An efficient algorithm to compute subsets of points in ℤn
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
VG'05 Proceedings of the Fourth Eurographics / IEEE VGTC conference on Volume Graphics
| Hi-index | 0.00 |
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.