TITLE: n-dimensional voronoi diagram
QUESTION [13 upvotes]: Hi, I need to compute the voronoi diagram of a set of points in $R^n$.
I'm quite unschooled on the topic, could someone point me to the right references so that I can 
a) understand the theory behind it;
b) implement an actual algorithm to compute it.

P.S. Googling I found out I need to know about euclidean graphs, but I
  couldn't find any decent introduction to it. Pointers are appreciated!

REPLY [3 votes]: R (a favorite open source, object oriented interactive statistical package) has what appears to be a suitably fast algorithm, but I've only used it in a problem with 20 some odd points or so.  
As the others have mentioned above, the Voronoi tessellation or mosaic is computed using the (dual graph which is the) Delaunay triangulation.  The R function 'veronoi.mosaic' in the package 'tripack' calls a FORTRAN routine.  If its convenient enough to do it in R then just call the veronoi.mosaic function (details on getting R and getting the tripack package follow). Otherwise, if you'd rather just use the internal FORTRAN subroutine, you can figure out the meaning of the arguments by looking at the veronoi.mosaic function in R (at the point at which the FORTRAN subroutine 'veronoi' is called) and work backwards.
In any case, all of its open source and works like a charm.
getting R:
http://cran.r-project.org/
the tripack package
http://cran.r-project.org/web/packages/tripack/index.html
Enjoy!
Best Regards,
Grant Izmirlian