(No) More Marching Cubes

Carr, Hamish

(No) More Marching Cubes

Files

081-090.pdf (1.9 MB)

Date

2007

Authors

Carr, Hamish

Publisher

The Eurographics Association

Abstract

Isosurfaces, one of the most fundamental volumetric visualization tools, are commonly rendered using the wellknown Marching Cubes cases that approximate contours of trilinearly-interpolated scalar fields. While a complete set of cases has recently been published by Nielson, the formal proof that these cases are the only ones possible and that they are topologically correct is difficult to follow. We present a more straightforward proof of the correctness and completeness of these cases based on a variation of the Dividing Cubes algorithm. Since this proof is based on topological arguments and a divide-and-conquer approach, this also sets the stage for developing tessellation cases for higher-order interpolants and for the quadrilinear interpolant in four dimensions. We also demonstrate that, apart from degenerate cases, Nielson's cases are in fact subsets of two basic configurations of the trilinear interpolant.

        @inproceedings{10.2312:VG/VG07/081-090
,
booktitle = {Eurographics/IEEE VGTC Symposium on Volume Graphics
},
editor = {H.-C. Hege and R. Machiraju and T. Moeller and M. Sramek
},
title = {{(No) More Marching Cubes
}},
author = {Carr, Hamish
},
year = {2007
},
publisher = {The Eurographics Association
},
ISSN = {1727-8376
},
ISBN = {978-3-905674-03-3
},
DOI = {10.2312/VG/VG07/081-090
}
}