Faces & Vertices of N Linear Constraints

Specific Domains Numerics
11

You can use incidentpoints to simplify the code.
CDD computes the incidence information and incidentpoints just retrieve this information. In your code sample, you recompute it.

using Polyhedra, CDDLib, JuMP, Statistics

model = Model()

@variables(model, begin
    x
    y
end)

@constraints(model, begin
    0 <= x <= 1.0
    0 <= y <= 1.0
    x <= y
end)

print(model)
poly = polyhedron(model, CDDLib.Library())

removehredundancy!(poly)
barycenters = [mean(incidentpoints(poly, hidx)) for hidx in eachindex(halfspaces(poly))]

I get the output

Feasibility
Subject to
 x - y ≤ 0.0
 x ∈ [0.0, 1.0]
 y ∈ [0.0, 1.0]
3-element Array{Array{Float64,1},1}:
 [0.5, 0.5]
 [0.0, 0.5]
 [0.5, 1.0]

Also: try to avoid things like hcat(points( vrep( poly ) )...) or vcat( barycenters... ). If you have millions of points, it will compile a hcat or vcat with millions of arguments which will be quite slow to compile !

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