Topology Preserving Marching Cubes-like Algorithms on the Face-Centered Cubic Grid

The well-known marching cubes algorithm is modified to apply to the face-centered cubic (fee) grid. Thus, the local configurations that are considered when extracting the local surface patches are not cubic anymore. This paper presents three different partitionings of the fee grid to be used for the local configurations. The three candidates are evaluated theoretically and experimentally and compared with the original marching cubes algorithm. It is proved that the reconstructed surface is topologically equivalent to the surface of the original object when the surface of the original object that is digitized is smooth and a sufficiently dense fee grid is used.