2D voronoi diagram for point and line-segment sites using incremental topology-oriented algorithm. C++ with python bindings. GPLv3.
C++ Python CMake Shell
Latest commit acbb94d Apr 24, 2016 @aewallin old work (?)


OpenVoronoi README. Last update 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.
The 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 released under GPLv3 (see COPYING).

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 

Launchpad PPA (not updated regularly)

Build, Test, and Code-coverage dashboard:
(not updated regularly! ToDo: set up continous build/test server + website)

The mailing-list for OpenVoronoi is at

There is a gallery of voronoi diagrams produced with OpenVoronoi at

Required Dependencies:
libqd-dev             http://crd.lbl.gov/~dhbailey/mpdist/
Boost graph library   
graphviz  (visualization for graph algorithms)

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 GPL. Provide short doxygen-formatted 
documentation in the code.

Other voronoi-diagram codes



This 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"

VRONI/Martin Held. This code is commercial and not available, as far as
we know. 
Patel (see References) seems to have independently implemented the
same algorithm, we don't know where this code is or under what license it is.

BSD-licensed code for 3D voronoi cell computation. May not be useful for 2D toolpath generation?

Really a mesh-generator for e.g. finite-element analysis. A constrained Delaunay triangulation could be used to generate a Voronoi diagram for point and line inputs.

References, Voronoi Diagram algorithms

Sugihara and Iri, (1992) "construction of the voronoi diagram for one 
million generators in single-precision arithmetic" 

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" 

Held, (1991) "On the Computational Geometry of Pocket Machining"
Lecture notes in computer science, vol 500

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

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

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

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
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

Rauch et al. (2009) "Improving trochoidal tool paths generation and implementation using process constraints modelling"
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"