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

• Published in 2003
In the collection
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 substitution 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 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.

### BibTeX entry

@article{CountingCasesInMarchingCubes,
title = {Counting Cases in Marching Cubes: Towards a Generic Algorithm for Producing Substitopes},
author = {David C. Banks and Stephen Linton},
url = {https://www.evl.uic.edu/cavern/rg/20040525{\_}renambot/Visualization-papers/papers/03/01250354.pdf http://ieeexplore.ieee.org/document/1250354},
urldate = {2016-09-28},
abstract = {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 substitution 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 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.},
comment = {},
collections = {Basically computer science},
year = 2003
}