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 C 1 surface in the limit. When correcting this flaw by adjusting the vertex rule, we discover a variant whose characteristic ring is z → z 2. 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 C 2 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 z 4/n, cos z and e z.
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Communicated by C.H. Cap.
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Karčiauskas, K., Peters, J. Lens-shaped surfaces and C 2 subdivision. Computing 86, 171–183 (2009). https://doi.org/10.1007/s00607-009-0060-9
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DOI: https://doi.org/10.1007/s00607-009-0060-9