Introductory tutorial bringing visual intuition into definitions of three basic concepts used in TDA - Voronoi diagrams, Delaunay complexes and Alpha complexes / Alpha filtration. In this video I show how to get from a two-dimensional point-cloud to each of those objects, describe several different ways how to look at them, and outline how they are connected to each other.
The visualisations were done in Wolfram Mathematica, and an interactive version is available as a demonstration in the Wolfram Demonstrations Project:
demonstrations.wolfram.com/Al...
A follow up tutorial on construction of Delaunay complex using a lifting to a paraboloid: • Computing Delaunay com...
This tutorial was contributed as part of the WinCompTop+AATRN Tutorial-a-thon in Spring 2021: sites.google.com/view/aatrn-t....