Abstract.
We present a new approach to the construction of piecewise polynomial or rational C k -spline surfaces of arbitrary topological structure. The basic idea is to use exclusively parametric smoothness conditions, and to solve the well-known problems at extraordinary points by admitting singular parametrizations. The smoothness of the spline surfaces is guaranteed by specifying a regular smooth reparametrization explicitly. The resulting space of topologically unrestricted rational B-splines (TURBS) is linear and possesses a natural refinement property. Compared with all known methods the construction principle of TURBS is of striking simplicity and the required polynomial bi-degree is essentially decreased from O(k 2 ) to d=2k+2 .
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January 5, 1996. Date revised: September 5, 1996.
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Reif, U. TURBS—Topologically Unrestricted Rational B-Splines. Constr. Approx. 14, 57–77 (1998). https://doi.org/10.1007/s003659900063
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DOI: https://doi.org/10.1007/s003659900063
- Key words. Arbitrary topology
- Spline surface
- Subdivision.
- AMS Classification. Primary 65D17, 65D07, 68U07.
- <lsiheader> <onlinepub>8 May, 1998
- <editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;R.A. DeVore
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