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Regular grid sampling structures in the plane are a common spatial framework for many studies. Constructing grids with desirable properties such as equality of area and shape is more di cult on a sphere. We studied the distortion characteristics of recursive partitions of the surface of the globe starting with the octahedron and icosahedron polyhedral models. We used ® ve di erent methods for mapping from the polyhedral model to the surface of the sphere: the Gnomonic projection, Fuller's Dymaxion projection, Snyder's equal area polyhedral projection, direct spherical subdivision, and a recursive polyhedral projection. We increased partition density using both a 4-fold and a 9-fold ratio at each level of recursive subdivision by subdividing to the 8th level with the 4-fold density ratio (65 536 cells per polyhedral face) and to the ® fth level with the 9-fold density ratio (59 049 cells per polyhedral face). We measured the area and perimeter of each cell at each level of recursion for each method on each model using each density ratio. From these basic measurements we calculated the range and standard deviation of the area measurement, and the mean, range, and standard deviation of a compactness measurement de® ned as the ratio of (the ratio of the perimeter to the area of the cell ) to (the ratio of the perimeter to the area of a spherical circle with the same area). We looked at these basic measurements and their statistics using graphs of variation with recursion level, sums of squares analyses of variation, histograms of the distributions, maps of the spatial variation, and correlograms. The Snyder projection performed best in area distortion and the Gnomonic projection performed best in compactness distortion. The Fuller projection and the Sphere method had moderate distortion in both area and compactness relative to the worst methods. There was little di erence in distortion performance between partitions using the 4-fold density ratio and those using the 9-fold density ratio. Partitions based on the icosahedron performed better for all statistics than those based on the octahedron.

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In recent years, a branch of computer graphics termed non-photorealistic rendering (NPR) has defined its own niche in the computer graphics community. While photorealistic rendering attempts to render virtual objects into images that cannot be distinguished from a photograph, NPR looks at techniques designed to achieve other ends. Its goals can be as diverse as imitating an artistic style, mimicking a look comparable to images created with specific reproduction techniques, or adding highlights and details to images. In doing so, NPR has overlapped the study of cartography concerned with representing terrain in two ways. First, NPR has formulated several techniques that are similar or identical to antecedent terrain rendering techniques including inclined contours and hachures. Second, NPR efforts to highlight or add information in renderings often focus on the use of innovative and meaningful combinations of visual variables such as orientation and color. Such efforts are similar to recent terrain rendering research focused on methods to symbolize disparate areas of slope and aspect on shaded terrain representations. We compare these fields of study in an effort to increase awareness and foster collaboration between researchers with similar interests.

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