This paper presents a fast glyph-placement algorithm for visualization of time-varying 2D flow. The method can be used to place many kinds of glyphs. Here it is applied to two in particular: arrows in a hedgehog diagram and streak lines. It works by overpopulating images with glyphs, and then decimating them. The decimation phase uses error diffusion, but extends this halftoning technique to solve the problem of coloring a collection of shapes which do not lie on a raster grid. Because error diffusion is a greedy algorithm, the method avoids iterative adjustments of glyph positions, and is fast. When used to visualize static flow fields, the resulting images are free of grid and clustering artifacts. It can be extended to visualize time-varying flow fields, by modifying the error diffusion algorithm further to maintain coherence between frames in an animation.

This paper presents a method for simulating decorative tile mosaics. Such mosaics are challenging because the square tiles that comprise them must be packed tightly and yet must follow orientations chosen by the artist. Based on an existing image and user-selected edge features, the method can both reproduce the image's colours and emphasize the selected edges by placing tiles that follow the edges. The method uses centroidal voronoi diagrams which normally arrange points in regular hexagonal grids. By measuring distances with an manhattan metric whose main axis is adjusted locally to follow the chosen direction field, the centroidal diagram can be adapted to place tiles in curving square grids instead. Computing the centroidal voronoi diagram is made possible by leveraging the z-buffer algorithm available in many graphics cards.

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Computing the light field due to an area light source remains an interesting problem in computer graphics. The paper presents a series approximation of the light field due to an unoccluded area source, by expanding the light field in spherical harmonics. The source can be nonuniform and need not be a planar polygon. The resulting formulas give expressions whose cost and accuracy can be chosen between the exact and expensive Lambertian solution for a diffuse polygon, and the fast but inexact method of replacing the area source by a point source of equal power. The formulas break the computation of the light vector into two phases: the first phase represents the light source's shape and brightness with numerical coefficients, and the second uses these coefficients to compute the light field at arbitrary locations. The author examines the accuracy of the formulas for spherical and rectangular Lambertian sources, and applies them to obtain light gradients. The author also shows how to use the formulas to estimate light from uniform polygonal sources, sources with polynomially varying radiosity, and luminous textures.