3-D Visualization of 2nd order tensors field with dynamic particles.

@inproceedings{BotterGM2011,
 abstract = { Many relevant physical quantities in geomodeling are represented by 2nd order tensors (e.g. stress, strain, permeability, metric, curvature, diffusivity). 3-D tensor field visualization is a challenge because 2nd order tensor are determined by nine components (or six for symmetric tensors) and rendering so many variables together raises both perception and computational issues. Visualization of scalar and 1st order tensor field (i.e. scalar and vector field) has already been widely studied [Piquet et al., 2010]. 2nd order tensors are generally visualized by rendering some selected eigen properties at some static sampling locations. We propose to make this sampling dynamic by using moving particles which are affected by the tensor field being visualized. The algorithm takes advantage of programmable graphics cards for updating, in an interactive way, particle position, velocity, color and/or shape according to the value of the sampled tensor.
Two visualization approaches are presented: with the first one, a single family of particles is rendered with a velocity depending on tensor value and other components of the tensor are mapped to remaining visual variables such as color or shape; with the second approach, several families of particles are used, distinguished by their color, and each family is dedicated to the visualization of one eigen vector according to the rank of its associated eigen value. This new method for rendering tensor field integrates the full information contained by each tensor and allows rendering it in the entire volume of interest at one time. We apply these methods to the visualization of permeability fields and discuss perceptual issues. },
 author = { Botter, Charlotte AND Laurent, Gautier AND Caumon, Guillaume },
 booktitle = { Proc. 31st Gocad Meeting, Nancy },
 title = { 3-D Visualization of 2nd order tensors field with dynamic particles. },
 year = { 2011 }
}