Julia wrapper for Delaunay/Voronoi library
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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.


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 and 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


Install the package by running


As mentioned, this package is a wrapper for a Fortran library. Compilation is performed with gfortran and I have only tested this on OS X Yosemite and Linux Mint.

To re-compile the Fortran code, run Pkg.build("Deldir").


This is not the only Julia package for Delaunay/Voronoi computations. I am aware of the pure Julia implementation VoronoiDelaunay and the Boost wrapper Voronoi.

However, Deldir has two qualities that 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.

Update 2016-05-05: I have made the pure Julia package VoronoiCells with similar functionalities that 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 0.5.0
Commit 3c9d753 (2016-09-19 18:14 UTC)
Platform Info:
  System: Linux (x86_64-linux-gnu)
  CPU: Intel(R) Core(TM) i7-3720QM CPU @ 2.60GHz
  BLAS: libopenblas (USE64BITINT DYNAMIC_ARCH NO_AFFINITY Sandybridge)
  LAPACK: libopenblas64_
  LIBM: libopenlibm
  LLVM: libLLVM-3.7.1 (ORCJIT, ivybridge)


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 in this package.


The Julia code in this package is MIT licensed and the Fortran code is licensed under GPL.