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## Copyright (C) 2024 David Legland
## 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.
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
%
% See also
% polygons2d, polylineLength
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2003-04-06
% Copyright 2003-2023 INRA - TPV URPOI - BIA IMASTE
%% 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
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