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2D voronoi diagram for point and line-segment sites using incremental topology-oriented algorithm. C++ with python bindings. GPLv3.
C++ Python CMake Shell
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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 work well and line-segment sites are being worked
on. The incremental topology-oriented algorithm is used (see References).
OpenVoronoi is written by Anders Wallin (anders.e.e.wallin "at"
and released under GPLv3 (see COPYING).

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

The mailing-list for OpenVoronoi is at!forum/opencamlib

There is a gallery of voronoi diagrams produced with OpenVoronoi at

git (required only for the version-string)
Boost graph library
Boost python (if python bindings are built)
libQD (a quad-precision arithmetic library). Available as package 
"liqd-dev" on ubuntu. See "

most python-examples use VTK and the VTK python bindings to visualize
the input geometry and the voronoi diagram. On ubuntu these are available 
in the packages
- libvtk (Ubuntu 11.10 has libvtk5.6)
- python-vtk

many examples use truetype-tracer (python module "ttt") for generating input data.

some examples and tests use the 2-opt random polygon generator from CGAL.
There is a boost-python module "rpg" which is used by these scripts.

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://
$ cd openvoronoi
$ mkdir bld
$ cd bld
$ cmake ../src
$ make
$ sudo make install

There are a few python-scrits in src/test/ that can be 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.

Other voronoi-diagram codes



Boost/Sweepline. This was a Google Summer of Code 2010 project, meant for inclusion in Boost.Polygon.
Integer input coordinates. Exact geometric predicates through geometric filtering. 
Uses Fortune's sweepline algorithm.
or perhaps

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.

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"

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 

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 

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"
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