This command finds the highest dimensional face of polyset that contains point.  A point in a set's interior will return polyset, while a point not in the set will return the empty set.

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

$c≔\mathrm{ExampleSets}:-\mathrm{Cube}\left(\right)\;$$\mathrm{origin\_location}≔\mathrm{LocatePoint}\left(\left[0\,0\,0\right]\,c\right)$

$c≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[-x_3\le 1\,x_3\le 1\,-x_2\le 1\,x_2\le 1\,-x_1\le 1\,x_1\le 1\right]\end{array}$

$\mathrm{origin\_location}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[-x_3\le 1\,x_3\le 1\,-x_2\le 1\,x_2\le 1\,-x_1\le 1\,x_1\le 1\right]\end{array}$

$\mathrm{cube\_face}≔\mathrm{LocatePoint}\left(\left[0\,0\,1\right]\,c\right)$

$\mathrm{cube\_face}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[x_3=1\,-x_2\le 1\,x_2\le 1\,-x_1\le 1\,x_1\le 1\right]\end{array}$

$\mathrm{Dimension}\left(\mathrm{cube\_face}\right)$

$2$

$\mathrm{outside\_cube}≔\mathrm{LocatePoint}\left(\left[2\,1\,1\right]\,c\right)$

$\mathrm{outside\_cube}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[0\le \mathrm{-1}\right]\end{array}$

$\mathrm{IsEmpty}\left(\mathrm{outside\_cube}\right)$

$\mathrm{true}$

The PolyhedralSets[LocatePoint] command was introduced in Maple 2015.

For more information on Maple 2015 changes, see Updates in Maple 2015.