Higher Order Singularities in Piecewise Linear Vector Fields

Piecewise linear interpolation of 2D scattered vector data is a classical, simple and fast scheme to process the discrete information provided by experiments or numerical simulations. Nevertheless, its major drawback is its low order that prevents satisfying approximation of non linear behaviors. For topology-based methods in particular, commonly applied in vector field visualization, it often restricts the structural features found to very few possible configurations which may be insufficient for interpretation. In this paper, on the contrary, we consider piecewise linear vector fields from the modeling viewpoint, showing that they can exhibit arbitrary complex topological features.