A Data Dependent Triangulation for Vector Fields

This article deals with dependencies of a piecewise linear vector field and the triangulation of the domain. It shows that the topology of the field may depend on the triangulation and gives a suitable choice to obtain a simple topology by changes of the triangulation. The main point is the appearance of pairs of critical points with positive and negative Poincaré index. Many of these occurences can be avoided by changing the grid. This is proved in the article. An algorithm is presented which uses these results to extract simpler topological skeletons than usual methods. Finally there are several examples comparing these algorithms to demonstrate the effects of the data-dependent triangulation.