using Polyhedra, CDDLib

P1 = polyhedron(vrep(randn(15, 2)), CDDLib.Library())

P2 = polyhedron(vrep(randn(15, 2)), CDDLib.Library())

Pint = intersect(P1, P2)

hrepiscomputed(P1), vrepiscomputed(P1)

hrepiscomputed(P2), vrepiscomputed(P2)

hrepiscomputed(Pint), vrepiscomputed(Pint)

npoints(Pint)

hrepiscomputed(Pint), vrepiscomputed(Pint)

using Plots

plot(P1, alpha=0.2, color="blue")
plot!(P2, color="red", alpha=0.2)
plot!(Pint, color="yellow", alpha=0.6)

Pch = convexhull(P1, P2)

npoints(Pch)

plot(P1, alpha=0.2, color="blue")
plot!(P2, color="red", alpha=0.2)
plot!(Pch, color="green", alpha=0.1)

hrepiscomputed(P1), hrepiscomputed(P2), hrepiscomputed(Pint)

# each of Q1 and Q2 has 15 vertices
Q1 = polyhedron(vrep(randn(15, 2)), CDDLib.Library())
Q2 = polyhedron(vrep(randn(15, 2)), CDDLib.Library())

# check that their convex hull has 30 vertices
Qch = convexhull(Q1, Q2)
npoints(Qch)

removevredundancy!(Qch)
npoints(Qch)