Tensor field design in volumes

The design of 3D tensor fields is important in several graphics applications such as procedural noise, solid texturing, and geometry synthesis. Different fields can lead to different visual effects. The topology of a tensor field, such as degenerate tensors, can cause artifacts in these applications. Existing 2D tensor field design systems cannot handle the topology of 3D tensor fields. We present, to our best knowledge, the first 3D tensor field design system. At the core of our system is the ability to specify and control the type, number, location, shape, and connectivity of degenerate tensors. To enable such capability, we have made a number of observations of tensor field topology that were previously unreported. We demonstrate applications of our method in volumetric synthesis of solid and geometry texture as well as anisotropic Gabor noise.