Counting Cases in Marching Cubes: Toward a Generic Algorithm for Producing Substitopes

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 a software system (“GAP”) 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 calculation confirms previously reported case-counts for large dimensions that are too large to check by hand, and predicts the number of cases that will arise in algorithms that have not yet been invented. CR Categories: G.2 [Discrete Mathematics]: Combinatorics— Counting problems; G.4 [Mathematical Software]: Algorithm Design and Analysis;

• Type: Conference
• Year: 2003
• Where: VISUALIZATION
• Authors: David C. Banks, Stephen A. Linton
• Keywords: Computational Group Theory, Generic Visualization Algorithm, Visualization, VISUALIZATION 2003, first Step