A generative classification of mesh refinement rules with lattice transformations

Ivrissimtzis, Ioannis; Dodgson, Neil; Sabin, Malcolm

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. 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.

Citation

Ivrissimtzis, I., Dodgson, N., & Sabin, M. (2004). A generative classification of mesh refinement rules with lattice transformations. Computer Aided Geometric Design, 21(1), 99-109. https://doi.org/10.1016/j.cagd.2003.08.001

• Journal Article Type: Article
• Publication Date: 2004-01
• Deposit Date: Feb 26, 2008
• Journal: Computer Aided Geometric Design
• Print ISSN: 0167-8396
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 21
• Issue: 1
• Pages: 99-109
• DOI: https://doi.org/10.1016/j.cagd.2003.08.001
• Keywords: Subdivision, Lattices, Classification, Mesh refinement.