A merged tuning of binary and ternary Loop's subdivision

Abstract In the vicinity of extraordinary vertices, the action of a primal, symmetric 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 diagonalized by a block-FFT. Exploiting the block-diagonalization of such matrices and having in mind the target of a specific class of schemes, 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 exact bounds of extraordinary rule weights for improved variants of two existing subdivision schemes.