I am trying to figure out why QHull and Polyhedra give different volume estimates for the same inputs. They agree in the 2D case, but diverge in the 3D case.
Results
2D
Polyhedra.jl: 0.982
QHull.jl: 0.982
3D
Polyhedra.jl: 4.987
QHull.jl: 0.932
Code
using QHull, Polyhedra
points1 = rand(1000, 2)
ph1 = polyhedron(vrep(points1))
hull1 = chull(points1)
println("2D")
println("Polyhedra.jl: $(round(volume(ph1), digits=3))")
println("QHull.jl: $(round(hull1.volume, digits=3))")
points2 = rand(1000, 3)
ph2 = polyhedron(vrep(points2))
hull2 = chull(points2)
println("3D")
println("Polyhedra.jl: $(round(volume(ph2), digits=3))")
println("QHull.jl: $(round(hull2.volume, digits=3))")