Graphics Gems V (IBM Version)

III.2

Surface Models and the Resolution of N-Dimensional Cell Ambiguity

Hill Steve,     Computing Laboratory University of Kent United Kingdom

Jonathan C. Roberts,     Computing Laboratory University of Kent United Kingdom

Introduction

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 sets show many sign alternations. ...