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deldir is an R package for computing Delaunay triangulations and Voronoi/Dirichlet tesselations. This Julia package wraps the Fortran code from deldir.


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add Deldir


The coordinates of the generators are specified as two vectors that are fed to deldir, the main function of this package:

x = rand(8)
y = rand(8)
del, vor, summ = deldir(x, y)

The output from deldir are three DataFrames: One for the topology of the Delaunay triangulation; one for topology of the Voronoi tesselation; one with a summary mainly related to the area of the triangles and Voronoi cells.

By default, deldir works with points in the unit rectangle, but other bounding rectangles can be specified as a third argument.

The area of the Voronoi cells are also available directly with the function voronoiarea.

Two functions are available to extract the edges of the Delaunay triangles and Voronoi cells in a "plot friendly" manner:

Dx, Dy = edges(del)
Vx, Vy = edges(vor)

Using the results from above this can be plotted using e.g. the Plots package:

using Plots
scatter(x, y, xlim = (0,1), ylim = (0,1), markersize = 6, label = "generators")
plot!(Dx, Dy, label = "Delaunay")
plot!(Vx, Vy, style = :dash, label = "Voronoi")

One realization looks like the following.

Delaunay & Voronoi edges


There are other Julia package for interacting with Voronoi cells and Delaunay triangulations. The deldir R package has been around for a long time and therefore it is my hope that the Fortran code give correct results. Furthermore, deldir has two qualities I value:

  • It interacts well with the bounding box.
  • It returns the area of the Voronoi cells in the same order as the input generators.

I am also the author of the pure Julia package VoronoiCells with similar functionalities. The VoronoiCells package executes much faster. Consider the time taken to run the voronoiarea functions of both packages with an increasing number of points:

Comparison of Deldir and VoronoiCells

The script generating this output is available in the examples folder. The comparison plot is made with

julia> versioninfo()
Julia Version 1.5.0
Commit 96786e22cc (2020-08-01 23:44 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: Intel(R) Core(TM) i5-8265U CPU @ 1.60GHz
  LIBM: libopenlibm
  LLVM: libLLVM-9.0.1 (ORCJIT, skylake)

(@v1.5) pkg> status
Status `~/.julia/environments/v1.5/Project.toml`
  [64db5801] Deldir v1.3.1
  [e3e34ffb] VoronoiCells v0.2.0

Compiled code

To make it easier to install Deldir the Fortran code is cross-compiled using the BinaryBuilder package and hosted in the Julia Packaging organization.

I am not using the latest version of the Fortran code, because there is a tighter coupling with R from version 0.1-16 and onwards. In particular, the use of the subroutines fexit and rexit from R cause problems even when linking against R's libraries.


Not all features of the R package are available. I have e.g. chosen to ignore options regarding dummy points.

Are you missing anything important? Check out the manual for the R package to see if the Fortran library supports it.


Rolf Turner is author of the deldir package for R as well as all Fortran code used in this package.