Context. To get fully acquainted with Voronoi diagrams, Delaunay triangulations and the relationship between the two. To investigate a computational side of these tessellations and an application...Show moreContext. To get fully acquainted with Voronoi diagrams, Delaunay triangulations and the relationship between the two. To investigate a computational side of these tessellations and an application in astronomy in the form of modeling the Cosmic Web. Aims. First of all, to present and understand Brown’s algorithm, its tools, benefits and drawbacks. Secondly, to familiarize ourselves with modern views on and models of the Cosmic Web, and one of the new interesting tools used, namely the Delaunay Tessellation Field Estimator (DTFE). In particular, we are interested in accessing the quality of its reconstructions quantitatively. Methods. Obvious key concepts are Voronoi diagrams and Delaunay triangulations. For the computational component inversion and complexity analysis are of importance. For the astronomical component, various sampling methods and Fourier transforms come into play. Results. It seems that Brown’s algorithm has clear benefits in higher dimensional computations, but for two and three dimensions there may be better alternatives. Even though the DTFE reconstructions of the Cosmic Web appear to be visually satisfying, it appears that it is actually very sensitive to Poisson noise in the point distribution and in principle, minor effects may seriously distort the actual underlying continuous distribution. Greater care needs to be taken to access this further. There are many further research topics open here.Show less
