Bloating

Bloating

LazySets.Bloating — Type.
Bloating{N<:AbstractFloat, S<:LazySet{N}} <:LazySet{N}

Type that represents a uniform expansion of a convex set in a given norm (also known as bloating).

Fields

  • X – convex set
  • ε – (positive) bloating factor
  • p – $p$-norm ($≥ 1$; default: $2$)

Notes

Bloating(X, ε, p) is equivalent to the Minkowski sum of X and a ball in the p-norm of radius ε centered in the origin O (i.e., X ⊕ Ballp(p, O, ε)).

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LazySets.dim — Method.
dim(B::Bloating)

Return the dimension of a bloated convex set.

Input

  • B – bloated convex set

Output

The ambient dimension of the bloated set.

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LazySets.σ — Method.
σ(d::AbstractVector{N}, B::Bloating{N}) where {N<:AbstractFloat}

Return the support vector of a bloated convex set in a given direction.

Input

  • d – direction
  • B – bloated convex set

Output

The support vector of the bloated set in the given direction.

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LazySets.ρ — Method.
ρ(d::AbstractVector{N}, B::Bloating{N}) where {N<:AbstractFloat}

Return the support function of a bloated convex set in a given direction.

Input

  • d – direction
  • B – bloated convex set

Output

The support function of the bloated set in the given direction.

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LazySets.isbounded — Method.
isbounded(B::Bloating)

Determine whether a bloated convex set is bounded.

Input

  • B – bloated convex set

Output

true iff the wrapped set is bounded.

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Base.isempty — Method.
isempty(B::Bloating)

Determine whether a bloated convex set is empty.

Input

  • B – bloated convex set

Output

true iff the wrapped set is empty.

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LazySets.an_element — Method.
an_element(B::Bloating)

Return some element of a bloated convex set.

Input

  • B – bloated convex set

Output

An element in the bloated convex set.

Algorithm

The implementation returns the result of an_element for the wrapped set.

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