Meshing of Diffusion Surfaces for Point-Based Tensor Field Visualization

The visualization of 3D vector and tensor fields in a 2D image is challenging because the large amount of information will either be mixed during projection to 2D or lead to severe occlusion problems. In this work we segment from the symmetric 3D tensor field regions dominated by stream tubes and regions dominated by diffusion surfaces. The diffusion surfaces are integrated with a higher order Runge–Kutta scheme and approximated with a triangle mesh. Our main contribution is to steer the integration with a face-based coding scheme, that allows direct compression of the integrated diffusion surfaces and ensures that diffusion surfaces of any topology can be created. Finally we sample the stream tubes and diffusion surfaces with points. The points from different entities are colored with different colors. We lit the points during rendering with a lighting model adapted to the tensor field. The resulting visualization of symmetric 3D tensor fields is sparse because of the sampling on points and allows for a deeper view inside the volumetric tensor field but also allows the simultaneous visualization of a dense set of tubes and surfaces.