Optimizing the topological and combinatorial complexity of isosurfaces

Since the publication of the original Marching Cubes algorithm, numerous variations have been proposed for guaranteeing water-tight constructions of triangulated approximations of isosurfaces. Most approaches divide the 3D space into cubes that each occupy the space between eight neighboring samples of a regular lattice. The portion of the isosurface inside a cube may be computed independently of what happens in the other cubes, provided that the constructions for each pair of neighboring cubes agree along their common face. The portion of the isosurface associated with a cube may consist of one or more connected components, which we call sheets. The topology and combinatorial complexity of the isosurface is influenced by three types of decisions made during its construction: (1) how to connect the four intersection points on each ambiguous face, (2) how to form interpolating sheets for cubes with more than one loop, and (3) how to triangulate each sheet. To determine topological prop...

• Type: Journal
• Year: 2005
• Where: CAD
• Authors: Carlos Andújar, Pere Brunet, Antoni Chica, Isabel Navazo, Jarek Rossignac, Alvar Vinacua
• Keywords: CAD 2005, Cube, Marching Cubes Algorithm, Theoretical Computer Science, Water-tight Constructions