Counting cases in substitope algorithms
MetadataShow full item record
We describe how to count the cases that arise in a family of visualization techniques, including Marching Cubes, Sweeping Simplices, Contour Meshing, Interval Volumes, and Separating Surfaces. Counting the cases is the first step toward developing a generic visualization algorithm to produce substitopes ( geometric substitutions of polytopes). We demonstrate the method using "GAP," a software system for computational group theory. The case-counts are organized into a table that provides a taxonomy of members of the family; numbers in the table are derived from actual lists of cases, which are computed by our methods. The calculations confirm previously reported case-counts for four dimensions that are too large to check by hand and predict the number of cases that will arise in substitope algorithms that have not yet been invented. We show how Polya theory produces a closed-form upper bound on the case counts.
Banks , D C , Linton , S A & Stockmeyer , P K 2004 , ' Counting cases in substitope algorithms ' IEEE Transactions on Visualization and Computer Graphics , vol. 10 , no. 4 , pp. 371-384 . DOI: 10.1109/TVCG.2004.6
IEEE Transactions on Visualization and Computer Graphics
(c) 2004 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.