Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / geometry-1.5.0 / polygons2d / parametrize.m

diff --git a/octave_packages/geometry-1.5.0/polygons2d/parametrize.m b/octave_packages/geometry-1.5.0/polygons2d/parametrize.m
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+%% 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