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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A degree estimate for subdivision surfaces of higher regularity


Author: Ulrich Reif
Journal: Proc. Amer. Math. Soc. 124 (1996), 2167-2174
MSC (1991): Primary 65D17, 65D07, 68U07
MathSciNet review: 1327042
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Abstract: Subdivision algorithms can be used to construct smooth surfaces from control meshes of arbitrary topological structure. In contrast to tangent plane continuity, which is well understood, very little is known about the generation of subdivision surfaces of higher regularity. This work presents a degree estimate for piecewise polynomial subdivision surfaces saying that curvature continuity is possible only if the bi-degree $d$ of the patches satisfies $d \ge 2k+2$, where $k$ is the order of smoothness on the regular part of the surface. This result applies to any stationary or non-stationary scheme consisting of masks of arbitrary size provided that some generic symmetry and regularity assumptions are fulfilled.


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Additional Information

Ulrich Reif
Affiliation: Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart Germany
Email: reif@mathematik.uni-stuttgart.de

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03366-7
PII: S 0002-9939(96)03366-7
Keywords: Subdivision, arbitrary topology, extraordinary vertex, curvature continuity, piecewise polynomial surface
Received by editor(s): December 6, 1994
Additional Notes: This work was supported by BMFT Projekt 03–HO7STU–2.
Communicated by: Peter Li
Article copyright: © Copyright 1996 American Mathematical Society