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This is the third and final image in a series of three
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This is the third (and final) image in a series of three Voronoi hierarchy images of the Cat's

May 28, 2010
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. [Third in a series of 3 related images. See Image 1.]

More about this Image This series of images of the Cats Eye Nebula show three resolutions of a Voronoi hierarchy. A Voronoi hierarchy 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 the series show three resolutions of a Voronoi hierarchy of the Cats-Eye Nebula. The first level contains 208 cells; the second contains 737 cells; and the final, 8284 cells. Using this algorithm, an excellent representation can be generated of the original image at a fraction of the original data size.

This work was supported in part by a grant from the National Science Foundation's Large Scientific and Software Data Set Visualization program under grant ACI 99-82251. (Year of image: 1999)


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