Closed smooth piecewise bicubic surfaces

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Closed smooth piecewise bicubic surfaces

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ACM Transactions on Graphics (TOG) archive
Volume 10 , Issue 4 (October 1991) table of contents

Pages: 342 - 365

Year of Publication: 1991

ISSN:0730-0301

Authors

S. L. Lee	National Univ. of Singapore, Kent Ridge Crescent, Singapore
A. A. Majid	Univ. of Science of Malaysia, Penang, Malaysia

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 3, Downloads (12 Months): 29, Citation Count: 2

Additional Information:

references cited by index terms review collaborative colleagues

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	A. A. Ball , D. J. T. Storry, Conditions for tangent plane continuity over recursively generated B-spline surfaces, ACM Transactions on Graphics (TOG), v.7 n.2, p.83-102, April 1988 [doi>10.1145/42458.42459]
	2	Wolfgang Böhm , Gerald Farin , Jürgen Kahmann, A survey of curve and surface methods in CAGD, Computer Aided Geometric Design, v.1 n.1, p.1-60, July 1984 [doi>10.1016/0167-8396(84)90003-7]
	3	CA~VLL, E., AND CLARX, J. Recursively generated B-spline surface on arbitrary topological meshes. Comput. Aided Des. 10, 6 (1978), 350-355.
	4	Hiroaki Chiyokura , Fumihiko Kimura, Design of solids with free-form surfaces, ACM SIGGRAPH Computer Graphics, v.17 n.3, p.289-298, July 1983
	5	Elaine Cohen , Tom Lyche , Larry L. Schumaker, Algorithms for degree-raising of splines, ACM Transactions on Graphics (TOG), v.4 n.3, p.171-181, July 1985 [doi>10.1145/282957.282962]
	6	Don, D., A~r) SASTN, M.A. Behavior of recursive subdivision surfaces near extraordinary points. Comput. Aided Des. 10, 6 (1978), 356-360.
	7	I. D. Faux , M. J. Pratt, Computational Geometry for Design and Manufacture, Halsted Press, New York, NY, 1979
	8	GOODMAN, T. N.T. Closed biquadratic surfaces. Constructive Approx. 7, 2 (1991), 149-160.
	9	T. N. T. Goodman , S. L. Lee, Geometrically continuous surfaces defind parametrically from piecewise polynomials, Proceedings on Mathematics of surfaces II, p.343-361, October 1987, Cardiff, United Kingdom
	10	John Gregory , Jörg Hahn, Geometric continuity and convex combination patches, Computer Aided Geometric Design, v.4 n.1-2, p.79-89, July 1987 [doi>10.1016/0167-8396(87)90026-4]
	11	A. K. Jones, Nonrectangular surface patches with curvature continuity, Computer-Aided Design, v.20 n.6, p.325-335, July/Aug. 1988 [doi>10.1016/0010-4485(88)90114-5]
	12	LIv, C.L. Introduction to Combinatorial Mathematics. McGraw-Hill, New York, 1968.
	13	Ahmad H. Nasri, Polyhedral subdivision methods for free-form surfaces, ACM Transactions on Graphics (TOG), v.6 n.1, p.29-73, Jan. 1987 [doi>10.1145/27625.27628]
	14	M A Sabin, Some negative results in N sided patches, Computer-Aided Design, v.18 n.1, p.38-44, Jan/Feb. 1986 [doi>10.1016/S0010-4485(86)80009-4]
	15	S T Tan , K C Chan, Bi-quadratic B-spline surfaces generated from arbitrary polyhedral meshes: a constructive approach, Computer Vision, Graphics, and Image Processing, v.39 n.2, p.144-166, Aug. 1987 [doi>10.1016/S0734-189X(87)80163-9]
	16	S T Tan , K C Chan, Generation of high order surfaces over arbitrary polyhedral meshes, Computer-Aided Design, v.18 n.10, p.411-423, Oct. 1986
	17	WATKINS, M. A. Problems in geometric continuity. Comput. Aided Des. 20, 8 (1988), 499-502.
	18	J J Van Wijk, Bicubic patches for approximating non-rectangular control-point meshes, Computer Aided Geometric Design, v.3 n.1, p.1-13, May 1986 [doi>10.1016/0167-8396(86)90021-X]

CITED BY 2

	Jörg Peters, Smoothing polyhedra made easy, ACM Transactions on Graphics (TOG), v.14 n.2, p.162-170, April 1995
	Jiansong Deng , Falai Chen , Xin Li , Changqi Hu , Weihua Tong , Zhouwang Yang , Yuyu Feng, Polynomial splines over hierarchical T-meshes, Graphical Models, v.70 n.4, p.76-86, July, 2008

INDEX TERMS

Primary Classification:
I. Computing Methodologies
I.3 COMPUTER GRAPHICS
I.3.5 Computational Geometry and Object Modeling
Subjects: Curve, surface, solid, and object representations

General Terms:
Algorithms, Design, Theory

Keywords:
B-splines, Be´zier representation, bicubic patches, closed surfaces, de Casteljau algorithm, geometric continuity, geometric modeling

REVIEW

"Carmen Curelet-Balan : Reviewer"

The authors investigate some approaches to the generation of two classes of closed smooth piecewise bicubic surfaces—the parametric bicubic B-spline surfaces in which the B-spline blending functions are defined on simple quadrilateral me more...

Collaborative Colleagues:

S. L. Lee: colleagues

A. A. Majid: colleagues

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