: [pline2 idx] = simplifyPolyline_geometry (pline)
: … = simplifyPolyline_geometry (…,property,value,…)

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 pline as a N-by-2 matrix. Rows correspond to the verices (compatible with polygons2d). The vector idx constains the indexes on vetices in pline that generates pline2, i.e. pline2 = pline(idx,:).

Parameters

‘'Nmax'’

Maximum number of vertices. Default value 1e3.

‘'Tol'’

Tolerance for the error criteria. Default value 1e-4.

‘'MaxIter'’

Maximum number of iterations. Default value 10.

‘'Method'’

Not implemented.

Run demo simplifyPolyline_geometry to see an example.

See also: curve2polyline, curveval, simplifyPolygon_geometry.

Demonstration 1

The following code

 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_geometry(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.

Produces the following figure

Figure 1

Demonstration 2

The following code

 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_geometry (P2);

 plot(P(:,1),P(:,2),'s',P2(:,1),P2(:,2),'o',P2s(:,1),P2s(:,2),'-ok');

 # ---------------------------------------------------------
 # Simplification of a polyline in the plane.

Produces the following figure

Figure 1

Package: geometry