## ABSTRACT

Much of the running time of theMarching Cubes algorithm and its variants is spent processing grid cubes that are not intersected by the isosurface. While it is theoretically possible for an isosurface to intersect every grid cube in the input, in practice a single isosurface intersects only a small fraction of the input grid cubes. A grid cube that is not intersected by a given isosurface is called an empty cube. Of course, whether a cube is empty depends upon the given isosurface.