Abstract.
We derive necessary and sufficient conditions for tangent plane and C k -continuity of stationary subdivision schemes near extraordinary vertices. Our criteria generalize most previously known conditions. We introduce a new approach to analysis of subdivision surfaces based on the idea of the universal surface . Any subdivision surface can be locally represented as a projection of the universal surface, which is uniquely defined by the subdivision scheme. This approach provides us with a more intuitive geometric understanding of subdivision near extraordinary vertices.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
February 16, 1998. Date revised: January 27, 1999. Date accepted: April 2, 1999.
Rights and permissions
About this article
Cite this article
Zorin, D. Smoothness of Stationary Subdivision on Irregular Meshes. Constr. Approx. 16, 359–397 (2000). https://doi.org/10.1007/s003659910016
Published:
Issue Date:
DOI: https://doi.org/10.1007/s003659910016