This command computes an interior point of the highest dimensional face for the given polyhedral set polyset.  If polyset is of lower dimension than its ambient space, then the point lies on the boundary of polyset, but the point is not an extreme point of the set.

The command returns NULL if there are no interior points in polyset. In other words, if polyset is a vertex or an empty set.  Otherwise, the command returns a list of rationals representing a point in polyset's coordinate space.

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

$c≔\mathrm{ExampleSets}:-\mathrm{Cube}\left(\right)\:$$p≔\mathrm{InteriorPoint}\left(c\right)$

$p≔\left[0\,0\,0\right]$

$\mathrm{triangle}≔\mathrm{PolyhedralSet}\left(\left[z=1\,-1\le y\,-1\le x\,x\le -y+1\right]\,\left[x\,y\,z\right]\right)$

$\mathrm{triangle}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x\,y\,z\right]\\ \mathrm{Relations}& \:& \left[z=1\,-y\le 1\,-x\le 1\,x+y\le 1\right]\end{array}$

$p≔\mathrm{InteriorPoint}\left(\mathrm{triangle}\right)$

$p≔\left[0\,0\,1\right]$

$\mathrm{face\_with\_p}≔\mathrm{LocatePoint}\left(p\,\mathrm{triangle}\right)$

$\mathrm{face\_with\_p}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x\,y\,z\right]\\ \mathrm{Relations}& \:& \left[z=1\,-y\le 1\,-x\le 1\,x+y\le 1\right]\end{array}$

$\mathrm{Dimension}\left(\mathrm{face\_with\_p}\right)$

$2$

$\mathrm{nops}\left(\mathrm{Coordinates}\left(\mathrm{face\_with\_p}\right)\right)$

$3$

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

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