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Lens-shaped surfaces and C2 subdivision.
- Source :
-
Computing . Nov2009, Vol. 86 Issue 2/3, p171-183. 13p. 2 Color Photographs, 18 Diagrams, 1 Chart. - Publication Year :
- 2009
-
Abstract
- Lens-shaped surfaces (with vertices of valence 2) arise for example in automatic quad-remeshing. Applying standard Catmull–Clark subdivision rules to a vertex of valence 2, however, does not yield a C1 surface in the limit. When correcting this flaw by adjusting the vertex rule, we discover a variant whose characteristic ring is z → z2. Since this conformal ring is of degree bi-2 rather than bi-3, it allows constructing a subdivision algorithm that works directly on the control net and generates C2 limit surfaces of degree bi-4 for lens-shaped surfaces. To further improve shape, a number of re-meshing and re-construction options are discussed indicating that a careful approach pays off. Finally, we point out the analogy between characteristic configurations and the conformal maps z4/ n, cos z and e z. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0010485X
- Volume :
- 86
- Issue :
- 2/3
- Database :
- Academic Search Index
- Journal :
- Computing
- Publication Type :
- Academic Journal
- Accession number :
- 44500291
- Full Text :
- https://doi.org/10.1007/s00607-009-0060-9