3.0 - Theory Index

This section has the purpose to introduce the theoretical concept behind the code in this module. For this reason we will give a brief overview of:

• Delaunay Triangulation in section 3.1
• Voronoy Diagram in section 3.2
• Alpha Structures in section 3.3
• Persistent Homology in section 3.4

In general we will assume $S$ a set of sites (namely points in $\mathbb R^D, D < \infty$). In the following we assume that $S$ is made of points in a general position (i.e. no $d+2$ points of $S$ lie on a common ball). Of course this condition is not general (regardless of the name); however there’s a technique called SoS which "simulates an infinitesimal perturbation of the points", so that they are in general position afterwards.