plus

PLUS Minkowski sum of two polytopes

 [R,P,Q] = plus(P,Q,Options)

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 DESCRIPTION
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 R=P+Q, or R=SUM(P,Q) computes Minkowski sum of two polytopes.
 One of the arguments can be a matrix in which case it is interpreted
 as a set of vertices of a polytope (each column is a vertex).
 This is useful for computing Minkowski sum of two polytopes that are
 not of the same dimension.

 NOTE: If Q ia a polyarray, Q=[Q1 Q2 ... Qn], then Q is considered
 as the space covered with polytopes Qi, and the plus.m computes P+Q according
 to the definition P+Q=\{x+y| x\in P and y\in Q\}=[(P+Q1) (P+Q2) ... (P+Qn)] 

 USAGE:
   R=P+Q
   R=plus(P,Q,Options)

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 INPUT
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 P,Q                     - Polytopes or arrays of polytopes
 Options.msolver         - 1=use projection, 2=use vertex based method
 Options.extreme_solver  - Which method to use for extreme points computation
                           (see help extreme)
 Options.lpsolver        - Which 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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 R   - polytope (or polytope array) describing the Minkowski sum
 P,Q - since this algorithm computes extreme points, they can be stored and
       returned back to the user (see help extreme)

 see also MINUS, EXTREME, MLDIVIDE