Multi-Parametric Toolbox Polytope library
Version 2.6 (R14SP3) 30-Mar-2006
Constructor and data accessing methods
polytope - Default constructor for polytope objects
double - Function used to access internal properties of the given polytope
display - Displays details about the given polytope
isbounded - Checks if a polytope is bounded
isconvex - Checks if a polytope array forms a convex union
isfulldim - Checks if a polytope is full dimensional
isinside - Checks if a given point lies in the interior of a given polytope
isminrep - Checks if a given polytope is in minimal representation
isnormal - Checks if a given polytope is in normalized description
dimension - Returns dimension of the given polytope
nconstr - Returns number of constraints that form an H-representation of a polytope
length - Returns number of elements in a polytope array
size - Returns size of the given polytope object
get - Get polytope properties
set - Used to modify internal properties of a given polytope object
Computational geometry functions
bounding_box - Compute a bounding box for a given polytope
domain - Computes polytope that is mapped to an another polytope using affine map
envelope - Computes envelope of n polytopes
extreme - Calculates extreme points of a given polytope
facetvoronoi - Calculates a "voronoi diagram for facets of a polytope"
hull - Convex hull of n polytopes
intersect - Intersection of 2 polytopes
plus - Minkowski sum
minus - Pontryagin difference
mldivide - Set difference
mtimes - Polytope multiplication
projection - Projection of a polytope or a polytope array
range - Affine transformation of a polytope
regiondiff - Region difference
regiondiffXU - Computes region difference in lifted XU space
slice - Orthogonal cut through polytope(s)
triangulate - Calculates triangulation of arbitrary polytopes
union - convex union computation
Overloaded relational operators
eq - Checks if two polytopes are equal (==)
ge - Checks if polytope P is a superset of polytope Q (>=)
gt - Checks if polytope P is a strict superset of polytope Q (>)
le - Checks if polytope P is a subset of polytope Q (<=)
lt - Checks if polytope P is a strict subset of polytope Q (<)
ne - Checks if two polytopes are not equal (~=)
Basic polytope functions
chebyball - Computes center and radius of the largest ball inscribed in a polytope
normalize - Normalizes a given polytope
reduce - Reduces the polytope by removing redundant inequalities
isredundant - Check if a constraint is redundant
plot - Plots polytope(s)
Other overloaded operators and functions
and - Intersection of n polytopes (&)
or - Convex union of n polytopes (|)
plus - Minkowski sum (+)
minus - Pontryagin difference (-)
mldivide - Set difference (\)
mtimes - Polytope multiplication (*)
uminus - Unary minus for a polytope (flips given polytope around the origin)
uplus - Unary plus for a polytope (reduces the given polytope)
horzcat - Concatenates polytopes into a polytope array [,]
vertcat - Concatenates polytopes into a polytope array [;]
end - Returns the last element in a given polytope array
fliplr - Flips array of polytopes
flipud - Flips array of polytopes
subsasgn - Indexed assignments for polytope objects
subsref - Indexed referencing for polytope objects
Other functions
distribpoints - Distribute n points such that distances between them are maximized
facetcircle - Returns largest circle inside facet 'ind' of polytope P
pelemfun - Execute an arbitrary function on each element of a polyarray
reduceunion - Removes some redundant elements from a polytope array
unique - Keeps only unique elements of a polytope array
volume - Calculates volume of a polytope
see help mpt
Authors: Michal Kvasnica, Pascal Grieder, Mato Baotic
kvasnica@control.ee.ethz.ch, grieder@control.ee.ethz.ch, baotic@control.ee.ethz.ch
For support, write to: mpt@control.ee.ethz.ch