Anisotropic Noise Samples

Anisotropic noise textures are interesting for many visualization and graphics applications. The spot samples can be used as input for texture generation, e.g., Line Integral Convolution (LIC), but can also be used directly for visualization by itself. They are especially suitable for the visualization of tensor fields that can be used to define a metric for the anisotropic density field. We present a novel method for generating stochastic samples to create anisotropic noise textures consisting of non-overlapping ellipses, whose size and density match a given metric. Our method supports an automatic packing of the elliptical samples resulting in textures similar to those generated by anisotropic reaction-diffusion. The texture generation algorithm combines ideas from sampling theory and mesh generation to meet our specific needs. We start building a candidate sample set by using stratified random uniform dense sampling. From these samples we chose appropriate samples such that they follow a generalized Poison disk distribution. In a last step we improve the sampling properties by performing an anisotropic Lloyd relaxation. We use an localized anisotropic Voronoi cell definition based on the work done by Labelle. But instead of computing the Voronoi tessellation explicitly we introduce a discretized approach which combines the Voronoi cell and centroid computation in one step. The sampling time grows linearly with the required number of samples. The resulting samples have nice sampling properties. For uniformly distributed samples, the quality can be measured by Fourier analysis tools.

Diffusion Tensor Example: