A geometric diagram and hybrid scheme for triangle subdivision

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. © 2006 Elsevier B.V. All rights reserved.

• Type: Journal
• Year: 2007
• Where: CAGD
• Authors: Angel Plaza, José P. Suárez, Graham F. Carey
• Keywords: CAGD 2007, Recursive Subdivision Schemes, Triangles, Triangles Longest Edge