# Piecewise linear hypersurfaces using the Marching Cubes Algorithm

Roberts, Jonathan C. and Hill, Steve (1999) Piecewise linear hypersurfaces using the Marching Cubes Algorithm. In: Erbacher, Robert F. and Chen, Philip C. and Wittenbrink, Craig M., eds. Visual Data Exploration and Analysis VI. Proceedings of SPIE . SPIE, pp. 170-181. ISBN 0-8194-3114-1. (doi:10.1117/12.342833) (KAR id:16559)

PDF
Language: English
 Preview
Postscript
Language: English
 Preview
Official URL
http://dx.doi.org/10.1117/12.342833

## Abstract

Surface visualization is very important within scientific visualization. The surfaces depict a value of equal density (an isosurface) or display the surrounds of specified objects within the data. Likewise, in two dimensions contour plots may be used to display the information. Thus similarly, in four dimensions hypersurfaces may be formed around hyperobjects. These surfaces (or contours) are often formed from a set of connected triangles (or lines). These piecewise segments represent the simplest non-degenerate object of that dimension and are named simplices. In four dimensions a simplex is represented by a tetrahedron, which is also known as a 3-simplex. Thus, a continuous n dimensional surface may be represented by a lattice of connected n-1 dimensional simplices. This lattice of connected simplices may be calculated over a set of adjacent n dimensional cubes, via for example the Marching Cubes Algorithm. We propose that the methods of this local-cell tiling method may be usefully-applied to four dimensions and potentially to N-dimensions. Thus, we organise the large number of traversal cases and major cases;: introduce the notion of a sub-case (that enables the large:number of cases to be further reduced); and describe three methods for implementing the Marching Cubes lookup table in four-dimensions.

Item Type: Book section 10.1117/12.342833 Marching Cubes; four dimensions; hypersurfaces; surfaces Q Science > QA Mathematics (inc Computing science) > QA 75 Electronic computers. Computer scienceQ Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming, Faculties > Sciences > School of ComputingFaculties > Sciences > School of Computing > Applied and Interdisciplinary Informatics Group F.D. Zabet 15 Apr 2009 12:52 UTC 05 Jul 2019 11:46 UTC https://kar.kent.ac.uk/id/eprint/16559 (The current URI for this page, for reference purposes)