Anisotropic noise samples
We present a practical approach to generate stochastic anisotropic samples with Poisson-disk characteristic over a two-dimensional domain. In contrast to isotropic samples, we understand anisotropic samples as nonoverlapping ellipses whose size and density match a given anisotropic metric. Anisotropic noise samples are useful for many visualization and graphics applications. The spot samples can be used as input for texture generation, for example, line integral convolution ( LIC), but can also be used directly for visualization. The definition of the spot samples using a metric tensor makes them especially suitable for the visualization of tensor fields that can be translated into a metric. Our work combines ideas from sampling theory and mesh generation to approximate generalized blue noise properties. To generate these samples with the desired properties, we first construct a set of nonoverlapping ellipses whose distribution closely matches the underlying metric. This set of samples is used as input for a generalized anisotropic Lloyd relaxation to distribute noise samples more evenly. Instead of computing the Voronoi tessellation explicitly, we introduce a discrete approach that combines the Voronoi cell and centroid computation in one step. Our method supports automatic packing of the elliptical samples, resulting in textures similar to those generated by anisotropic reaction-diffusion methods. We use Fourier analysis tools for quality measurement of uniformly distributed samples. The resulting samples have nice sampling properties, for example, they satisfy a blue noise property where low frequencies in the power spectrum are reduced to a minimum.
blue noise tensor field visualization glyph packing anisotropic voronoi diagram