The ConvexHull command computes the convex hull of the set of input points.

If points is a Matrix, then each row of points is treated as a point. If it is a list of lists, then each sublist is a point.

All entries of points must evaluate to floating-point values when evalf is applied. This happens as a preprocessing step.

If the option output=volume is specified, the volume of the convex hull is returned. Note that the volume of a 2-D convex hull is its area.

For 2-D inputs, the command returns a list of integer references into the input points list or Matrix defining the convex hull in counterclockwise order.

For 2-D inputs, the command discards duplicate or collinear points.

For 3-D or higher dimensional inputs, the command returns a list of n element lists; each inner list specifies the vertices of a simplicial facet as integer references.

The maximum allowed dimension is 11.

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

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

$\mathrm{xy}≔\left[\left[0\,0\right]\,\left[0\,0\right]\,\left[1\,0\right]\,\left[2\,0\right]\,\left[0\,1\right]\,\left[1\,1\right]\,\left[2\,1\right]\,\left[0\,2\right]\,\left[1\,2\right]\,\left[2\,2\right]\right]$

$\mathrm{xy}≔\left[\left[0\,0\right]\,\left[0\,0\right]\,\left[1\,0\right]\,\left[2\,0\right]\,\left[0\,1\right]\,\left[1\,1\right]\,\left[2\,1\right]\,\left[0\,2\right]\,\left[1\,2\right]\,\left[2\,2\right]\right]$

$\mathrm{ConvexHull}\left(\mathrm{xy}\right)$

$\left[1\,4\,10\,8\right]$

$\mathrm{xyz}≔\left[\left[0\,0\,0\right]\,\left[0\,0\,1\right]\,\left[0\,1\,0\right]\,\left[0\,1\,1\right]\,\left[1\,0\,0\right]\,\left[1\,0\,1\right]\,\left[1\,1\,0\right]\,\left[1\,1\,1\right]\right]$

$\mathrm{xyz}≔\left[\left[0\,0\,0\right]\,\left[0\,0\,1\right]\,\left[0\,1\,0\right]\,\left[0\,1\,1\right]\,\left[1\,0\,0\right]\,\left[1\,0\,1\right]\,\left[1\,1\,0\right]\,\left[1\,1\,1\right]\right]$

$h≔\mathrm{ConvexHull}\left(\mathrm{xyz}\right)$

$h≔\left[\left[7\,3\,1\right]\,\left[5\,7\,1\right]\,\left[6\,5\,1\right]\,\left[2\,6\,1\right]\,\left[6\,7\,5\right]\,\left[7\,6\,8\right]\,\left[3\,4\,1\right]\,\left[4\,2\,1\right]\,\left[7\,4\,3\right]\,\left[4\,7\,8\right]\,\left[4\,6\,2\right]\,\left[6\,4\,8\right]\right]$

$\mathrm{plots}:-\mathrm{display}\left(\mathrm{map}\left(x\mapsto \mathrm{plottools}:-\mathrm{polygon}\left(\mathrm{xyz}\left[x\right]\right)\,h\right)\right)$

$m≔\mathrm{LinearAlgebra}:-\mathrm{RandomMatrix}\left(50\,3\right)$

$h≔\mathrm{ConvexHull}\left(m\right)$

$h≔\left[\left[48\,20\,45\right]\,\left[45\,2\,29\right]\,\left[13\,39\,29\right]\,\left[2\,13\,29\right]\,\left[13\,2\,31\right]\,\left[35\,13\,31\right]\,\left[16\,45\,29\right]\,\left[16\,48\,45\right]\,\left[2\,24\,31\right]\,\left[20\,24\,45\right]\,\left[24\,2\,45\right]\,\left[13\,40\,39\right]\,\left[40\,13\,35\right]\,\left[40\,47\,39\right]\,\left[40\,35\,21\right]\,\left[47\,40\,21\right]\,\left[1\,47\,21\right]\,\left[47\,1\,48\right]\,\left[20\,1\,21\right]\,\left[1\,20\,48\right]\,\left[16\,5\,48\right]\,\left[5\,47\,48\right]\,\left[5\,16\,29\right]\,\left[36\,20\,21\right]\,\left[35\,36\,21\right]\,\left[36\,35\,31\right]\,\left[47\,6\,39\right]\,\left[5\,6\,47\right]\,\left[39\,6\,29\right]\,\left[6\,5\,29\right]\,\left[32\,24\,20\right]\,\left[36\,32\,20\right]\,\left[24\,32\,31\right]\,\left[32\,36\,31\right]\right]$

$\mathrm{plots}:-\mathrm{display}\left(\mathrm{map}\left(x\mapsto \mathrm{plottools}:-\mathrm{polygon}\left(m\left[x\right]\right)\,h\right)\,\mathrm{axes}=\mathrm{none}\right)$

$\mathrm{ConvexHull}\left(m\,\mathrm{output}=\mathrm{volume}\right)$

$4.53480266666666791\times {10}^6$

The ComputationalGeometry[ConvexHull] command was introduced in Maple 2018.

For more information on Maple 2018 changes, see Updates in Maple 2018.