Surface Models and the Resolution of N -Dimensional Cell Ambiguity

Publisher Summary This chapter describes 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. The volume's surface exists at a point of zero value—it intersects any cube edge whose vertex values have opposing signs. Ambiguities occur in the cells whose vertex sets 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 that engender the need for resolution as a central concern in surface modeling. This chapter reviews and illustrates the disambiguation strategies described in the literature. It highlights that in an ideal surface algorithm, the features of the surface geometry should match those of the underlying surface. In particular, if the original surface is continuous, the representational model must preserve this continuity. The chapter also reviews disambiguation techniques that require the computation of additional values or vertices for the decision.