftypefnx {Function File} {@dots{} = } simplifypolyline (@dots{},@var{property},@var{value},@dots{})
+%% Simplify or subsample a polyline using the Ramer-Douglas-Peucker algorithm,
+%% a.k.a. the iterative end-point fit algorithm or the split-and-merge algorithm.
+%%
+%% The @var{pline} as a N-by-2 matrix. Rows correspond to the
+%% verices (compatible with @code{polygons2d}). The vector @var{idx} constains
+%% the indexes on vetices in @var{pline} that generates @var{pline2}, i.e.
+%% @code{pline2 = pline(idx,:)}.
+%%
+%% @strong{Parameters}
+%% @table @samp
+%% @item 'Nmax'
+%% Maximum number of vertices. Default value @code{100}.
+%% @item 'Tol'
+%% Tolerance for the error criteria. Default value @code{1e-4}.
+%% @item 'MaxIter'
+%% Maximum number of iterations. Default value @code{10}.
+%% @item 'Method'
+%% Not implemented.
+%% @end table
+%%
+%% Run @code{demo simplifypolyline} to see an example.
+%%
+%% @seealso{curve2polyline, curveval}
+%% @end deftypefn
+
+function [pline idx] = simplifypolyline (pline_o, varargin)
+
+  # --- Parse arguments --- #
+  parser = inputParser ();
+  parser.FunctionName = "simplifypolyline";
+  parser = addParamValue (parser,'Nmax', 100, @(x)x>0);
+  parser = addParamValue (parser,'Tol', 1e-4, @(x)x>0);
+  parser = addParamValue (parser,'MaxIter', 100, @(x)x>0);
+  parser = parse(parser,varargin{:});
+
+  Nmax      = parser.Results.Nmax;
+  tol       = parser.Results.Tol;
+  MaxIter   = parser.Results.MaxIter;
+
+  clear parser
+  msg = ["Maximum number of points reached with maximal error %g." ...
+       " Increase '%s' if the result is not satisfactory."];
+  # ------ #
+
+  [N dim] = size(pline_o);
+  idx = [1 N];
+
+  for iter = 1:MaxIter
+    % Find the point with the maximum distance.
+    [dist ii] = maxdistance (pline_o, idx);
+
+    if dist < tol;
+      break;
+    end
+
+    idx(end+1) = ii;
+    idx = sort(idx);
+
+    if length(idx) >= Nmax
+      warning('geometry:MayBeWrongOutput', sprintf(msg,dist,'Nmax'));
+      break;
+    end
+
+  end
+  if iter == MaxIter
+    warning('geometry:MayBeWrongOutput', sprintf(msg,dist,'MaxIter'));
+  end
+
+  pline = pline_o(idx,:);
+endfunction
+
+function [dist ii] = maxdistance (p,idx)
+
+  edges = [p(idx(1:end-1),:) p(idx(2:end),:)];
+  %% Calculate distance between all points and edges
+  %% What is better? this or a only comparing the points that are between the extrema
+  %% of each edge.
+  [d pos] = distancePointEdge (p, edges);
+
+  %% Filter out all points outside the edges
+  tf = pos == 0 | pos == 1;
+  d(tf) = -1;
+
+  [dist j] = max(d(:));
+  ii = ind2sub (size(d),j);
+
+end
+
+%!demo
+%! t     = linspace(0,1,100).';
+%! y     = polyval([1 -1.5 0.5 0],t);
+%! pline = [t y];
+%!
+%! figure(1)
+%! clf
+%! plot (t,y,'-r;Original;','linewidth',2);
+%! hold on
+%!
+%! tol    = [8 2  1 0.5]*1e-2;
+%! colors = jet(4);
+%!
+%! for i=1:4
+%!   pline_ = simplifypolyline(pline,'tol',tol(i));
+%!   msg = sprintf('-;%g;',tol(i));
+%!   h = plot (pline_(:,1),pline_(:,2),msg);
+%!   set(h,'color',colors(i,:),'linewidth',2,'markersize',4);
+%! end
+%! hold off
+%!
+%! % ---------------------------------------------------------
+%! % Four approximations of the initial polyline with decreasing tolerances.