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

• Published in 2003
• Added on 2016-09-28

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.

Links

• https://www.evl.uic.edu/cavern/rg/20040525_renambot/Visualization-papers/papers/03/01250354.pdf
• http://ieeexplore.ieee.org/document/1250354

Other information

BibTeX entry

@article{CountingCasesInMarchingCubes,
	key = {CountingCasesInMarchingCubes},
	type = {article},
	title = {Counting Cases in Marching Cubes: Towards a Generic Algorithm for Producing Substitopes},
	author = {David C. Banks and Stephen Linton},
	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 = {},
	date_added = {2016-09-28},
	date_published = {2003-12-07},
	urls = {https://www.evl.uic.edu/cavern/rg/20040525{\_}renambot/Visualization-papers/papers/03/01250354.pdf,http://ieeexplore.ieee.org/document/1250354},
	collections = {Basically computer science},
	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},
	year = 2003
}