An efficient algorithm to compute the genus of discrete surfaces and applications to turbulent flows

TL;DR

This paper introduces a fast, memory-efficient algorithm for calculating the genus of 3D surfaces from scalar field data, enabling detailed analysis of complex turbulent flow structures without triangulation.

Contribution

The paper presents a novel algorithm that computes the genus directly from scalar field thresholding, avoiding triangulation and improving efficiency for large datasets.

Findings

Algorithm accurately computes genus of complex surfaces.

Application demonstrates usefulness in turbulent flow analysis.

Method outperforms traditional triangulation-based approaches.

Abstract

A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a structured-collocated grid, and does not require any triangulation of the data. This makes the algorithm fast, memory-efficient and suitable for large datasets. Applications to the characterization of complex surfaces in turbulent flows are presented to illustrate the method.