Interpolatory rank-1 vector subdivision schemes

Computer Aided Geometric Design

Volumn 21, Issue 4, 2004, Pages 341-351

  Conti, Costanza ^a   Zimmermann, Georg ^b  

^a UNIVERSITY OF FLORENCE   (Italy)

^b UNIVERSITY OF HOHENHEIM   (Germany)

Author keywords

Data preservation; Interpolatory; Subdivision schemes; Vector valued

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; FUNCTIONS; INTERPOLATION; ITERATIVE METHODS; MATRIX ALGEBRA; SET THEORY; VECTORS;

DATA PRESERVATION; INTERPOLATORY; SUBDIVISION SCHEMES; VECTOR VALUED;

COMPUTER AIDED DESIGN;

EID: 1842558556     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cagd.2003.11.003     Document Type: Article

References (22)

1. Cavaretta A.S., Dahmen W., Micchelli C.A. Stationary subdivision. Mem. Amer. Math. Soc. 93:1991;1-186.
2. Chaikin G.M. An algorithm for high speed curve generation. Comput. Graphics Image Process. 3:1991;346-349.
3. Cohen N., Dyn A., Levin D. Stability and inter-dependence of matrix subdivision schemes. Fontanella F., Jetter K., Laurent P.J. Advanced Topics in Multivariate Approximation. 1996;33-45 World Scientific, Singapore.
4. Conti C., Jetter K. A new subdivision method for bivariate splines on the four-directional mesh. J. Comput. Appl. Math. 119:2000;936-952.
5. Dahmen W., Micchelli C.A. Biorthogonal wavelet expansion. Constr. Approx. 13:1997;293-328.
6. Deslauriers G., Dubuc S. Symmetric iterative interpolation. Constr. Approx. 5:1989;49-68.
7. Doo D., Sabin M. Behaviour of recursive division surfaces near extraordinary points. Computer-Aided Design. 10:1978;356-360.
8. Dubuc S. Interpolation through an iterative scheme. J. Math. Anal. Appl. 114:1986;185-204.
9. Dyn N. Subdivision schemes in computer-aided geometric design. Light W. Advances in Numerial Analysis, vol. II: Wavelets, Subdivision Algorithms and Radial Basis Functions. 1992;36-104 Clarendon Press, Oxford.
10. Dyn N. Interpolatory subdivision. Principles of Multiresolution in Geometric Modelling. Summer School Lecture Notes, Munich. 2001;71-88.
11. Dyn N., Gregory J.A., Levin D. A four-point interpolatory subdivision scheme for curve design. Computer Aided Geometric Design. 4:1987;257-268.
12. Dyn N., Gregory J.A., Levin D. A butterfly subdivision scheme for surface interpolation. ACM Trans. Graph. 9:1990;160-169.
13. Dyn N., Gregory J.A., Levin D. Analysis of uniform binary subdivision schemes for curve design. Constr. Approx. 7:1991;127-147.
14. Dyn N., Levin D. Interpolatory subdivision scheme for the generation of curves and surfaces. Haussmann W., Jetter K. Multivariate Approximation and Interpolation. 1990;91-106 Birkhäuser, Basel.
15. Dyn N., Levin D. Analysis of Hermite-type subdivision schemes. Chui C.K., Schumaker L.L. Approximation Theory VIII, 2, Wavelets and Multilevel Approximation. 1995;117-124 World Scientific, Singapore.
16. Dyn N., Levin D. Analysis of Hermite-interpolatory subdivision schemes. Spline Functions and the Theory of Wavelets. CRM Proc. Lecture Notes. 1996;105-113 Amer. Math. Soc. Providence.
17. Dyn N., Levin D. Matrix subdivision-analysis by factorization. Bojanov B.D. Approximation Theory. 2002;187-211 Darba, Sofia.
18. Goodman T.N.T. Pairs of refinable functions. Fontanella F., Jetter K., Laurent P.J. Advanced Topics in Multivariate Approximation. 1996;139-154 World Scientific, Singapore.
19. Jia R.Q., Riemenschneider S., Zhou D.X. Vector subdivision schemes and multiple wavelets. Math. Comp. 67:1998;1533-1563.
20. Kobbelt L. Interpolatory subdivision on open quadrilateral nets with arbitrary topology. Proceedings of Eurographics 96, Computer Graphic Forum. 1996;409-420.
21. Micchelli C.A., Sauer T. Regularity of multiwavelets. Adv. Comput. Math. 7:1997;455-545.
22. Micchelli C.A., Sauer T. On vector subdivision. Math. Z. 229:1998;621-674.