Methods for tensor field visualization
Kenneth I. Joy, Bernd Hamann, Louis Feng · 2010
I introduce two new methods for tensor field visualization in this dissertation. They are built on the idea that physical tensor quantities can be transformed into metrics which in turn can be visualized. This approach helps to distill information in the tensor field and present them for a specific application. They are especially appropriate for the visualization of stress and strain tensor fields which play an important role in many application areas including mechanics and solid state physics. The first technique is a global method using line integral convolution (LIC). It creates a fabric like visualization of the tensor field and shows regions of compression and expansion. These are features due to the applied physical forces represented in the tensor data. This texture based approach is intuitive to understand and provides many free parameters such as size, color, and density for users to map various tensor quantities. The second method is a practical way to generate stochastic anisotropic samples that approximate Poisson-disk characteristic over a two-dimensional domain. In contrast with isotropic samples, anisotropic samples are non-overlapping ellipses whose size and density match a given anisotropic metric. Anisotropic noise samples are useful for many visualization and graphics applications. The spot samples not only can be used as input for texture generation, for example, LIC, but also can be used directly for visualization. My work combines ideas from sampling theory and mesh generation. To generate these samples with the desired properties, first I construct a set of non-overlapping ellipses whose distribution closely matches the underlying metric. This set of samples is then used as input for a generalized anisotropic Lloyd relaxation to distribute noise samples more evenly. Instead of computing the Voronoi tessellation explicitly, I introduce a discrete approach that combines the Voronoi cell and centroid computation in one step. This method supports automatic packing of the elliptical samples, resulting in textures similar to those generated by anisotropic reaction-diffusion.