1 %% Copyright (C) 2003-2011 David Legland <david.legland@grignon.inra.fr>
2 %% Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
3 %% All rights reserved.
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30 %% @deftypefn {Function File} {@var{par} = } parametrize (@var{poly})
31 %% @deftypefnx {Function File} {@var{par} = } parametrize (@var{px},@var{py})
32 %% @deftypefnx {Function File} {@var{par} = } parametrize (@dots{},@var{normalize})
34 %% Parametrization of a curve, based on edges length
36 %% Returns a parametrization of the curve defined by the serie of points,
37 %% based on euclidean distance between two consecutive points.
38 %% POLY is a N-by-2 array, representing coordinates of vertices. The
39 %% result PAR is N-by-1, and contains the cumulative length of edges until
40 %% corresponding vertex. The function also accepts the polygon as two inputs
41 %% @var{px} and @var{py} representinx coordinates x and y respectively.
42 %% When optional argument @var{normalize} is non-empty @var{par} is rescaled
43 %% such that the last element equals 1, i.e. @code{@var{par}(end)==1}.
47 %% % Parametrize a circle approximation
48 %% poly = circleToPolygon([0 0 1], 200);
49 %% p = parametrize(poly);
53 %% p = parametrize(poly,'norm');
57 %% p = parametrize(poly,true);
63 %% @seealso{polygons2d, polylineLength}
65 function par = parametrize(varargin)
68 % extract vertex coordinates
69 if size(varargin{1}, 2) > 1
70 % vertices in a single array
72 normalize = numel(varargin) > 1;
73 elseif size(varargin{1}, 2) == 1 && numel(varargin) >= 2
74 % points as separate arrays
75 pts = [varargin{1} varargin{2}];
76 normalize = numel(varargin) > 2;
79 %% Parametrize polyline
81 % compute cumulative sum of euclidean distances between consecutive
82 % vertices, setting distance of first vertex to 0.
84 % process points in 2D
85 par = [0 ; cumsum(hypot(diff(pts(:,1)), diff(pts(:,2))))];
87 % process points in arbitrary dimension
88 par = [0 ; cumsum(sqrt(sum(diff(pts).^2, 2)))];
91 % eventually rescale between 0 and 1