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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 [poly2, keepInds] = simplifyPolyline(poly, tol)
%SIMPLIFYPOLYLINE Douglas-Peucker simplification of a polyline.
%
% POLY2 = simplifyPolyline(POLY, TOL)
% Simplifies the input polyline using the Douglas-Peucker algorithm.
%
% Example
% elli = [20 30 40 20 30];
% poly = ellipseToPolygon(elli, 500);
% poly2 = simplifyPolyline(poly, 1); % use a tolerance equal to 1
% figure; hold on;
% drawEllipse(elli);
% drawPoint(poly2, 'mo');
%
% See also
% polygons2d, simplifyPolygon, resamplePolyline, smoothPolyline
%
% References
% http://en.wikipedia.org/wiki/Ramer-Douglas-Peucker_algorithm
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2012-05-04, using Matlab 7.9.0.529 (R2009b)
% Copyright 2012-2023 INRA - Cepia Software Platform
% number of vertices
n = size(poly, 1);
% initial call to the recursive function
keepInds = recurseSimplify(1, n);
% keep first and last vertices
keepInds = [1 keepInds n];
% create the resulting polyline
poly2 = poly(keepInds, :);
%% Inner function that is called recursively on polyline portions
function innerInds = recurseSimplify(i0, i1)
% find the furthest vertex
mid = furthestPointIndex(i0, i1);
% case of no further simplification
if isempty(mid)
innerInds = mid;
return;
end
% recursively subdivide each portion
mid1 = recurseSimplify(i0, mid);
mid2 = recurseSimplify(mid, i1);
% concatenate indices of all portions
innerInds = [mid1 mid mid2];
end
%% Inner function for finding index of furthest point in POLY
function ind = furthestPointIndex(i0, i1)
% for single edges, return empty result
if i1 - i0 < 2
ind = [];
return;
end
% vertices of the current edge
v0 = poly(i0, :);
v1 = poly(i1, :);
% find vertex with the greatest distance
dists = distancePointEdge(poly(i0+1:i1-1, :), [v0 v1]);
[maxi, ind] = max(dists);
% update index only if distance criterion is verified
if maxi > tol
ind = i0 + ind;
else
ind = [];
end
end
end
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