IsInInterior - Maple Help

PolyhedralSets

 IsInInterior
 test if a polyhedral set is contained in the interior of another

 Calling Sequence IsInInterior(ps1, ps2)

Parameters

 ps1, ps2 - polyhedral sets

Description

 • Returns true if the polyhedral set ps1 is contained in the interior of the highest dimensional face of ps2, that is if ps1 is a subset of ps2 and the intersections between the facets of ps1 and the facets of ps2 are empty.

Examples

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

A small cube resides in the interior of a larger cube.

 > $\mathrm{c_big}≔\mathrm{ExampleSets}:-\mathrm{Cube}\left(\left[-1..1,-1..1,-1..1\right]\right)$
 ${\mathrm{c_big}}{≔}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\mathrm{Relations}}& {:}& \left[{-}{{x}}_{{3}}{\le }{1}{,}{{x}}_{{3}}{\le }{1}{,}{-}{{x}}_{{2}}{\le }{1}{,}{{x}}_{{2}}{\le }{1}{,}{-}{{x}}_{{1}}{\le }{1}{,}{{x}}_{{1}}{\le }{1}\right]\end{array}$ (1)
 > $\mathrm{c_small}≔\mathrm{ExampleSets}:-\mathrm{Cube}\left(\left[-\frac{1}{10}..\frac{1}{10},-\frac{1}{10}..\frac{1}{10},-\frac{1}{10}..\frac{1}{10}\right]\right)$
 ${\mathrm{c_small}}{≔}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\mathrm{Relations}}& {:}& \left[{-}{{x}}_{{3}}{\le }\frac{{1}}{{10}}{,}{{x}}_{{3}}{\le }\frac{{1}}{{10}}{,}{-}{{x}}_{{2}}{\le }\frac{{1}}{{10}}{,}{{x}}_{{2}}{\le }\frac{{1}}{{10}}{,}{-}{{x}}_{{1}}{\le }\frac{{1}}{{10}}{,}{{x}}_{{1}}{\le }\frac{{1}}{{10}}\right]\end{array}$ (2)
 > $\mathrm{IsInInterior}\left(\mathrm{c_small},\mathrm{c_big}\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{Plot}\left(\left[\mathrm{c_big},\mathrm{c_small}\right],\mathrm{faceoptions}=\left[\mathrm{transparency}=\left[0.5,0.\right]\right]\right)$

The empty set is not in the interior of any other set.

 > $\mathrm{IsInInterior}\left(\mathrm{ExampleSets}:-\mathrm{EmptySet}\left(3\right),\mathrm{ExampleSets}:-\mathrm{Cube}\left(\right)\right)$
 ${\mathrm{false}}$ (4)

Compatibility

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