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Surface models and the resolution of N-Dimensional cell ambiguity
Steve Hill and Jonathan C. Roberts
In Alan W. Paeth, editor, Graphics Gems V, pages 182-196. Academic Press, May 1995.Abstract
The representation of n-dimensional continuous surfaces often employs a discrete lattice of n-dimensional cube cells. For instance, the marching cubes method locates the surface lying between adjacent vertices of the n-cube edges in which the cell vertices represent discrete sample values (Lorensen and Cline 1987). The volume's surface exists at a point of zero value: it intersects any cube edge whose vertex values have opposing sign.
Ambiguities occur in the cells whose vertex set show many sign alternations. Geometrically, the surface intersects one face of the (unknown variable n)$-cube through each of its four edges. It is these special cases which engenders the need for resolution as a central concern in surface modeling. This gem reviews and illustrates the disambiguation strategies described in the literature.
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@incollection{189,
author = {Steve Hill and Jonathan C. Roberts},
title = {Surface Models and the Resolution of {N}-{D}imensional Cell Ambiguity},
month = {May},
year = {1995},
pages = {182-196},
keywords = {determinacy analysis, Craig interpolants},
note = {},
doi = {},
url = {http://www.cs.kent.ac.uk/pubs/1995/189},
ISBN = {0-12-543455-3},
booktitle = {Graphics Gems V},
editor = {Alan W. Paeth},
publisher = {Academic Press},
}