Interpolating an unlimited number of curves meeting at extraordinary points on subdivision surfaces

Computer Graphics Forum

Volumn 22, Issue 1, 2003, Pages 87-97

  Nasri, Ahmad H ^a  

^a AMERICAN UNIVERSITY OF BEIRUT   (Lebanon)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; CONSTRAINT THEORY; CURVE FITTING; INTERPOLATION;

INTERPOLATING CURVES;

THREE DIMENSIONAL COMPUTER GRAPHICS;

EID: 0037355566     PISSN: 01677055     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-8659.t01-1-00648     Document Type: Article

References (20)

1. U. Reif. A Unified approach to subdivision algorithms near extraordinary vertices. Computer Aided Geometric Design, 12:153-174, 1995.
2. J. Peters and U. Reif. Analysis of generalized B-spline subdivision algorithms. SIAM Journal On Numerical Analysis, 35(2):728-748, 1998.
3. D. Zorin and P. Schröder. Subdivision for modeling and animation. In ACM SIGGRAPH Course Notes. 2000.
4. J. Warren and H. Weimer. Subdivision Methods For Geometric Design: A Constructive Approach. Morgan Kaufmann Publishers, 2002.
5. A. Nasri and M. Sabin. Taxonomy of interpolation constraints in recursive subdivision curves. The Visual Computer, 18(4):259-272, 2002.
6. A. Nasri and M. Sabin. Taxonomy of interpolation constraints in recursive subdivision surfaces. The Visual Computer, 18(5-6):382-403, 2002.
7. H. Biermann, A. Levin and D. Zorin. Piecewise smooth subdivision surfaces with normal control. In Computer Graphics Proceedings, ACM SIGGRAPH 2000, pp. 113-120. 2000.
8. A. Levin. Interpolating nets of curves by somooth subdivision surfaces. In Computer Graphics Proceedings, SIGGRAPH 99, pp. 57-64. 1999.
9. T. Sederberg, J. Zheng, D. Sewell and M. Sabin. Non-uniform recursive subdivision surfaces. In Computer Graphics Proceedings, ACM SIGGRAPH 98, pp. 387-394. 1998.
10. M. Halstead, M. Kass and T. De Rose. Efficient, fair interpolation using Catmull-Clark surfaces. In Computer Graphics Proceedings, ACM SIGGRAPH 93, pp. 35-44. 1993.
11. J. Schweitzer. Analysis and applications of subdivision surfaces, Ph.D. Thesis, University Of Washington Seattle, 1996.
12. A. Nasri. Constructing polygonal complexes with shape handles for curve interpolation by subdivision surfaces. Computer Aided Design, 33:753-765, 2001.
13. A. Nasri. Recursive subdivision of polygonal complexes and its applications in CAGD. Computer Aided Geometric Design, 17:595-619, 2000 Presented also at the 5th SIAM Conferene On Geometric Design, Nashville, 1997.
14. A. Nasri and A. Abbas. Designing Catmull-Clark subdivision surfaces with curve interpolation constraints. Computers & Graphics, 26(3):393-400, 2002.
15. D. Doo and M. Sabin. Behaviour of recursive division surfaces near extraordinary points. In Rosalee Wolfe (ed), Seminal Graphics, Acm Press, pp. 177-181. 1988.
16. A. Nasri. A polygonal approach for interpolating meshes of curves by subdivisin surfaces. In Proceedings of Geometric Modeling and Processing 2000, IEEE, Hong Kong, pp. 262-273. 10-12 April 2000.
17. E. Catmull and J. Clark. Recursively generated b-spline surfaces on arbitrary tmeshes. In Rosalee Wolfe (ed), Seminal Graphics, Acm Press, pp. 183-188. 1998.
18. M. G. Chaikin. An algorithm for high speed curve generation. Computer Graphics And Image Processing, 3(12):346-349, 1974.
19. A. Nasri. Desinging subdivision surfaces interpolating triangular meshes of curves. American University of Beirut, Computer Science, 2002 Technical Report, TR-2002/4
20. A. Levy, T. Munzner and M. Philips. Geomview 1.6.6 GL version, http: //www.Geomview.org.