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Plot

Polyhedra contains utilities to visualize either a 2-dimensional or a 3-dimensional polyhedron, see Polyhedron for how to construct a polyhedron, e.g. from its H- or V-representation.

2D plotting with Plots

A 2-dimensional polytope, i.e. bounded polyhedron, can be visualized with Plots. Suppose for instance that we want to visualize the polyhedron having the following H-representation:

julia> using Polyhedra

julia> h = HalfSpace([1, 1], 1) ∩ HalfSpace([-1, 0], 0) ∩ HalfSpace([0, -1], 0)
H-representation Polyhedra.Intersection{Int64,Array{Int64,1},Int64}:
3-element iterator of HalfSpace{Int64,Array{Int64,1}}:
 HalfSpace([1, 1], 1)
 HalfSpace([-1, 0], 0)
 HalfSpace([0, -1], 0)

The H-representation cannot be given to Plots directly, it first need to be transformed into a polyhedron:

julia> p = polyhedron(h)
Polyhedron DefaultPolyhedron{Rational{BigInt},Polyhedra.Intersection{Rational{BigInt},Array{Rational{BigInt},1},Int64},Polyhedra.Hull{Rational{BigInt},Array{Rational{BigInt},1},Int64}}:
3-element iterator of HalfSpace{Rational{BigInt},Array{Rational{BigInt},1}}:
 HalfSpace(Rational{BigInt}[1//1, 1//1], 1//1)
 HalfSpace(Rational{BigInt}[-1//1, 0//1], 0//1)
 HalfSpace(Rational{BigInt}[0//1, -1//1], 0//1)

The polyhedron can be given to Plots as follows

julia> using Plots

julia> plot(p)

See Polyhedral Function and 3D Plotting a projection of the 4D permutahedron for example notebooks.

3D plotting with Plots

A 3-dimensional polyhedron can be visualized with either MeshCat or Makie. Unbounded polyhedron are supported by truncating the polyhedron into a polytope and not triangularizing the faces in the directions of unbounded rays.

Suppose for instance that we want to visualize the polyhedron having the following H-representation:

julia> using Polyhedra

julia> v = convexhull([0, 0, 0]) + conichull([1, 0, 0], [0, 1, 0], [0, 0, 1])
V-representation Polyhedra.Hull{Int64,Array{Int64,1},Int64}:
1-element iterator of Array{Int64,1}:
 [0, 0, 0],
3-element iterator of Ray{Int64,Array{Int64,1}}:
 Ray([1, 0, 0])
 Ray([0, 1, 0])
 Ray([0, 0, 1])

The V-representation cannot be given to MeshCat or Makie directly, it first need to be transformed into a polyhedron:

julia> p = polyhedron(v)
Polyhedron DefaultPolyhedron{Rational{BigInt},Polyhedra.Intersection{Rational{BigInt},Array{Rational{BigInt},1},Int64},Polyhedra.Hull{Rational{BigInt},Array{Rational{BigInt},1},Int64}}:
1-element iterator of Array{Rational{BigInt},1}:
 Rational{BigInt}[0//1, 0//1, 0//1],
3-element iterator of Ray{Rational{BigInt},Array{Rational{BigInt},1}}:
 Ray(Rational{BigInt}[1//1, 0//1, 0//1])
 Ray(Rational{BigInt}[0//1, 1//1, 0//1])
 Ray(Rational{BigInt}[0//1, 0//1, 1//1])

Then, we need to create a mess from the polyhedron:

julia> m = Polyhedra.Mesh(p)
Polyhedra.Mesh{3,Rational{BigInt},DefaultPolyhedron{Rational{BigInt},Polyhedra.Intersection{Rational{BigInt},Array{Rational{BigInt},1},Int64},Polyhedra.Hull{Rational{BigInt},Array{Rational{BigInt},1},Int64}}}(convexhull([0//1, 0//1, 0//1]) + convexhull(Ray(Rational{BigInt}[1//1, 0//1, 0//1]), Ray(Rational{BigInt}[0//1, 1//1, 0//1]), Ray(Rational{BigInt}[0//1, 0//1, 1//1])))

Polyhedra.Mesh

The polyhedron can be plotted with MeshCat as follows

julia> using MeshCat

julia> vis = Visualizer()

julia> setobject!(vis, m)

julia> open(vis)

To plot it in a notebook, replace open(vis) with IJuliaCell(vis).

To plot it with Makie instead, you can use for instance mesh or wireframe.

julia> import Makie

julia> Makie.mesh(m, color=:blue)

julia> Makie.wireframe(m)

See 3D Plotting a projection of the 4D permutahedron for an example notebook.