Closed surfaces defined from biquadratic splines
- 56 Downloads
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 classification41A15 41A05 41A63
Key words and phrasesClosed surface Biquadratic B-spline Rectangular patch complex
Unable to display preview. Download preview PDF.
- 3.T. D.De Rose (1985): Geometric Continuity: A Parameterization Independent Measure of Continuity for Computer-Aided Geometric Design. Ph.D. Thesis, Computer Science Division, University of California at Berkely.Google Scholar
- 5.T. N. T. Goodman, S. L. Lee (1987):Geometrically continuous surfaces defined parametrically from piecewise polynomials. In: The Mathematics of Surfaces, II (R. Martin, ed.). Oxford: Clarendon, pp. 343–361.Google Scholar
- 6.J. A. Gregory, J. M. Hahn (1987):Geometric continuity and convex combination patches. Comput. Aided Geometric Design,4:79–89.Google Scholar
- 7.J. A. Gregory, V. Lau, J. Zhou (1990):Smooth parametric surfaces and n-sided patches. In: Computation of Curves and Surfaces (W. Dahmen, M. Gasca, C. A. Micchelli, eds.). NATO ASI Series C, vol. 307. London: Kluwer, pp. 457–498.Google Scholar
- 8.J. J. Van Wijk (1986):Bicubic patches for approximating non-rectangular control-point meshes. Comput. Aided Geometric Design,3:1–13.Google Scholar