Strategies for Visualizing Tensor Fields in more than two Dimensions

Tensor field visualization aims at the depiction of the full information contained in the underlying data set or the extraction and display of specific features. Here, we focus on the first task and evaluate various methods with regard to their power of providing an intuitive visual representation. Tensor fields are reviewed in a differential geometric context and we provide a coordinate-free derivation of various mathematical properties of tensor fields. An overview and classification of glyph-based methods is given and their usability for time-dependent tensor fields is discussed. Selected innovative methods are presented in more detail (tensor cones, tensor glow, tensor splats, tensor schlieren).