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 fields defined 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.

Proceedings of Eurographics