Debruijn counting for visualization algorithms

Abstract

We describe how to determine the number of cases that arise in visualization algorithms such as Marching Cubes by applying the deBruijn extension of Pólya counting. This technique constructs a polynomial, using the cycle index, encoding the case counts that arise when a discrete function (or “color”) is evaluated at each vertex of a polytope. The technique can serve as a valuable aid in debugging visualization algorithms that extend Marching Cubes, Separating Surfaces, Interval Volumes, Sweeping Simplices, etc., to larger dimensions and to more colors.