Subdivision Schemes for Thin Plate Splines

Computer Graphics Forum

Volumn 17, Issue 3, 1998, Pages 303-313

  Weimer, Henrik ^a   Warren, Joe ^a  

^a Rice University   (United States)

Author keywords

Fair surfaces; Optimization; Scattered data interpolation; Subdivision; Surface modeling; Thin plate splines; Variational design

Indexed keywords

EID: 0001051304     PISSN: 01677055     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-8659.00277     Document Type: Article

References (24)

1. S. Brenner and L. Scott, The mathematical theory of finite element methods, Springer-Verlag (1994).
2. E. Catmull and J. Clark, Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes, Computer Aided Design 10, 6, pp. 350-355 (1978).
3. A. Cavaretta, W. Dahmen and C. Micchelli, Stationary Subdivision, Memoirs of the AMS, 453 (1991).
4. CPLEX Optimization, Inc, Using the CPLEX Callable Library (1995).
5. D. Doo and M. Sabin, Analysis of the Behavior of Recursive Division Surfaces near extraordinary Points, Computer Aided Geometric Design, 10, 6, pp. 356-360 (1978).
6. J. Duchon, Splines minimizing rotation invariant semi-norms in Sobolev spaces, in W. Schempp and K. Zeller (eds.): Constructive Theory of Functions of several variables : proceedings of a conference held at Oberwolfach, April 25-May 1, 1976, Lecture Notes in Mathematics, 571, pp. 85-100, Springer-Verlag (1977).
7. N. Dyn, D. Levin and J. A. Gregory, A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control, Transactions on Graphics, 9, 2, pp. 160-169 (1990).
8. R. Franke, Thin Plate Splines with Tension, in R. E. Barnhill and W. Böhm (eds.), Surfaces in CADG 1984, North-Holland, pp. 87-95 (1985),
9. H. Hoppe, T. DeRose, T. Duchamp, M. Halstead, H. Jin, J. McDonald, J. Schweitzer and W. Stuetzle, Piecewise Smooth Surface Reconstruction, Computer Graphics Proceedings, Annual Conference Series, pp. 295-300 (1994).
10. J. Hoschek and D. Lasser, Grundlagen der Geometrischen Datenverarbeitung, 2nd edition, B. G. Teubner (1992).
11. L. Kobbelt, A variational approach to subdivision, Computer Aided Geometric Design, 13, pp. 743-761 (1992).
12. L. Kobbelt, Interpolatory Subdivision on Open Quadrilateral Nets with Arbitrary Topology, Proceedings of Eurographics 1996, Computer Graphics Forum, pp. 409-420 (1996).
13. L. Kobbelt, Discrete Fairing, Proceedings of the Seventh IMA Conference on Mathematics of Surfaces (1996).
14. L. Kobbelt and P. Schröder, Constructing Variationally Optimal Curves through Subdivision, California Institute of Technology, Department of Computer Science, Technical Report CS-TR-97-05 (1997).
15. J. Lane and R. Riesenfeld, A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-2, 1, pp. 35-46 (1980).
16. C. Loop, Smooth subdivision surfaces based on triangles, Master's thesis, Department of Mathematics, University of Utah (1987).
17. J.-L. Mallet, Discrete smooth interpolation in geometric modeling, Computer Aided Design, 24, 4, pp. 178-191 (1992).
18. J. Meinguet, Multivariate Interpolation at Arbitrary Points Made Simple, Journal of Applied Mathematics and Physics, 30, pp. 292-304 (1979).
19. J. T. Oden and J. N. Reddy, An Introduction to the Mathematical Theory of Finite Elements, John Wiley & Sons (1976).
20. U. Reif, A unified approach to subdivision algorithms near extraordinary vertices, Computer Aided Geometric Design, 12, pp. 153-174 (1995).
21. J. Warren, Subdivision methods for geometric design, to appear, Morgan Kaufman.
22. J. Warren, Subdivision schemes for variational problems, to appear in Computer Aided Geometric Design.
23. D. Zorin, P. Schröder and W. Sweldens, Interpolating Subdivision for Meshes with Arbitrary Topology, Computer Graphics Proceedings, Annual Conference Series, pp. 189-192 (1996).
24. D. Zorin, P. Schröder and W. Sweldens, Interactive multiresolution mesh editing, Computer Graphics Proceedings, Annual Conference Series, pp. 295-268 (1997).