using Polyhedra
import GLPK
lib = DefaultLibrary{Float64}(GLPK.Optimizer)

P1 = polyhedron(vrep([
    -1.9 -1.7
    -1.8  0.5
     1.7  0.7
     1.9 -0.3
     0.9 -1.1
]), lib)

P2 = polyhedron(vrep([
    -2.5 -1.1
    -0.8  0.8
     0.1  0.9
     1.8 -1.2
     1.3  0.1
]), lib)

Pch = convexhull(P1, P2)

hrepiscomputed(P1), hrepiscomputed(P2), hrepiscomputed(Pch)

npoints(Pch)

removevredundancy!(Pch)
npoints(Pch)

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

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