A marching algorithm for isosurface extraction from face-centered cubic lattices

Abstract

This work provides a novel method that extracts isosurfaces from face-centered cubic (FCC) lattices. It has been theoretically shown that sampling volumetric data on an FCC lattice tiled with rhombic dodecahedra is more efficient than sampling them on a Cartesian lattice tiled with cubes, in that the FCC lattice can represent the same data set as a Cartesian lattice with the same accuracy, yet with approximately 23% fewer samples. This fact, coupled with the good properties of rhombic dodecahedra, encouraged us to develop this related isosurface extraction technique. Thanks to the sparser sampling required by the FCC lattices, the de facto standard isosurface extraction algorithm, namely marching cubes, is accelerated significantly, as demonstrated. This reduced sampling rate also leads to a decrement in the number of triangles of the extracted models when compared to the marching cubes result. Finally, the topological consistency problem of the original marching cubes algorithm is also resolved. We show the potential of our algorithm with an indirect volume-rendering application.