A generative classification of mesh refinement rules with lattice transformations

Authors:
I. P. Ivrissimtzis;N. A. Dodgson;M. A. Sabin
Affiliations:
MPI Informatik, Stuhlsatzenhausweg 85, D-66123 Saarbrücken, Germany;University of Cambridge, Computer Laboratory, William Gates Building, 15 J J Thomson Avenue, Cambridge CB3 0FD, UK;Numerical Geometry Ltd., 26 Abbey Lane, Lode, Cambridge CB5 9EP, UK
Venue:
Computer Aided Geometric Design
Year:
2004

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Abstract

We give a classification of subdivision refinement rules using similarity transformations of lattices. Our work expands recent results in the classification of primal triangular subdivision (Alexa, 2002). In the examples we concentrate on the cases with a low ratio of similarity and find new univariate and bivariate refinement rules with the lowest possible such ratio, showing that this very low ratio usually comes at the expense of symmetry.