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Tensor Splats Werner Benger*,** and Hans-Christian Hege*

Summary: Tensor Splats
Werner Benger*,** and Hans-Christian Hege*
* Zuse Institute Berlin, D-14195 Berlin-Dahlem, Germany
** Max-Planck Institute for Gravitational Physics, D-14476 Golm, Germany
A new general-purpose technique for the visualization of time-dependent symmetric positive definite tensor fields of rank
two is described. It is based on a splatting technique that is built from tiny transparent glyph primitives which are capable
of incorporating the full orientational information content of a tensor. The result is an information-rich image that allows to
read off the preferred orientations in a tensor field. It is useful for analyzing slices or volumes of a three-dimensional tensor
field and can be overlaid with standard volume rendering or color mapping. The application of the rendering technique is
demonstrated on numerically simulated general relativistic data and a measured diffusion tensor field of a human brain.
Keywords: tensor field visualization, metric, splatting, volume rendering, general relativity, diffusion tensor images
Tensor fields are the primary computational quantities in general relativity. They also occur in material sciences as well
as in computational fluid dynamics. With the recent advances in magneto-resonance equipment, they are also encountered
in medicine from diffusion tensor images. Unfortunately, appropriate visualization tools are not widely available. Even
people working with tensor fields sometimes think of them as purely abstract objects or as a collection of numbers, which
are inspected individually. However, a tensor should be treated as an entity and visualized without reduction to single scalar
or vector fields, as all such reductions result in information loss. Visualizing tensor fields therefore poses the difficulty of
communicating six quantities per point in a data volume, even in the simplest case of a symmetric three-dimensional


Source: Andrzejak, Artur - Konrad-Zuse-Zentrum für Informationstechnik Berlin


Collections: Computer Technologies and Information Sciences