Why are vertices of every LazySets.VPolygon or VPolytope given as 1 D Array and not based on the shape of the object?

A = rand(HPolyhedron,dim=3)
Av = tovrep(A)

gives an 11-element Array{Array{Float64,1},1} and not a 3 Dimensional array of 11 elements, also how can i convert these vertices to BasicGeometry.Point3d without using a loop?

Hi @adropintheriver,

Why are vertices […] given as 1 D Array and not based on the shape of the object?

I guess because it is simple to reason about a polytope described in vertex representation as a one-dimensional array of “vertices”. In LazySets there is a type VPolygon to deal with the two-dimensional case, which is special in many ways (e.g. lots of very efficient algorithms exist only for the 2D case). I don’t think there would be a practical benefit of adding the dimension as part of the type. (Please note that you can always instantiate such sets using statically sized arrays from StaticArrays, which do know the “shape” of the object in advance hence can benefit from lower-level optimizations.)

About the question on the shape, an array-of-arrays can be reshaped into a single array in different ways, e.g.

julia> using LazySets

julia> V = rand(VPolytope, dim=3);

julia> typeof(V)

julia> vlist = vertices_list(V);  # array of arrays

julia> typeof(vlist)

julia> length(vlist) # number of vertices

julia> R = reduce(hcat, vlist)
3×12 Array{Float64,2}:

About the question on the package GeometryBasics.jl, evaluating GeometryBasics.Point3 on each vertex should do it? (Why wouldn’t you use a loop?).

julia> P = [Point3(x) for x in vlist]
12-element Array{Point{3,Float64},1}:

Hope this helps.