Louis Feng

Shell maps

A shell map is a bijective mapping between shell space and texture space that can be used to generate small-scale features on surfaces using a variety of modeling techniques. The method is based upon the generation of an offset surface and the construction of a tetrahedral mesh that fills the space between the base surface and its offset. By identifying a corresponding tetrahedral mesh in texture space, the shell map can be implemented through a straightforward barycentric-coordinate map between corresponding tetrahedra. The generality of shell maps allows texture space to contain geometric objects, procedural volume textures, scalar fields, or other shell-mapped objects.

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..

Tensor Field Visualization Using a Metric Interpretation

This chapter introduces a visualization method specifically tailored to the class of tensor fields with properties similar to stress and strain tensors. Such tensor fields play an important role in many application areas such as structure mechanics or solid state physics. The presented technique is a global method that represents the physical meaning of these tensor fields with their central features: regions of compression or expansion. The method consists of two steps: first, the tensor field is interpreted as a distortion of a flat metric with the same topological structure; second, the resulting metric is visualized using a texture-based approach. The method supports an intuitive distinction between positive and negative eigenvalues.

Dense Glyph Sampling for Visualization

We present a simple and efficient approach to generate a dense set of anisotropic, spatially varying glyphs over a two-dimensional domain. Such glyph samples are useful for many visualization and graphics applications. The glyphs are embedded in a set of nonoverlapping ellipses whose size and density match a given anisotropic metric. An additional parameter controls the arrangement of the ellipses on lines, which can be favorable for some applications, for example, vector fields and distracting for others. To generate samples with the desired properties, we combine ideas from sampling theory and mesh generation. We start with constructing a first 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 samples more evenly.