The SimpleClosedPath command returns a list of indices of the points in P so that they form a non-self-intersecting polygon in counterclockwise orientation.

The algorithm starts with an anchor point a and sorts the remaining points by the angle of the segment they form with a. The angle is not computed explicitly, but rather PointOrientation is used to determine the order implicitly.

$\mathrm{with}\left(\mathrm{ComputationalGeometry}\right)\:$

$P≔\left[\left[0.17\,0.13\right]\,\left[0.39\,0.74\right]\,\left[0.76\,0.68\right]\,\left[0.93\,0.85\right]\,\left[0.036\,0.66\right]\,\left[0.96\,0.79\right]\,\left[0.92\,0.42\right]\,\left[0.14\,0.80\right]\,\left[0.48\,0.96\right]\,\left[0.97\,0.16\right]\,\left[0.96\,0.96\right]\,\left[0.55\,0.28\right]\,\left[0.098\,0.63\right]\,\left[0.91\,0.13\right]\,\left[0.91\,0.82\right]\right]$

$P≔\left[\left[0.17\,0.13\right]\,\left[0.39\,0.74\right]\,\left[0.76\,0.68\right]\,\left[0.93\,0.85\right]\,\left[0.036\,0.66\right]\,\left[0.96\,0.79\right]\,\left[0.92\,0.42\right]\,\left[0.14\,0.80\right]\,\left[0.48\,0.96\right]\,\left[0.97\,0.16\right]\,\left[0.96\,0.96\right]\,\left[0.55\,0.28\right]\,\left[0.098\,0.63\right]\,\left[0.91\,0.13\right]\,\left[0.91\,0.82\right]\right]$

$\mathrm{plots}:-\mathrm{polygonplot}\left(P\,\mathrm{style}=\mathrm{line}\right)$

$\mathrm{path}≔\mathrm{SimpleClosedPath}\left(P\right)$

$\mathrm{path}≔\left[1\,14\,10\,7\,12\,6\,3\,15\,4\,11\,9\,2\,8\,13\,5\right]$

$\mathrm{plots}:-\mathrm{polygonplot}\left(\left[\mathrm{seq}\left(P\left[i\right]\,i\mathbf{in}\mathrm{path}\right)\right]\,\mathrm{style}=\mathrm{line}\right)$

$\mathrm{ch}≔\mathrm{ConvexHull}\left(P\right)$

$\mathrm{ch}≔\left[10\,11\,9\,8\,5\,1\,14\right]$

$M≔\mathrm{plots}:-\mathrm{display}\left(\mathrm{Matrix}\left(2\,4\,\left[\mathrm{seq}\left(\mathrm{plots}:-\mathrm{polygonplot}\left(\left[\mathrm{seq}\left(P\left[i\right]\,i\mathbf{in}\mathrm{SimpleClosedPath}\left(P\,c\right)\right)\right]\,'\mathrm{color}'=c\,'\mathrm{scaling}'='\mathrm{constrained}'\,'\mathrm{title}'=\mathrm{cat}\left(''anchor=''\,c\right)\right)\,c\mathbf{in}\mathrm{ch}\right)\,'\mathrm{INTERFACE\_PLOT}\left(\mathrm{AXESSTYLE}\left(\mathrm{NONE}\right)\right)'\right]\right)\right)$

The ComputationalGeometry[SimpleClosedPath] command was introduced in Maple 2023.

For more information on Maple 2023 changes, see Updates in Maple 2023.