parametrize

PARAMETRIZE Parametrization of a polyline, based on edges lengths.

   PAR = parametrize(POLY);
   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.

   PAR = parametrize(PX, PY);
   is the same, but specify points coordinates in separate column vectors.

   PAR = parametrize(..., 'normalize', 1);
   PAR = parametrize(..., 'normalize', true);
   Rescales the result such that the last element of PAR is 1.
 
   Example
     % Parametrize a circle approximation
     poly = circleToPolygon([0 0 1], 200);
     p = parametrize(poly);
     p(end)
     ans = 
         6.2829

   See also:
   polygons2d, polylineLength

   ---------
   author : David Legland
   INRA - TPV URPOI - BIA IMASTE
   created the 06/04/2003.

0001 function par = parametrize(varargin)
0002 %PARAMETRIZE Parametrization of a polyline, based on edges lengths.
0003 %
0004 %   PAR = parametrize(POLY);
0005 %   Returns a parametrization of the curve defined by the serie of points,
0006 %   based on euclidean distance between two consecutive points.
0007 %   POLY is a N-by-2 array, representing coordinates of vertices. The
0008 %   result PAR is N-by-1, and contains the cumulative length of edges until
0009 %   corresponding vertex.
0010 %
0011 %   PAR = parametrize(PX, PY);
0012 %   is the same, but specify points coordinates in separate column vectors.
0013 %
0014 %   PAR = parametrize(..., 'normalize', 1);
0015 %   PAR = parametrize(..., 'normalize', true);
0016 %   Rescales the result such that the last element of PAR is 1.
0017 %
0018 %   Example
0019 %     % Parametrize a circle approximation
0020 %     poly = circleToPolygon([0 0 1], 200);
0021 %     p = parametrize(poly);
0022 %     p(end)
0023 %     ans =
0024 %         6.2829
0025 %
0026 %   See also:
0027 %   polygons2d, polylineLength
0028 %
0029 %   ---------
0030 %   author : David Legland
0031 %   INRA - TPV URPOI - BIA IMASTE
0032 %   created the 06/04/2003.
0033 %
0034 
0035 
0036 %% Process inputs
0037 
0038 % extract vertex coordinates
0039 if size(varargin{1}, 2) > 1
0040     % vertices in a single array
0041     pts = varargin{1};
0042     varargin(1) = [];
0043     
0044 elseif length(varargin) == 2
0045     % points as separate arrays
0046     pts = [varargin{1} varargin{2}];
0047     varargin(1:2) = [];
0048     
0049 end
0050 
0051 % by default, do not normalize
0052 normalize = false;
0053 
0054 % extract options
0055 while length(varargin) > 1
0056     param = varargin{1};
0057     switch lower(param)
0058         case 'normalize'
0059             normalize = varargin{2};
0060         otherwise
0061             error('Unknown parameter name: %s', param);
0062     end
0063     varargin(1:2) = [];
0064 end
0065 
0066 
0067 %% Parametrize polyline
0068 
0069 % compute cumulative sum of euclidean distances between consecutive
0070 % vertices, setting distance of first vertex to 0.
0071 if size(pts, 2) == 2
0072     % process points in 2D
0073     par = [0 ; cumsum(hypot(diff(pts(:,1)), diff(pts(:,2))))];
0074 else
0075     % process points in arbitrary dimension
0076     par = [0 ; cumsum(sqrt(sum(diff(pts).^2, 2)))];
0077 end
0078 
0079 % eventually rescale between 0 and 1
0080 if normalize
0081     par = par / par(end);
0082 end
0083