Glyphs for non-linear vector field singularities

Abstract

Glyphs are a widespread technique to depict local properties of different kinds of fields. In this paper we present a new glyph for singularities in non-linear vector fields. We do not simply show the properties of the derivative at the singularities as most previous methods do, but instead illustrate the behavior that goes beyond the local linear approximation. We improve the concept of linear neighborhoods to determine the size of the vicinity from which we derive the data for the glyph. To obtain data from outside this neighborhood we use integration in the vector field. The gathered information is used to depict convergence and divergence of the flow, and non-linear behavior in general. These properties are communicated by color, radius, the overall shape of the glyphs and streamlets on their surface. This way we achieve a depiction of the non-linear behavior of the flow around the singularities.