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Image:	$This is the third (and final) image in a series of three Voronoi hierarchy images of the Cat's Eye Nebula. The image shows excellent representation of the original image at a fraction of the original data size. All elliptical paths now show clearly. [See other two images in the series: Voronoi Hierarchy of the Cats-Eye Nebula Image 1 and Image 3.]<BR> <BR> This image of the Cats-Eye Nebula is the first in a series of three illustrations that show three resolutions of a Voronoi hierarchy. A <I>Voronoi hierarchy</I> is a new, general form of multiresolution hierarchies. The method can be applied to a variety of data, including scattered data, arbitrarily gridded data, and data on multi-dimensional domains. To create a Voronoi hierarchy, an initial Voronoi diagram must first be created to represent the coarsest level of detail. Second, points are inserted into the existing diagram to create higher levels of resolution. At each iteration of the algorithm, we identify a set of cells with high errors. Inserting points where the maximal errors occur leads to excellent results. The three illustrations in this series show three resolutions of a Voronoi hierarchy for an image of the Cats-Eye Nebula. The first level contains 208 cells, the second contains 737 cells, and the final 8284 cells. Using this algorithm, we can generate an excellent representation of the original image at a fraction of the original data size.<BR> <BR> This work was supported in part by a grant from the National Science Foundation's Large Scientific and Software Data Set Visualization program, grant ACI 99-82251. Thumbnail$
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Last Modified: Jan 31, 2001