This command computes the convex hull of a sequence of polyhedral sets, returning the result as a new PolyhedralSet.

The method = hrepresentation option computes the convex hull using the H-Representation of the polyhedral sets, forming their convex hull by accumulating the sets of relations.

The method = vrepresentation option constructs a convex hull using the V-Representation of the polyhedral sets, computing their vertices and rays and combining the results to form a new set.

There is also a ConvexHull command in the ComputationalGeometry package. The Convex Hulls Example Worksheet discusses both commands and the usefulness of each.

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

$\mathrm{tetrahedron}≔\mathrm{PolyhedralSet}\left(\frac{3}{2}\left[\left[1\,1\,1\right]\,\left[1\,-1\,-1\right]\,\left[-1\,1\,-1\right]\,\left[-1\,-1\,1\right]\right]\right)\:$$\mathrm{cube}≔\mathrm{ExampleSets}:-\mathrm{Cube}\left(\right)\:$$\mathrm{Plot}\left(\left[\mathrm{tetrahedron}\,\mathrm{cube}\right]\,\mathrm{faceoptions}=\left[\mathrm{transparency}=\left[0.25\,0.\right]\right]\right)$

$\mathrm{convhull}≔\mathrm{ConvexHull}\left(\mathrm{tetrahedron}\,\mathrm{cube}\right)\:$$\mathrm{Plot}\left(\mathrm{convhull}\right)$

$\mathrm{tetrahedron}\mathbf{subset}\mathrm{convhull}$

$\mathrm{true}$

$\mathrm{cube}\mathbf{subset}\mathrm{convhull}$

$\mathrm{true}$

$\mathrm{triangle}≔\mathrm{PolyhedralSet}\left(\left[0\le x\,0\le y\,x+y\le 1\,z=0\right]\right)\:$$\mathrm{pnt}≔\mathrm{PolyhedralSet}\left(\left[\left[0\,0\,1\right]\right]\,\left[x\,y\,z\right]\right)\:$$\mathrm{Plot}\left(\left[\mathrm{triangle}\,\mathrm{pnt}\right]\,\mathrm{orientation}=\left[-30\,70\,0\right]\right)$

$\mathrm{tetra}≔\mathrm{ConvexHull}\left(\mathrm{pnt}\,\mathrm{triangle}\right)\;$$\mathrm{Plot}\left(\mathrm{tetra}\,\mathrm{orientation}=\left[-30\,70\,0\right]\right)$

$\mathrm{tetra}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x\,y\,z\right]\\ \mathrm{Relations}& \:& \left[-z\le 0\,z\le 1\,-y\le 0\,-x\le 0\,x+y+z\le 1\right]\end{array}$

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

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