@TechReport{ it:2016-012,
author = {Marco Donatelli and Paola Novara and Lucia Romani and
Stefano Serra-Capizzano and Debora Sesana},
title = {Surface Subdivision Algorithms and Structured Linear
Algebra: a Computational Approach to Determine Bounds of
Extraordinary Rule Weights},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2016},
number = {2016-012},
month = jul,
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.}
}