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

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.