Tensor Invariants and Glyph Design

Abstract

Tensors provide a mathematical language for the description of many physical phenomena. They appear everywhere were the dependence of multiple vec- tor fields is approximated as linear. Due to this generality they occur in various appli- cation areas, either as result or intermediate product of simulations. As different as these applications, is the physical meaning and relevance of particular mathematical properties. In this context, domain specific tensor invariants that describe the enti- ties of interest play a crucial role. Due to their importance, we propose to build any tensor visualization upon a set of carefully chosen tensor invariants. In this chapter we focus on glyph-based representations, which still belong to the most frequently used tensor visualization methods. For the effectiveness of such visualizations the right choice of glyphs is essential. This chapter summarizes some common glyphs, mostly with origin in mechanical engineering, and link their interpretation to spe- cific tensor invariants.