A geometric diagram and hybrid scheme for triangle subdivision

Authors:
Ángel Plaza;José P. Suárez;Graham F. Carey
Affiliations:
Department of Mathematics, University of Las Palmas de Gran Canaria (ULPGC), Spain;Department of Cartography and Graphic Engineering, ULPGC, Spain;Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, Austin, TX, USA
Venue:
Computer Aided Geometric Design
Year:
2007

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Abstract

We introduce a geometrical diagram to study the improvement in shape of triangles generated by iterative application of triangle subdivision. The four Triangles Longest Edge (4TLE) subdivision pattern and a new hybrid 4T Longest-Edge/Self-Similar (hybrid 4TLE-SS) scheme are investigated in this way. The map diagram provides a convenient way to visualize the evolution and migration of element shapes leading to a better understanding of the improvement process and the effect of recursive subdivision schemes. A complex variable mapping analysis supports the diagram and similarity class specifications. Numerical comparisons confirm the superiority of the new hybrid scheme.