Incidence information

[blegat]

We should overwrite the method that will be defined in JuliaPolyhedra/Polyhedra.jl#67 since CDD has this information.

[oyamad]

What would be the optimal strategy for this? Something like the following?

mutable struct Polyhedron{T<:PolyType} <: Polyhedra.Polyhedron{T}
    ine::Union{Nothing, CDDInequalityMatrix{T}}
    ext::Union{Nothing, CDDGeneratorMatrix{T}}
    poly::Union{Nothing, CDDPolyhedra{T}}
    incidence::Union{Nothing, Vector{BitSet}}  # <- Add new field to store incidence infomation
    hlinearitydetected::Bool
    vlinearitydetected::Bool
    noredundantinequality::Bool
    noredundantgenerator::Bool
end

# Copy incidence information from p.poly to p.incidence
function getincidence(p::Polyhedron)
    poly = getpoly(p)
    p.incidence = poly.inequality ? copyincidence(poly) : copyinputincidence(poly)
end

Then overwrite Base.get(p::Polyhedron{T}, inc::Incident{T, ElemT}; tol) in https://github.com/JuliaPolyhedra/Polyhedra.jl/blob/42ae3253abde94424d10dde44a20a11c3e869d45/src/incidence.jl#L7-L17 by accessing p.incidence?

[blegat]

Yes exactly, that's also how I imagine that this should be done