Smooth surface interpolation to scattered data using interpolatory subdivision algorithms

Computers and Mathematics with Applications

Volumn 32, Issue 3, 1996, Pages 93-110

  Qu, R ^a   Agarwal, R P ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Approximation; Scattered data interpolation; Subdivision algorithm; Surface interpolation; Triangulation

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; COMPUTER AIDED DESIGN; COMPUTER GRAPHICS; DATA STRUCTURES; ERRORS; ESTIMATION; IMAGE ANALYSIS; INTERPOLATION; TRIANGULATION;

ERROR ESTIMATES; EXTRAORDINARY POINT ANALYSIS; INTERPOLATORY SUBDIVISION ALGORITHMS; INTERPOLATORY SURFACES; LOCAL SUBDIVISION MATRIX ANALYSIS; SCATTERED DATA; SURFACE INTERPOLATION;

ALGORITHMS;

EID: 0030212554     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/0898-1221(96)00115-0     Document Type: Article

References (24)

1. N. Dyn, J.A. Gregory and D. Levin, A 4-point interpolatory subdivision scheme for curve design, Computer Aided Geometric Design 4, 257-268, (1987).
2. N. Dyn, J.A. Gregory and D. Levin, Analysis of uniform binary subdivision scheme for curve design, TR/09, Dept. of Maths. and Stats., Brunel University, Britain, (1988).
3. N. Dyn, J.A. Gregory and D. Levin, Uniform subdivision algorithms for curves and surfaces, TR/08, Dept. of Maths. and Stats., Brunel University, Britain, (1991).
4. A.C. Cavaretta and C.M. Micchelli, The design of curves and surfaces by subdivision, In Mathematical Methods in Computer Aided Geometric Design, (Edited by T. Lyche and L.L. Schumaker), pp. 115-154, New York, (1989).
5. A. Cavaretta, C. Micchelli and W. Dahmen, Stationary subdivision, AMS Memoirs 93 (453), (1991).
6. W. Dahmen, N. Dyn and D. Levin, On the convergence rates of subdivision algorithms for box spline surfaces, Constr. Approx. 1, 305-322, (1985).
7. W. Dahmen and C.A. Micchelli, Subdivision algorithms for the generation of box splines surfaces, Computer Aided Geometric Design 1, 115-129, (1984).
8. I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure. Appl. Math. 41, 909-996, (1988).
9. G. Deslauriers and S. Dubuc, Symmetric iterative interpolation, Constr. Approx. 5, 49-68, (1989).
10. G. Deslauriers and S. Dubuc, Interpolation dyadic, Fractals, Dimensions non Entieres et Applications, (Edited by G. Cherbit), pp. 44-45, Masson, Paris, (1987).
11. S. Dubuc, Interpolation through an iterative scheme, J. Math. Anal. and Appl. 144, 185-204, (1986).
12. W. Boehm, G. Farin and J. Kahmann, A survey of curve and surface methods in CAGD, Computer Aided Geometric Design 1, 1-60, (1984).
13. D. Doo and M. Sabin, Behaviour of recursive division surfaces near extraordinary points, Computer Aided Design 10, 356-360, (1978).
14. J.A. Gregory and R. Qu, An analysis of the butterfly scheme over uniform triangulations, Presented at the Chamonix Conference on Curves and Surfaces, France, June 1990.
15. J.P. Mongeau and S. Dubuc, Continuous and differentiable multidimensional iterative interpolation, Linear Algebra and Application 180, 95-120, (1993).
16. R. Qu, Recursive subdivision algorithms for curve and surface design, Ph.D. Thesis, Department of Mathematics and Statistics, Brunel University, Britain, (August 1990).
17. nd SPIE Conference on Curves and Surfaces, pp. 423-436, Boston, (1991).
18. R. Qu and J.A. Gregory, A 10-point interpolatory recursive subdivision algorithm for the generation of parametric surfaces, TR/01, Dept. of Math. and Stats., Brunel University, Britain, (1991).
19. R. Qu, Curve and surface interpolation by recursive subdivision algorithms, Computer Aided Drafting, Design and Manufacturing 4 (2), 28-39, (1994).
20. R. Qu, Curves generated by a three-term difference algorithm, Mathl. Comput. Modelling 22 (2), 49-64, (1995).
21. R. Qu, Filling polygonal holes by subdivision algorithms, Annals of Numerical Mathematics, (1996) (to appear).
22. R. Qu and R.P. Agarwal, A cross difference approach to the analysis of subdivision algorithms, Neural, Parallel and Scientific Computations 3, 393-416, (1995).
23. R. Qu, An approach to the improvement of surface triangulations by subdivision algorithms, (preprint).
24. E. Cohen, T. Lyche and R. Riesenfeld, Discrete box-splines and refinement algorithms, Computer Aided Geometric Design 1, 131-148, (1984).