AffineHull - Maple Help

PolyhedralSets

 AffineHull
 affine hull of a polyhedral set

 Calling Sequence AffineHull(polyset)

Parameters

 polyset - polyhedral set

Description

 • This command computes the affine hull for the given polyhedral set polyset, returning the result as a new PolyhedralSet.
 • The affine hull of a line segment is the whole line and that of a 2-D face in a 3-D space is the plane containing the face.

Examples

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

Construct a 2-D triangle in 3-D space

 > $\mathrm{ps1}≔\mathrm{PolyhedralSet}\left(\left[\left[1,0,0\right],\left[0,1,0\right],\left[0,0,1\right]\right]\right)$
 ${\mathrm{ps1}}{≔}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\mathrm{Relations}}& {:}& \left[{-}{{x}}_{{3}}{\le }{0}{,}{-}{{x}}_{{2}}{\le }{0}{,}{{x}}_{{2}}{+}{{x}}_{{3}}{\le }{1}{,}{{x}}_{{1}}{+}{{x}}_{{2}}{+}{{x}}_{{3}}{=}{1}\right]\end{array}$ (1)

Compute its affine hull, which is the plane passing through all of its vertices

 > $\mathrm{aff_ps1}≔\mathrm{AffineHull}\left(\mathrm{ps1}\right)$
 ${\mathrm{aff_ps1}}{≔}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\mathrm{Relations}}& {:}& \left[{{x}}_{{1}}{+}{{x}}_{{2}}{+}{{x}}_{{3}}{=}{1}\right]\end{array}$ (2)
 > $\mathrm{Plot}\left(\left[\mathrm{ps1},\mathrm{aff_ps1}\right]\right)$

The affine hull of an empty set is also an empty set

 > $\mathrm{ps2}≔\mathrm{PolyhedralSet}\left(\left[1\le 0\right],\left[x\right]\right):$$\mathrm{aff_ps2}≔\mathrm{AffineHull}\left(\mathrm{ps2}\right)$
 ${\mathrm{aff_ps2}}{≔}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{x}\right]\\ {\mathrm{Relations}}& {:}& \left[{0}{\le }{-1}\right]\end{array}$ (3)
 > $\mathrm{IsEmpty}\left(\mathrm{ps2}\right)$
 ${\mathrm{true}}$ (4)

Compatibility

 • The PolyhedralSets[AffineHull] command was introduced in Maple 2015.