Clipped Voronoi Tessellations

Clipping to the Convex Hull

One issue that may arise when dealing with Voronoi tessellations is the presence of unbounded polygons occurring on the boundary. One way to deal with this is to clip polygons to the convex hull of the tessellation. We describe how to also clip the tessellation to a generic convex polygon, instead of just the convex hull, in this tutorial.

In the example below, we clip the tessellation to the convex hull of the point set by using clip=true in the keyword arguments.

using DelaunayTriangulation
using CairoMakie
using StableRNGs

rng = StableRNG(123)
points = randn(rng, 2, 50)
tri = triangulate(points; rng)
vorn = voronoi(tri)

Voronoi Tessellation.
    Number of generators: 50
    Number of polygon vertices: 92
    Number of polygons: 50
    Weighted: false

clipped_vorn = voronoi(tri, clip = true)

Voronoi Tessellation.
    Number of generators: 50
    Number of polygon vertices: 119
    Number of polygons: 50
    Weighted: false

Note that the clipping has put more polygon vertices in. We compare the clipped tessellations below.

fig = Figure()
ax1 = Axis(fig[1, 1], title = "Unclipped", width = 600, height = 400)
ax2 = Axis(fig[1, 2], title = "Clipped", width = 600, height = 400)
voronoiplot!(ax1, vorn, show_generators = false, colormap = :matter, strokewidth = 4)
voronoiplot!(ax2, clipped_vorn, show_generators = false, colormap = :matter, strokewidth = 4)
resize_to_layout!(fig)
fig

As you can see, the unbounded polygons, and any polygons that included points outside of the convex hull, have now been clipped to the convex hull.

Just the code

An uncommented version of this example is given below. You can view the source code for this file here.

using DelaunayTriangulation
using CairoMakie
using StableRNGs

rng = StableRNG(123)
points = randn(rng, 2, 50)
tri = triangulate(points; rng)
vorn = voronoi(tri)

clipped_vorn = voronoi(tri, clip = true)

fig = Figure()
ax1 = Axis(fig[1, 1], title = "Unclipped", width = 600, height = 400)
ax2 = Axis(fig[1, 2], title = "Clipped", width = 600, height = 400)
voronoiplot!(ax1, vorn, show_generators = false, colormap = :matter, strokewidth = 4)
voronoiplot!(ax2, clipped_vorn, show_generators = false, colormap = :matter, strokewidth = 4)
resize_to_layout!(fig)
fig

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