Extraction of Critical Nets Based on a Discrete Gradient Vector Field

In this paper we address the problem of representing the topology of discrete scalar fieldsdefined on triangulated domains in two and three dimensions. To this aim, we use the notion of
discrete gradient vector field that we have introduced in [3] to classify critical points and extract
a critical net representing the main features of a scalar field defined on a two-dimensional
domain. The nature of the critical points provided by the discrete gradient vector field is quite
different from those obtained in the differentiable case. Thus, we show that our critical net
generalizes classical critical nets corresponding to (the classical differentiable) Morse functions.