Home > mpt > @polytope > private > chebyball_f.m

# chebyball_f

## PURPOSE

CHEBYBALL_F Computes center and radius of the largest ball inscribed in a polytope

## SYNOPSIS

function [xc,R,lambda] = chebyball_f(H,K,Options)

## DESCRIPTION

```CHEBYBALL_F Computes center and radius of the largest ball inscribed in a polytope

[xc,R,lambda] = chebyball_f(H,K,Options)

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DESCRIPTION
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Returns center and radius of a largest ball that can be inscribed in a polytope P

NOTE: internal routine. Takes matrices H and K as input, not a polytope!

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INPUT
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H,K               - Matrices defining the polytope, i.e. Hx<=K
Options.lpsolver  - LP solver to use (see help mpt_solveLP)

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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xc                - Center of Chebyshev's ball
R                 - Radius of Chebyshev's ball
lambda            - Set of lagrangian multipliers

## 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)
This function is called by:
• and AND Intersection of n polytopes
• dointersect DOINTERSECT Checks if two polytopes / polyarrays intersect
• domain DOMAIN Computes polytope that is mapped to an another polytope using affine map
• envelope ENVELOPE Computes envelope of n polytopes
• extreme EXTREME Calculates extreme points of a given polytope
• intersect INTERSECT Intersection of 2 polytopes or polytope arrays
• le LE Checks if polytope P is a subset of polytope Q
• lt LT Checks if polytope P is a strict subset of polytope Q
• regiondiff REGIONDIFF Region difference
• regiondiffXU REGIONDIFFXU Computes region difference in lifted XU space
• union UNION convex union computation

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