--- /dev/null
+%% Copyright (C) 2003-2011 David Legland <david.legland@grignon.inra.fr>
+%% Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%% 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.
+%%
+%% 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{par} = } parametrize (@var{poly})
+%% @deftypefnx {Function File} {@var{par} = } parametrize (@var{px},@var{py})
+%% @deftypefnx {Function File} {@var{par} = } parametrize (@dots{},@var{normalize})
+%%
+%% Parametrization of a curve, based on edges length
+%%
+%% Returns a parametrization of the curve defined by the serie of points,
+%% based on euclidean distance between two consecutive points.
+%% POLY is a N-by-2 array, representing coordinates of vertices. The
+%% result PAR is N-by-1, and contains the cumulative length of edges until
+%% corresponding vertex. The function also accepts the polygon as two inputs
+%% @var{px} and @var{py} representinx coordinates x and y respectively.
+%% When optional argument @var{normalize} is non-empty @var{par} is rescaled
+%% such that the last element equals 1, i.e. @code{@var{par}(end)==1}.
+%%
+%% Example
+%% @example
+%% % Parametrize a circle approximation
+%% poly = circleToPolygon([0 0 1], 200);
+%% p = parametrize(poly);
+%% p(end)
+%% ans =
+%% 6.2829
+%% p = parametrize(poly,'norm');
+%% p(end)
+%% ans =
+%% 1
+%% p = parametrize(poly,true);
+%% p(end)
+%% ans =
+%% 1
+%% @end example
+%%
+%% @seealso{polygons2d, polylineLength}
+%% @end deftypefn
+function par = parametrize(varargin)
+ %% Process inputs
+
+ % extract vertex coordinates
+ if size(varargin{1}, 2) > 1
+ % vertices in a single array
+ pts = varargin{1};
+ normalize = numel(varargin) > 1;
+ elseif size(varargin{1}, 2) == 1 && numel(varargin) >= 2
+ % points as separate arrays
+ pts = [varargin{1} varargin{2}];
+ normalize = numel(varargin) > 2;
+ end
+
+ %% Parametrize polyline
+
+ % compute cumulative sum of euclidean distances between consecutive
+ % vertices, setting distance of first vertex to 0.
+ if size(pts, 2) == 2
+ % process points in 2D
+ par = [0 ; cumsum(hypot(diff(pts(:,1)), diff(pts(:,2))))];
+ else
+ % process points in arbitrary dimension
+ par = [0 ; cumsum(sqrt(sum(diff(pts).^2, 2)))];
+ end
+
+ % eventually rescale between 0 and 1
+ if normalize
+ par = par / par(end);
+ end
+
+endfunction