Description

The goal of this project is to generate stochastic anisotropic samples with Poisson-disk characteristic over a two-dimensional domain. In contrast to isotropic samples, we understand anisotropic samples as 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 can be used as input for texture generation, e.g., line integral convolution (LIC), but can also be used directly for visualization. The definition of the spot samples by 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 generate these samples with the desired properties we construct a first set of non-overlapping 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 which 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, e.g., they satisfy a blue noise property where low frequencies in the power spectrum are reduced to a minimum. Further information is available in the detailed project description.

Members

Ingrid Hotz, Zuse Institute Berlin
Andrea Kratz, Zuse Institute Berlin
Nino Kettlitz, Zuse Institute Berlin
Louis Feng, IDAV, University of California Davis
Bernd Hamann , IDAV, University of California Davis

Responsible

Ingrid Hotz

Duration

Started 01/2005