Conditions for tangent plane continuity over recursively generated B-spline surfaces

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Conditions for tangent plane continuity over recursively generated B-spline surfaces

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ACM Transactions on Graphics (TOG) archive
Volume 7 , Issue 2 (April 1988) table of contents

Pages: 83 - 102

Year of Publication: 1988

ISSN:0730-0301

Authors

A. A. Ball	Loughborough Univ. of Technology, Loughborough, Leicestershire, UK
D. J. T. Storry	Loughborough Univ. of Technology, Loughborough, Leicestershire, UK

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 7, Downloads (12 Months): 47, Citation Count: 20

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abstract references cited by index terms review collaborative colleagues

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ABSTRACT

The continuity properties of recursively generated B-spline surfaces over an arbitrary topology have been related to the eigenproperties of the local subdivision transformation. In this paper a discrete Fourier transform technique is employed to derive these eigenproperties for a general choice of subdivision weightings. Conditions on these weightings are identified for tangent plane continuity at the extraordinary points and a geometric interpretation is given.

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	BALL, A. A., AND STORR~, D. J. T. Recursively generated B-spline surfaces. In CAD84, Proceedings (Brighton, Sussex, U.K., Apr. 3-5). Butterworth, Woburn, Mass., 1984, pp. 112-119.
	2	A A Ball , D J T Storry, A matrix approach to the analysis of recursively generated B-spline surfaces, Computer-Aided Design, v.18 n.10, p.437-442, Oct. 1986
	3	CATMULL, E., AND CLARK, J. Recursively generated B-spline surfaces on arbitrary topological meshes. Comput. Aided Des. 10 (1978), 350-355.
	4	Doo, D., AND SABIN, M.A. Behaviour of recursive division surfaces near extraordinary points. Comput. Aided Des. 10 (1978), 356-360.
	5	GORDON, W. J., AND RIESENFELD, R.F. B-spline curves and surfaces. In Computer Aided Geometric Design. Academic Press, New York, 1974.
	6	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]
	7	STORRY, D. J. T. B-spline surfaces over an irregular topology by recursive subdivision. Ph.D. dissertation, Loughborough Univ. of Technology, Leicestershire, England, 1985.

CITED BY 20

	Thomas W. Sederberg , Jianmin Zheng , David Sewell , Malcolm Sabin, Non-uniform recursive subdivision surfaces, Proceedings of the 25th annual conference on Computer graphics and interactive techniques, p.387-394, July 1998
	Jos Stam, Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values, Proceedings of the 25th annual conference on Computer graphics and interactive techniques, p.395-404, July 1998
	S. L. Lee , A. A. Majid, Closed smooth piecewise bicubic surfaces, ACM Transactions on Graphics (TOG), v.10 n.4, p.342-365, Oct. 1991
	A. A. Ball , D. J. T. Storry, An investigation of curvature variations over recursively generated B-spline surfaces, ACM Transactions on Graphics (TOG), v.9 n.4, p.424-437, Oct. 1990
	Chhandomay Mandal , Hong Qin , Baba C. Vemuri, Dynamic smooth subdivision surfaces for data visualization, Proceedings of the 8th conference on Visualization '97, p.371-ff., October 18-24, 1997, Phoenix, Arizona, United States
	Jörg Peters, Patching Catmull-Clark meshes, Proceedings of the 27th annual conference on Computer graphics and interactive techniques, p.255-258, July 2000
	Mark Halstead , Michael Kass , Tony DeRose, Efficient, fair interpolation using Catmull-Clark surfaces, Proceedings of the 20th annual conference on Computer graphics and interactive techniques, p.35-44, September 1993
	Denis Zorin , Peter Schröder , Wim Sweldens, Interpolating Subdivision for meshes with arbitrary topology, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, p.189-192, August 1996
	Li Guiqing , Li Hua, Blending parametric patches with subdivision surfaces, Journal of Computer Science and Technology, v.17 n.4, p.498-506, July 2002
	Luiz Velho, Stellar subdivision grammars, Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing, June 23-25, 2003, Aachen, Germany
	Hong Qin , Chhandomay Mandal , Baba C. Vemuri, Dynamic Catmull-Clark Subdivision Surfaces, IEEE Transactions on Visualization and Computer Graphics, v.4 n.3, p.215-229, July 1998
	K. Karĉiauskas , Jörg Peters , U. Reif, Shape characterization of subdivision surfaces: case studies, Computer Aided Geometric Design, v.21 n.6, p.601-614, July 2004
	Chhandomay Mandal , Hong Qin , Baba C. Vemuri, Dynamic Modeling of Butterfly Subdivision Surfaces, IEEE Transactions on Visualization and Computer Graphics, v.6 n.3, p.265-287, July 2000
	I. P. Ivrissimtzis , H.-P. Seidel, Evolutions of polygons in the study of subdivision surfaces, Computing, v.72 n.1-2, p.93-103, April 2004
	Loïc Barthe , Leif Kobbelt, Subdivision scheme tuning around extraordinary vertices, Computer Aided Geometric Design, v.21 n.6, p.561-583, July 2004
	Jian J. Zhang, Smooth surface representation over irregular meshes, Handbook of computer animation, Springer-Verlag, London, 2003
	Evelyne Vanraes , Adhemar Bultheel, A tangent subdivision scheme, ACM Transactions on Graphics (TOG), v.25 n.2, p.340-355, April 2006
	Charles K. Chui , Qingtang Jiang, Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices, Computer Aided Geometric Design, v.23 n.5, p.419-438, July 2006
	Martin Bertram , Mark A. Duchaineau , Bernd Hamann , Kenneth I. Joy, Bicubic subdivision-surface wavelets for large-scale isosurface representation and visualization, Proceedings of the conference on Visualization '00, p.389-396, October 2000, Salt Lake City, Utah, United States
	Huawei Wang , Kai Tang , Kaihuai Qin, Biorthogonal wavelets based on gradual subdivision of quadrilateral meshes, Computer Aided Geometric Design, v.25 n.9, p.816-836, December, 2008

INDEX TERMS

Primary Classification:
G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS
G.1.1 Interpolation
Subjects: Smoothing

Additional Classification:
G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS
G.1.1 Interpolation
Subjects: Spline and piecewise polynomial interpolation
G.1.3 Numerical Linear Algebra
Subjects: Eigenvalues and eigenvectors (direct and iterative methods)

I. Computing Methodologies
I.3 COMPUTER GRAPHICS
I.3.5 Computational Geometry and Object Modeling
Subjects: Geometric algorithms, languages, and systems

J. Computer Applications
J.6 COMPUTER-AIDED ENGINEERING
Subjects: Computer-aided design (CAD)

General Terms:
Algorithms, Design, Theory

REVIEW

"Alexander H. Kushkulei : Reviewer"

The authors study some properties of surfaces which can be constructed by iteratively “knocking off” corners of an arbitrary polyhedron. Various versions of this recursive subdivision technique were proposed and evaluated by Catmull more...

Collaborative Colleagues:

A. A. Ball: colleagues

D. J. T. Storry: colleagues

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