Summary
We describe how to determine the number of cases that arise in visualization al- gorithms 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.
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Banks, D.C., Stockmeyer, P.K. (2009). DeBruijn Counting for Visualization Algorithms. In: Möller, T., Hamann, B., Russell, R.D. (eds) Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b106657_4
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DOI: https://doi.org/10.1007/b106657_4
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