Code covered by the BSD License

# geom2d

### David Legland (view profile)

13 Jun 2005 (Updated )

Geometry library for matlab. Performs geometric computations on points, lines, circles, polygons...

parametrize(varargin)
```function par = parametrize(varargin)
%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
%
%   polygons2d, polylineLength
%
%   ---------
%   author : David Legland
%   INRA - TPV URPOI - BIA IMASTE
%   created the 06/04/2003.
%

%% Process inputs

% extract vertex coordinates
if size(varargin{1}, 2) > 1
% vertices in a single array
pts = varargin{1};
varargin(1) = [];

elseif length(varargin) == 2
% points as separate arrays
pts = [varargin{1} varargin{2}];
varargin(1:2) = [];

end

% by default, do not normalize
normalize = false;

% extract options
while length(varargin) > 1
param = varargin{1};
switch lower(param)
case 'normalize'
normalize = varargin{2};
otherwise
error('Unknown parameter name: %s', param);
end
varargin(1:2) = [];
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

```