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A generative classification of mesh refinement rules with lattice transformations

I.P. Ivrissimtzis, N.A. Dodgson, M.A. Sabin

September 2002, 13 pages

An updated, improved version of this report has been published in Computer Aided Geometric Design 22(1):99–109, January 2004 [doi:10.1016/j.cagd.2003.08.001]. The classification scheme is slightly different in the CAGD version. Please refer to the CAGD version in any work which you produce.

Abstract

We give a classification of the subdivision refinement rules using sequences of similar lattices. Our work expands and unifies recent results in the classification of primal triangular subdivision [Alexa, 2001], and results on the refinement of quadrilateral lattices [Sloan, 1994, 1989]. In the examples we concentrate on the cases with 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.

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BibTeX record

@TechReport{UCAM-CL-TR-542,
  author =	 {Ivrissimtzis, I.P. and Dodgson, N.A. and Sabin, M.A.},
  title = 	 {{A generative classification of mesh refinement rules with
         	   lattice transformations}},
  year = 	 2002,
  month = 	 sep,
  url = 	 {http://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-542.pdf},
  institution =  {University of Cambridge, Computer Laboratory},
  number = 	 {UCAM-CL-TR-542}
}