Home > mpt > @polytope > facetcircle.m

# facetcircle

## PURPOSE

FACETCIRCLE Returns largest circle inside facet 'ind' of polytope P

## SYNOPSIS

function [x,R]=facetcircle(P,ind,Options)

## DESCRIPTION

```FACETCIRCLE Returns largest circle inside facet 'ind' of polytope P

[x,R]=facetcircle(P,ind,Options);

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DESCRIPTION
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Given the polyhedron P={Hx<=K}, returns the center x and the radius R of the
largest circle inside facet 'ind' of P. Note that R indicates how 'small' the
facet 'ind' is, while x is a good 'center' for this facet. This corresponds to
the chebychev ball in lower dimensional stpace. The routine returns R<0 if
facet 'ind' is "empty", i.e. the facet is redundant.

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INPUT
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P                - Polytope
ind              - index of facet, or vector of indices of facets
Options.lpsolver - LP solver to use (see help mpt_solveLP)
Options.abs_tol  - absolute tolerance
Options.verbose  - level of verbosity

Note: If Options is missing or some of the fields are not defined, the default
values from mptOptions will be used

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OUTPUT
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x, R   -  Center and radius of the largest circle inside the given facet

## CROSS-REFERENCE INFORMATION

This function calls:
• length LENGTH Returns number of regions over which the explicit control law is defined
• end END Returns the last element in a given polytope array
• length LENGTH Returns number of elements in a polytope array
• size SIZE Returns size of the given polytope object
• mpt_solveLPs MPT_SOLVELPS Interface to various LP solvers ("safe" version)
• mpt_solverInfo MPT_SOLVERINFO returns information about a given solver
This function is called by:
• mpt_greedyMerging MPT_GREEDYMERGING Greedy merging of polyhedra
• mpt_mplp_ver1 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver2 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver3 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver4 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver5 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver7 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_optInfControl MPT_OPTINFCONTROL Solves the infinite-time constrained optimal control problem for LTI systems
• mpt_mpqp MPT_MPQP Explicitly solves the given quadratic program (QP)

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