# Tensor splats

@inproceedings{Benger2004TensorS, title={Tensor splats}, author={Werner Benger and Hans-Christian Hege}, booktitle={IS\&T/SPIE Electronic Imaging}, year={2004} }

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 directional information content of a tensor. The result is an information-rich image that allows to read off the preferred directions in a tensor field. It is useful for analyzing slices or volumes of a three-dimensional…

## 17 Citations

### Superquadric Glyphs for Symmetric Second-Order Tensors

- Computer ScienceIEEE Transactions on Visualization and Computer Graphics
- 2010

This work generalizes a previous method of superquadric glyphs for positive-definite tensors by drawing upon a larger portion of the superquadrics shape space, supplemented with a coloring that indicates the tensor's quadratic form.

### Diffusion Tensor Visualization with Glyph Packing

- BiologyIEEE Transactions on Visualization and Computer Graphics
- 2006

This work adapt particle systems originally developed for surface modeling and anisotropic mesh generation to enhance the utility of glyph-based tensor visualizations, by carefully distributing glyphs throughout the field into a dense packing.

### Asymmetric Tensor Field Visualization for Surfaces

- Computer ScienceIEEE Transactions on Visualization and Computer Graphics
- 2011

A hybrid visualization technique in which hyperstreamlines and elliptical glyphs are used in real and complex domains, respectively, which enables a more faithful representation of flow behaviors inside complex domains and leads to an efficient tensor field visualization system for domain scientists.

### An Evaluation of Glyph Perception for Real Symmetric Traceless Tensor Properties

- Computer ScienceComput. Graph. Forum
- 2010

A perceptual study of four tensor glyphs for symmetric, real, traceless tensors was performed to evaluate the effectiveness of visually communicating the properties and discusses the significant differences found between the methods as guidance to the use of these Glyphs for trACeless tensor visualization.

### HOT-lines: tracking lines in higher order tensor fields

- Computer ScienceVIS 05. IEEE Visualization, 2005.
- 2005

This paper unites the definition of streamlines and tensor lines and generalizes Tensor lines to those applications where second order tensor representations fail and points out similarities of symmetric higher order tensors and spherical harmonics.

### Visualization and Analysis of Second‐Order Tensors: Moving Beyond the Symmetric Positive‐Definite Case

- Computer ScienceComput. Graph. Forum
- 2013

This review focuses on second‐order tensors that are not diffusion tensors, and discusses the strengths and limitations of existing methods when dealing with such tensors as well as challenges introduced by them.

### Hybrid visualization of asymmetric tensor fields : glyphs and hyperstreamlines

- Computer Science
- 2010

A hybrid visualization approach in which hyperstreamlines are used to illustrate the tensors in the real domains and glyphs are employed in complex domains and this enables an effective visualization of the physical patterns everywhere and also provides a more intuitive illustration of elliptical patterns in the complex domains.

### Fast and Memory Efficient GPU-Based Rendering of Tensor Data

- Computer Science
- 2011

A method to display a large amount of superquadric glyphs is presented and its use for visualization of measured secondorder tensor data in diffusion tensor imaging (DTI) and to stress and strain tensors of computational fluid dynamic and material simulations is demonstrated.

### Asymmetric tensor visualization with glyph and hyperstreamline placement on 2D manifolds

- Computer Science
- 2009

A hybrid visualization approach is presented in which hyperstreamlines are used to illustrate the tensors in the real domains while glyphs are employed for complex domains, which enables an effective visualization of the flow patterns everywhere and also provides a more intuitive illustration of elliptical flow patterns in the complex domains.

### ANALYSING CURVED SPACETIMES WITH TENSOR SPLATS

- Physics
- 2006

A new visualization technique for visualizing three-dimensional symmetric positivedeﬁnite tensor ﬁelds of rank two is described. It supports studying the spatialprojection of a spacetime metric. The…

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