compute convex hull of a set of points in n dimensions
a list of n element lists or an m by n Matrix representing m n-dimensional points
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 ConvexHulls command in the PolyhedralSets package. The Convex Hulls Example Worksheet discusses both commands and the usefulness of each.
xy ≔ 0,0,0,0,1,0,2,0,0,1,1,1,2,1,0,2,1,2,2,2
Note that xy contains duplicate and collinear points
Convex hull of the unit cube.
xyz ≔ 0,0,0,0,0,1,0,1,0,0,1,1,1,0,0,1,0,1,1,1,0,1,1,1
h ≔ ConvexHull⁡xyz
Convex hull of 50 random points in 3-D.
m ≔ LinearAlgebra:-RandomMatrix⁡50,3
h ≔ ConvexHull⁡m
The ComputationalGeometry[ConvexHull] command was introduced in Maple 2018.
For more information on Maple 2018 changes, see Updates in Maple 2018.
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