--- /dev/null
+%% Copyright (c) 2012 Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%%
+%% This program is free software: you can redistribute it and/or modify
+%% it under the terms of the GNU General Public License as published by
+%% the Free Software Foundation, either version 3 of the License, or
+%% any later version.
+%%
+%% This program is distributed in the hope that it will be useful,
+%% but WITHOUT ANY WARRANTY; without even the implied warranty of
+%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+%% GNU General Public License for more details.
+%%
+%% You should have received a copy of the GNU General Public License
+%% along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {[@var{pline2} @var{idx}] = } simplifypolyline (@var{pline})
+%% @deftypefnx {Function File} {@dots{} = } simplifypolyline (@dots{},@var{property},@var{value},@dots{})
+%% Simplify or subsample a polyline using the Ramer-Douglas-Peucker algorithm,
+%% a.k.a. the iterative end-point fit algorithm or the split-and-merge algorithm.
+%%
+%% The @var{pline} as a N-by-2 matrix. Rows correspond to the
+%% verices (compatible with @code{polygons2d}). The vector @var{idx} constains
+%% the indexes on vetices in @var{pline} that generates @var{pline2}, i.e.
+%% @code{pline2 = pline(idx,:)}.
+%%
+%% @strong{Parameters}
+%% @table @samp
+%% @item 'Nmax'
+%% Maximum number of vertices. Default value @code{1e3}.
+%% @item 'Tol'
+%% Tolerance for the error criteria. Default value @code{1e-4}.
+%% @item 'MaxIter'
+%% Maximum number of iterations. Default value @code{10}.
+%% @item 'Method'
+%% Not implemented.
+%% @end table
+%%
+%% Run @code{demo simplifypolyline} to see an example.
+%%
+%% @seealso{curve2polyline, curveval}
+%% @end deftypefn
+
+function [pline idx] = simplifypolyline (pline_o, varargin)
+%% TODO do not print warnings if user provided Nmax or MaxIter.
+
+ # --- Parse arguments --- #
+ parser = inputParser ();
+ parser.FunctionName = "simplifypolyline";
+ parser = addParamValue (parser,'Nmax', 1e3, @(x)x>0);
+ toldef = 1e-4;%max(sumsq(diff(pline_o),2))*2;
+ parser = addParamValue (parser,'Tol', toldef, @(x)x>0);
+ parser = addParamValue (parser,'MaxIter', 100, @(x)x>0);
+ parser = parse(parser,varargin{:});
+
+ Nmax = parser.Results.Nmax;
+ tol = parser.Results.Tol;
+ MaxIter = parser.Results.MaxIter;
+
+ clear parser toldef
+ msg = ["simplifypolyline: Maximum number of points reached with maximum error %g." ...
+ " Increase %s if the result is not satisfactory."];
+ # ------ #
+
+ [N dim] = size(pline_o);
+ idx = [1 N];
+
+ for iter = 1:MaxIter
+ % Find the point with the maximum distance.
+ [dist ii] = maxdistance (pline_o, idx);
+
+ tf = dist > tol;
+ n = sum(tf);
+ if all(!tf);
+ break;
+ end
+
+ idx(end+1:end+n) = ii(tf);
+ idx = sort(idx);
+
+ if length(idx) >= Nmax
+ %% TODO remove extra points
+ warning('geometry:MayBeWrongOutput', sprintf(msg,max(dist),'Nmax'));
+ break;
+ end
+
+ end
+ if iter == MaxIter
+ warning('geometry:MayBeWrongOutput', sprintf(msg,max(dist),'MaxIter'));
+ end
+
+ pline = pline_o(idx,:);
+endfunction
+
+function [dist ii] = maxdistance (p, idx)
+
+ %% Separate the groups of points according to the edge they can divide.
+ func = @(x,y) x:y;
+ idxc = arrayfun (func, idx(1:end-1), idx(2:end), "UniformOutput",false);
+ points = cellfun (@(x)p(x,:), idxc, "UniformOutput",false);
+
+ %% Build the edges
+ edges = [p(idx(1:end-1),:) p(idx(2:end),:)];
+ edges = mat2cell (edges, ones(1,size(edges,1)), 4)';
+
+ %% Calculate distance between the points and the corresponding edge
+ [dist ii] = cellfun(@dd, points,edges,idxc);
+
+endfunction
+
+function [dist ii] = dd (p,e,idx)
+ [d pos] = distancePointEdge(p,e);
+ [dist ii] = max(d);
+ ii = idx(ii);
+endfunction
+
+%!demo
+%! t = linspace(0,1,100).';
+%! y = polyval([1 -1.5 0.5 0],t);
+%! pline = [t y];
+%!
+%! figure(1)
+%! clf
+%! plot (t,y,'-r;Original;','linewidth',2);
+%! hold on
+%!
+%! tol = [8 2 1 0.5]*1e-2;
+%! colors = jet(4);
+%!
+%! for i=1:4
+%! pline_ = simplifypolyline(pline,'tol',tol(i));
+%! msg = sprintf('-;%g;',tol(i));
+%! h = plot (pline_(:,1),pline_(:,2),msg);
+%! set(h,'color',colors(i,:),'linewidth',2,'markersize',4);
+%! end
+%! hold off
+%!
+%! % ---------------------------------------------------------
+%! % Four approximations of the initial polyline with decreasing tolerances.
+
+%!demo
+%! P = [0 0; 3 1; 3 4; 1 3; 2 2; 1 1];
+%! func = @(x,y) linspace(x,y,5);
+%! P2(:,1) = cell2mat( ...
+%! arrayfun (func, P(1:end-1,1),P(2:end,1), ...
+%! 'uniformoutput',false))'(:);
+%! P2(:,2) = cell2mat( ...
+%! arrayfun (func, P(1:end-1,2),P(2:end,2), ...
+%! 'uniformoutput',false))'(:);
+%!
+%! P2s = simplifypolyline (P2);
+%!
+%! plot(P(:,1),P(:,2),'s',P2(:,1),P2(:,2),'o',P2s(:,1),P2s(:,2),'-ok');
+%!
+%! % ---------------------------------------------------------
+%! % Simplification of a polyline in the plane.
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff