Surface Models and the Resolution of N-Dimensional Cell Ambiguity

The representation of n-dimensional continuous surfaces often employs a discrete lattice of n-dimensional cube cells. For instance, the marching cubes method locates the surface lying between adjacent vertices of the n-cube edges in which the cell vertices represent discrete sample values (Lorensen and Cline 1987). The volume's surface exists at a point of zero value: it intersects any cube edge whose vertex values have opposing sign. Ambiguities occur in the cells whose vertex set show many sign alternations. Geometrically, the surface intersects one face of the n-cube through each of its four edges. It is these special cases which engenders the need for resolution as a central concern in surface modeling. This gem reviews and illustrates the disambiguation strategies described in the literature.