Constructive Approximation

, Volume 7, Issue 1, pp 149–160 | Cite as

Closed surfaces defined from biquadratic splines

  • T. N. T. Goodman


In order to construct closed surfaces with continuous unit normal, this paper studies certain spaces of spline functions on meshes of four-sided faces. The functions restricted to the faces are biquadratic polynomials or, in certain special cases, bicubic polynomials. A basis is constructed of positive functions with “small” support which sum to 1 and reduce to tensor-product biquadratic B-splines away from certain “singular” vertices. It is also shown that the space is suitable for interpolating data at the midpoints of the faces.

AMS classification

41A15 41A05 41A63 

Key words and phrases

Closed surface Biquadratic B-spline Rectangular patch complex 


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Copyright information

© Springer-Verlag New York Inc 1991

Authors and Affiliations

  • T. N. T. Goodman
    • 1
    • 2
  1. 1.Department of Mathematical SciencesDundee UniversityDundeeScotland
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA

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