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# hull

## PURPOSE

HULL Convex hull of n polytopes

## SYNOPSIS

function [P,Pn]=hull(Pn,Options)

## DESCRIPTION

```HULL Convex hull of n polytopes

[P,Pn]=hull(Pn,Options)

---------------------------------------------------------------------------
DESCRIPTION
---------------------------------------------------------------------------
Computes a convex hull of n polytopes given by the polytope array Pn

USAGE:
P = hull([P1 P2 P3])
P = hull(Pn,Options)
[P,Pn] = hull(Pn)
[P,Pn] = hull(Pn,Options)

NOTE:
Convex hull requires computing extreme points, what can be expensive.
Thats why also the second output argument should be always retrieved,
since once the extreme points are computed for the input argument,
they can be stored for future faster calculation
(see help extreme)

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INPUT
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Pn                      - Polytope array
Options.extreme_solver  - Which method to use for vertex enumeration
(0 - brute force enumeration, 3 - CDD)
(see help mpt_init)
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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P     - convex hull of polytopes stored in Pn
Pn    - extreme points have been computed and stored for the input argument

## 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
• extreme EXTREME Calculates extreme points of a given polytope
• hull HULL Convex hull of n polytopes
• isbounded ISBOUNDED Checks if a polytope is bounded
• length LENGTH Returns number of elements in a polytope array
• mpt_error MPT_ERROR Function called if MPT toolbox is not initialized
• mpt_solverInfo MPT_SOLVERINFO returns information about a given solver
• hull HULL Converts vertices/polytope array into an H-representation polytope
This function is called by:
• extreme EXTREME Calculates extreme points of a given polytope
• hull HULL Convex hull of n polytopes
• isconvex ISCONVEX Checks if a polytope array forms a convex union
• merge MERGE merges polytopes together
• plus PLUS Minkowski sum of two polytopes
• polytope POLYTOPE Default constructor for the POLYTOPE object
• projection PROJECTION Projection of a polytope or a polytope array
• triangulate TRIANGULATE Calculates triangulation of arbitrary polytopes
• mpt_feasibleStates MPT_FEASIBLESTATES returns equidistantly spaced data points in feasible set
• mpt_randPWASys MPT_RANDPWASYS generates random PWA systems
• mpt_iterative MPT_ITERATIVE Computes a time-optimal or low-complexity explicit controller for LTI systems
• mpt_simplexContr MPT_SIMPLEXCONTR Computes a piecewise affine feedback law defined over simplices
• mpt_optMerge ===============================================================================
• mpt_optMergeDivCon ===============================================================================
• mpt_control MPT_CONTROL Main control routine. Computes explicit controller for a given problem
• mpt_init MPT_INIT Initializes the MPT toolbox
• mpt_simplify MPT_SIMPLIFY simplifies a given explicit controller by merging regions with identical control law

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