A matrix approach to the analysis of recursively generated B-spline surfaces
Computer-Aided Design
Conditions for tangent plane continuity over recursively generated B-spline surfaces
ACM Transactions on Graphics (TOG)
A novel FEM-based dynamic framework for subdivision surfaces
Proceedings of the fifth ACM symposium on Solid modeling and applications
Dynamic Catmull-Clark Subdivision Surfaces
IEEE Transactions on Visualization and Computer Graphics
Dynamic Modeling of Butterfly Subdivision Surfaces
IEEE Transactions on Visualization and Computer Graphics
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: case studies
Computer Aided Geometric Design
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The continuity properties of recursively generated B-spline surfaces over an arbitrary topology have been related to the eigenproperties of the local subdivision tranformation, and conditions have been established on the subdivision weightings for tangent plane continuity at extraordinary points. In this paper, curves through an extradordinary point, which align in both the tagent and binormal direction, are identified, and their curvatures are compared either side of the point. Further restrictions on the subdivision weightings are derived to optimize the curvature properties of the surface. In general continuity of curvature is not attained.