A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Simple regularity criteria for subdivision schemes
SIAM Journal on Mathematical Analysis
Box splines
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Computer Aided Geometric Design
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Computing the Smoothness Exponent of a Symmetric Multivariate Refinable Function
SIAM Journal on Matrix Analysis and Applications
Geometric Modelling, Dagstuhl, Germany, 1996
Polynomial generation and quasi-interlpolation in stationary non-uniform subdivision
Computer Aided Geometric Design
Modified subdivision surfaces with continuous curvature
ACM SIGGRAPH 2006 Papers
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
On the curvature of guided surfaces
Computer Aided Geometric Design
ACM SIGGRAPH 2009 papers
Integration of CAD and boundary element analysis through subdivision methods
Computers and Industrial Engineering
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This paper presents a new subdivision scheme that operates over an infinite triangulation, which is regular except for a single extraordinary vertex. The scheme is based on the quartic three-directional Box-spline scheme, and is guaranteed to generate C2 limit functions whenever the valency n of the extraordinary vertex is in the range 4 ≤ n ≤ 20. The new scheme differs from the commonly used subdivision schemes by the fact that it applies special subdivision rules near edges of the original triangulation, which emanate from the extraordinary vertex, and not only in the vicinity of the extraordinary vertex.