On a numerical algorithm for computing topological characteristics of three-dimensional bodies

TL;DR

This paper introduces a numerical algorithm that leverages discretized Morse theory to compute topological features of 3D bodies efficiently, focusing on critical points and their classifications.

Contribution

The paper presents a novel algorithm combining discretized Morse theory with simple critical point analysis for topological characterization of 3D objects.

Findings

Algorithm accurately computes topological invariants

Efficient handling of Morse and degenerate critical points

Applicable to complex 3D geometries

Abstract

We present an algorithm for computing the main topological characteristics of three-dimensional bodies. The algorithm is based on a discretization of Morse theory and uses discrete analogs of smooth functions with only nondegenerate (Morse) and the simplest degenerate critical points.