2D voronoi diagram for point and line-segment sites using incremental topology-oriented algorithm. C++ with python bindings. Licensed under LGPL2.1.
Python C++ CMake Shell
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Updates: 2018-07 (change to LGLP), 2015-02-12.

The OpenVoronoi project aims to produce an algorithm for calculating the 2D voronoi-diagram for point, line-segment, and circular-arc sites. Currently point-sites and line-segment sites work. Arc-sites are being worked on. The incremental topology-oriented (Sugihara-Iri and/or Held) algorithm is used (see References).

The core algorithm is in C++ with python bindings using Boost Python. There are many python examples that use VTK for visualization. As of 2018 VTK 6 is used for visualizations. Some tests use a random polygon generator (https://github.com/aewallin/randompolygon) and a font-geometry generator based on FreeType (https://github.com/aewallin/truetype-tracer)

OpenVoronoi is written by Anders Wallin (anders.e.e.wallin "at" gmail.com) and initially released under GPLv3. In July 2018, license was changed to LGPL2.1 (see COPYING) with permission and cooperation of all contributors (Issue #35).

In February 2015 Rogach published a Java port called jopenvoronoi (https://github.com/Rogach/jopenvoronoi)

Voronoi diagrams are used for many purposes in computational geometry, but the motivation for OpenVoronoi has mainly been 2D offset-generation (see offset.hpp) for cnc mill toolpath calcuations. An experimental approximate medial-axis filter (medial_axis.hpp) has been added.

The OpenVoronoi project is at https://github.com/aewallin/openvoronoi

Launchpad PPA (not updated regularly) https://launchpad.net/~anders-e-e-wallin/+archive/cam

Build, Test, and Code-coverage dashboard: http://my.cdash.org/index.php?project=OpenVoronoi (not updated regularly! ToDo: set up continuous build/test server + website)

The mailing-list for OpenVoronoi is at https://groups.google.com/forum/?hl=en#!forum/opencamlib

There is a gallery of voronoi diagrams produced with OpenVoronoi at https://picasaweb.google.com/106188605401091280402/OpenVoronoiExamples

Required Dependencies:

Optional Dependencies:

  • git (required only for the version-string)
  • python (if python bindings are built/used)
  • Boost python (if python bindings are built)
  • doxygen (for building documentation)
  • asymptote (to build white-paper figures)
  • lyx (to build white-paper)
  • libvtk (many python-scripts use VTK for visualization)
  • python-vtk (VTK python bindings)
  • truetype-tracer https://github.com/aewallin/truetype-tracer (some tests)
  • randompolygon https://github.com/aewallin/randompolygon (some tests)

Build/Install instructions

From PPA:

sudo add-apt-repository ppa:anders-e-e-wallin/cam
sudo apt-get update
sudo apt-get install openvoronoi

From source:

$ git clone git://github.com/aewallin/openvoronoi.git
$ cd openvoronoi
$ mkdir bld
$ cd bld
$ cmake ../src
$ make
$ sudo make install


Doxygen documentation can be built with "make doc" A white-paper on the algorithm and solvers in LyX format is located in /doc. It has its own CMakeLists.txt file which builds a PDF file.


Both c++ and python tests are found in src/test/. These are run with CTest. In the build-directory either "make test" or "ctest" will run all tests. You can run only tests that have e.g. "ttt" in the test-name with "ctest -R ttt" Currently the tests do not produce any output (png or svg output could be an option?)


  • doc/ has documentation in lyx format, with figures in asymptote format.
    Build a PDF with the CMakeLists.txt in this directory.
  • cpp_examples/ has c++ examples (more needed)
  • python_examples/ has Python examples. Many use VTK and VTK's python bindingd for visualization.
  • src/ has the source for the main algorithm
  • src/solvers has vd-vertex solver code
  • src/py has python wrapping code
  • src/common has common classes not specific to voronoi diagrams
  • src/utility input and output from OpenVoronoi to/from various formats


See the TODO file. Fork the github repo, create a feature branch, commit yor changes, test. Make a short description of your changes and create a pull request. Follow the coding-style of the existing code. One fix/feature per pull request. Contributed code must comply with the LGPL. Provide short doxygen-formatted documentation in the code.

Other voronoi-diagram codes

Boost.Polygon.Voronoi was a Google Summer of Code project in 2010. Integer input coordinates. Exact geometric predicates through geometric filtering. Uses Fortune's sweepline algorithm. Boostcon video: "Sweep-Line Algorithm for Voronoi Diagrams of Points, Line Segments and Medial Axis of Polygons in the Plane" http://blip.tv/boostcon/sweep-line-algorithm-for-voronoi-diagrams-of-points-line-segments-and-medial-axis-of-polygons-in-the-plane-5368229

Patel (see References) seems to have independently implemented the VRONI/Held algorithm, bu we don't know where this code is or under what license it is.


Sugihara and Iri, (1992) "construction of the voronoi diagram for one million generators in single-precision arithmetic" http://dx.doi.org/10.1109/5.163412

Imai (1996) "A Topology-Oriented Algorithm for the Voronoi Diagram of Polygons" http://www.cccg.ca/proceedings/1996/cccg1996_0019.pdf

Sugihara, Iri, Inagaki, Imai, (2000) "topology oriented implementation - an approach to robust geometric algorithms" http://dx.doi.org/10.1007/s004530010002

Held, (1991) "On the Computational Geometry of Pocket Machining" Lecture notes in computer science, vol 500 http://www.amazon.com/Computational-Geometry-Machining-Lecture-Computer/dp/3540541039/

Held, (2001) "VRONI: an engineering approach to the reliable and efficient computation of Voronoi diagrams of points and line segments" http://dx.doi.org/10.1016/S0925-7721(01)00003-7

Martin Held, Stefan Huber, (2009) "Topology-oriented incremental computation of Voronoi diagrams of circular arcs and straight-line segments", Computer-Aided Design, Volume 41, Issue 5, May 2009, Pages 327-338 http://dx.doi.org/10.1016/j.cad.2008.08.004

Nirav B. Patel (2005), "Voronoi diagrams, robust and efficient implementation", Binghamton University, State University of New York, 2005, MSc thesis. (this thesis is not accompanied by code, or much implementation detail)

Kim D-S, (1998), "Polygon offsetting using a Voronoi diagram and two stacks" Computer Aided Design, Vol. 30, No. 14, pp 1069-1076 http://dx.doi.org/10.1016/S0010-4485(98)00063-3

Chen, Fu "An optimal approach to multiple tool selection and their numerical control path generation for aggressive rough machining of pockets with free-form boundaries" Computer Aided Design 43 (2011) 651-663 http://dx.doi.org/10.1016/j.cad.2011.01.020

todo: Burnikel-papers?

References, HSM or Trochoidal paths:

Martin Held, Christian Spielberger (2009). "A smooth spiral tool path for high speed machining of 2D pockets", Computer-Aided Design, Volume 41, Issue 7, July 2009, Pages 539-550 http://dx.doi.org/10.1016/j.cad.2009.04.002 See also www.cosy.sbg.ac.at/~cspiel/projects/hsm/isvd08.pdf and www.cosy.sbg.ac.at/~held/teaching/seminar/seminar_2010-11/hsm.pdf

Gershon Elber, Elaine Cohen, Sam Drake, "MATHSM: medial axis trasform toward high speed machining of pockets", Computer Aided Design 37 (2004) 241-250 http://dx.doi.org/10.1016/j.cad.2004.05.008

Rauch et al. (2009) "Improving trochoidal tool paths generation and implementation using process constraints modelling" http://dx.doi.org/10.1016/j.ijmachtools.2008.12.006 This paper has formulas for maximum depth of cut for circular and trochoidal clearing paths

Ibaraki (2010) "On the removal of critical cutting regions by trochoidal grooving" http://dx.doi.org/10.1016/j.precisioneng.2010.01.007