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!
> 
> 
> 



$n$-dimensional Voronoi diagram
Often Voronoi diagrams are constructed from their duals, Delaunay triangulations.
The Delaunay triangulation of a point set in $d$ dimensions can be obtained from the convex hull
of a lifting of the points into $d+1$ dimensions. This relationship is explained in many sources,
including [*The Handbook of Discrete and Computational Geometry*](https://www.routledge.com/Handbook-of-Discrete-and-Computational-Geometry-Third-Edition/Toth-ORourke-Goodman/p/book/9781498711395) (Chapters 22, 23).


Implementing this on your own is quite a project, so you might first investigate what is available.
Qhull performs the computations; see [www.qhull.org](http://www.qhull.org/).
$d$-dimensional Delaunay triangulation computations are part of [CGAL](https://www.cgal.org/), specifically the module on [dD Convex Hulls and Delaunay Triangulations](https://doc.cgal.org/Manual/3.2/doc_html/cgal_manual/Convex_hull_d/Chapter_main.html).
You could use [polymake](https://polymake.org/doku.php) to convert from the Delaunay triangulation to its corresponding Voronoi diagram.
Finally, there are papers written on specific versions of your problem, for example:
["An Explicit Solution for Computing the Euclidean $d$-dimensional Voronoi Diagram of Spheres in a Floating-Point Arithmetic,"](https://doi.org/10.1007/3-540-44842-X_84 "In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. zbMATH review at https://zbmath.org/?q=an:1049.68009") by Marina Gavrilova, 2003.


(Incidentally, "Euclidean graphs" play a relatively minor role in this topic.)


