Clipped Voronoi Tessellations

Clipping to a Generic Convex Polygon

In this tutorial we show how to clip a Voronoi tessellation to more generic convex polygons (non-convex polygons are not currently supported) than just a convex hull or a rectangle. This is done by using the clip_polygon keyword argument in voronoi.

We start by clipping the tessellation to a rectangle, showing an alternative to the previous tutorial. To start, we load in the packages we need and generate some data.

using DelaunayTriangulation
using DelaunayTriangulation: EllipticalArc
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

To define the polygon, we define the points and vertices just as we would, for example, the boundary of a triangulation.

xmin, xmax, ymin, ymax = -1/2, 1/2, -1.0, 1.0
clip_points = ((xmin, ymin), (xmax, ymin), (xmax, ymax), (xmin, ymax))
clip_vertices = (1, 2, 3, 4, 1)
clip_polygon = (clip_points, clip_vertices)

(((-0.5, -1.0), (0.5, -1.0), (0.5, 1.0), (-0.5, 1.0)), (1, 2, 3, 4, 1))

Now we simply pass the polygon into voronoi.

clipped_vorn = voronoi(tri, clip = true, clip_polygon = clip_polygon)

Voronoi Tessellation.
    Number of generators: 50
    Number of polygon vertices: 115
    Number of polygons: 26
    Weighted: false

Now let's look at the results.

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)
xlims!(ax1, -2, 2)
ylims!(ax1, -2, 2)
lines!(ax1, [clip_points..., clip_points[begin]], color = :black, linewidth = 4, linestyle = :dash)
voronoiplot!(ax2, clipped_vorn, show_generators = false, colormap = :matter, strokewidth = 4)
xlims!(ax2, -2, 2)
ylims!(ax2, -2, 2)
resize_to_layout!(fig)
fig

We can clip to any convex polygon that we want to. For example, below we clip to an elliptical boundary.

rng = StableRNG(123333)
points = randn(rng, 2, 50)
tri = triangulate(points; rng)
vorn = voronoi(tri)
ellip = EllipticalArc((1/2, 0.0), (1/2, 0.0), (0.0, 0.0), 1/2, 1.0, 0.0)
t = LinRange(0, 1, 50)
clip_points = ellip.(t)
clip_vertices = [1:(length(clip_points)-1); 1]
clip_polygon = (clip_points, clip_vertices)
clipped_vorn = voronoi(tri, clip = true, clip_polygon = clip_polygon)
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)
xlims!(ax1, -2, 2)
ylims!(ax1, -2, 2)
lines!(ax1, [clip_points..., clip_points[begin]], color = :black, linewidth = 4, linestyle = :dash)
voronoiplot!(ax2, clipped_vorn, show_generators = false, colormap = :matter, strokewidth = 4)
xlims!(ax2, -2, 2)
ylims!(ax2, -2, 2)
resize_to_layout!(fig)
fig

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 DelaunayTriangulation: EllipticalArc
using CairoMakie
using StableRNGs

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

xmin, xmax, ymin, ymax = -1/2, 1/2, -1.0, 1.0
clip_points = ((xmin, ymin), (xmax, ymin), (xmax, ymax), (xmin, ymax))
clip_vertices = (1, 2, 3, 4, 1)
clip_polygon = (clip_points, clip_vertices)

clipped_vorn = voronoi(tri, clip = true, clip_polygon = clip_polygon)

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)
xlims!(ax1, -2, 2)
ylims!(ax1, -2, 2)
lines!(ax1, [clip_points..., clip_points[begin]], color = :black, linewidth = 4, linestyle = :dash)
voronoiplot!(ax2, clipped_vorn, show_generators = false, colormap = :matter, strokewidth = 4)
xlims!(ax2, -2, 2)
ylims!(ax2, -2, 2)
resize_to_layout!(fig)
fig

rng = StableRNG(123333)
points = randn(rng, 2, 50)
tri = triangulate(points; rng)
vorn = voronoi(tri)
ellip = EllipticalArc((1/2, 0.0), (1/2, 0.0), (0.0, 0.0), 1/2, 1.0, 0.0)
t = LinRange(0, 1, 50)
clip_points = ellip.(t)
clip_vertices = [1:(length(clip_points)-1); 1]
clip_polygon = (clip_points, clip_vertices)
clipped_vorn = voronoi(tri, clip = true, clip_polygon = clip_polygon)
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)
xlims!(ax1, -2, 2)
ylims!(ax1, -2, 2)
lines!(ax1, [clip_points..., clip_points[begin]], color = :black, linewidth = 4, linestyle = :dash)
voronoiplot!(ax2, clipped_vorn, show_generators = false, colormap = :matter, strokewidth = 4)
xlims!(ax2, -2, 2)
ylims!(ax2, -2, 2)
resize_to_layout!(fig)
fig

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