/usr/share/octave/packages/geometry-1.7.0/polygons2d/parametrize.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## 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
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## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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## -*- 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
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