Surface Subdivision Algorithms and Structured Linear Algebra: a Computational Approach to Determine Bounds of Extraordinary Rule Weights

Abstract. In the vicinity of extraordinary vertices, the action of a primal subdivision scheme for the construction of arbitrary topology surfaces can be represented by structured matrices that form a hybrid matrix algebra related to the block-circulant algebra. Exploiting the block diagonalization of such matrices, we can easily take into consideration the constraints to be satisfied by their eigenvalues and provide an efficient computational approach for determining the ranges of variability of the weights defining the extraordinary rules. Application examples of this computational strategy are shown to find the bounds of extraordinary rule weights for improved variants of two existing subdivision schemes.