An extended triangulation to the Marching Cubes 33 algorithm

The Marching Cubes algorithm is arguably the most popular isosurface extraction algorithm. Since its inception, two problems have lingered, namely, triangle quality and topology correctness. Although there is an extensive literature to solve them, topology correctness is achieved in detriment of triangle quality and vice versa. In this paper, we present an extended version of the Marching Cubes 33 algorithm (a variation of the Marching Cubes algorithm which guarantees topological correctness), called Extended Marching Cubes 33. In the proposed algorithm, the grid vertex are labeled with “+,” “ −,” and “=,” according to the relationship between its scalar field value and the isovalue. The inclusion of the “=” grid vertex label naturally avoids degenerate triangles. As an application of our method, we use the proposed triangulation to improve the quality of the triangles in the generated mesh while preserving its topology as much as possible.