Interaction of Light and Tensor Fields

We present three methods of visualizing tensor fields that offer new ways of looking at tensor volumes. All three methods are based on the interaction of simulated light and the tensor field. Conceptually, rays are shot from a certain direction into the tensor volume. These rays are influenced by the surrounding tensor field and bent as they traverse through the volume. The tensor is visualized by both the nature of the bent rays and by the collection of rays deposited on a receiving plate. The former is similar to streamlines, but shows paths of greatest influence by the tensor field. The latter is similar to caustic effects from photon maps, but shows the convergence or divergence of the rays through the tensor volume. We also use the concept of treating the tensor volume as a special lens that distorts an image. Using backward ray tracing through the tensor volume, we generate image distortions that also show internal properties of the tensor field. A key advantage of these techniques is that they can work directly with non-symmetric tensor fields without first decomposing them into components.