Two-sided patches suitable for inclusion in a B-spline surface
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Mathematical Methods for Curves and Surfaces
Concentric tessellation maps and curvature continuous guided surfaces
Computer Aided Geometric Design
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Subdivision Surfaces
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
An introduction to guided and polar surfacing
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
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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 .