Another way could be CGAL is a software project that provides easy access to efficient and reliable geometric algorithms in the form of a C++ library. CGAL is used in various areas needing geometric computation, such as geographic information systems, computer aided design, molecular biology, medical imaging, computer graphics, and robotics. The library offers data structures and algorithms like triangulations, Voronoi diagrams, Boolean operations on polygons and polyhedra, point set processing, arrangements of curves, surface and volume mesh generation, geometry processing, alpha shapes, convex hull algorithms, shape analysis, AABB and KD trees...

http://www.cgal.org/

http://www.cgal.org/

Thanks for the replies, which are already very helpful. I will try out both alternatives.

So bottom line is, that some implementation is needed at least to get the job done, unless I want to buy a complete software?

I'm not afraid to that but just wanted to know whether the effort is necessary or whether there's already a perfect solution around.

So after a bit of playing around, I know how to build Voronoi Diagrams with R but Treemaps are not working. The suggested Tutorial (https://www.stat.auckland.ac.nz/~paul/Reports/VoronoiTreemap/voronoiTreeMap.html) is helpful and describes the R implementation very well but unfortunately relies on C++ code, which I tried to compile by myself without success. What am I doing wrong?

Not being a C++ expert, I'm pretty much lost here...

I agree with R suggestion: free and very functional software.

Here is my example of R code for a treemap:

Code R script for a Treemap, Mariana Trench project

You can see the output picture as a pdf here:

https://github.com/paulinelemenkova/38-R-Treemap

Program SFTessellation demonstrates obtaining a Voronoi tessellation. The program uses a random number generator to generate starting points (pixel generators). of the cells and creates a different mosaic on each run. You can download a program from http://zhelezov.byethost14.com/SFTessellation.zip