Extraction of Critical Points and Nets Based on Discrete Gradient Vector Field

Abstract

In this paper we address the problem of representing the topology of discrete scalar fields defined on triangulated domains. To this aim, we use the notion of discrete gradient vector field that we have introduced in [4] to classify the critical points of a scalar field defined over a two-dimensional domain that generalizes the nature of critical points in the differentiable case. Then we sketch an algorithm for extracting a critical net in the discrete case.