Find the closest pair of points in L using the classic divide and conquer approach. The answer is returned as an expression sequence with two elements: the distance between a closest pair, and a list with the indices of a pair of points that are closest.

A value n can be given with the cutoff option to customize when the algorithm switches to a brute force search. The default value of 6 has been found to work very well in most cases. A value greater than half the number of points in L will cause the command to work entirely by brute force search.

Setting the infolevel of CompGeomPlot to 4 will cause the command to display a graphical trace of the computation.

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

$\mathrm{ClosestPointPair}\left(\left[\left[0\,1\right]\,\left[2\,2\right]\,\left[1\,1\right]\,\left[4\,4\right]\right]\right)$

$1,\left[1\,3\right]$

$L≔\left[\mathrm{seq}\left(\mathrm{seq}\left(\mathrm{seq}\left(\left[i\,j\,k\right]\,i=0..4\,0.25\right)\,j=0..4\,0.25\right)\,k=0..4\,0.25\right)\,\left[1.85\,1.85\,1.85\right]\right]\:$

$d,p≔\mathrm{ClosestPointPair}\left(L\right)$

$d,p≔0.1732050808,\left[2150\,4914\right]$

$L\left[p\left[1\right]\right],L\left[p\left[2\right]\right]$

$\left[1.75\,1.75\,1.75\right],\left[1.85\,1.85\,1.85\right]$

The ComputationalGeometry[ClosestPointPair] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.