Piecewise developable surface approximation of general NURBS surfaces, with global error bounds

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4077 LNCS, Issue , 2006, Pages 143-156

  Subag, Jacob ^a   Elber, Gershon ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER AIDED DESIGN; COMPUTER AIDED MANUFACTURING; MATHEMATICAL MODELS; SET THEORY; SHEET METAL;

NURBS SURFACE; PLANAR SHEETS; SURFACE APPROXIMATION;

COMPUTATIONAL GEOMETRY;

EID: 33749355241     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11802914_11     Document Type: Conference Paper

References (20)

1. G. Aumann. Interpolation with developable Bezier patches. Computer Aided Geometric Design, 8(5):409-420, 1991.
2. J. Bloomenthal and B. Wyvill, editors. Introduction to Implicit Surfaces. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 1997. Section 2.6.4.
3. M. P. D. Carmo. Differential Geometry of Curves and Surfaces, pages 195-197. Prentice-Hall, 1976.
4. H.-Y. Chen, I.-K. Lee, S. Leopoldseder, H. Pottmann, T. Randrup, and J. Wallner. On surface approximation using developable surfaces. Graphical Models and Image Processing, 61(2):110-124, 1999.
5. X. Chen, R. F. Riesenfeld, and E. Cohen. Degree reduction for NURBS symbolic computation on curves. In preparation.
6. E. Cohen, R. F. Riesenfeld, and G. Elber. Geometric Modeling with Splines, chapter 9. A K Peters, 2001.
7. G. Elber. Irit solid modeler, http://www.cs.technion.ac.il/~irit
8. G. Elber. Model fabrication using surface layout projection. Computer-aided Design, 27(4):283-291, April 1995.
9. G. Elber and E. Cohen. Second-order Surface Analysis Using Hybrid Symbolic and Numeric Operator. ACM Trans. Graph, 12(2): 160-178, 1993.
10. G. Elber and M.-S. Kim. Geometric constraint solver using multivariate rational spline functions. In The Sixth ACM/IEEE Symposium on Solid Modeling and Applications, Ann Arbor, Michigan, pages 1-10, June 2001.
11. J. Hass, R. T. Farouki, C. Y. Han, X. Song, and T. W. Sederberg. Guaranteed consistency of surface intersections and trimmed surfaces using a coupled topology resolution and domain decomposition scheme. To appear in Advances in Computational Mathematics, 2005. http://mae.ucdavis.edu/~farouki/ index.html
12. J. Hoschek. Approximation of surfaces of revolution by developable surfaces. Computer-Aided Design, 30(10):757-763, 1998.
13. J. Hoschek and H. Pottmann. Interpolation and approximation with developable B-spline surfaces. In M. Dæhlen, T. Lyche, and L. L. Schumaker, editors, Proceedings of the first Conference on Mathematical Methods for Curves and Surfaces (MMCS-94), pages 255-264, Nashville, USA, June 16-21 1995. Vanderbilt University Press.
14. S. Leopoldseder and H. Pottmann. Approximation of developable surfaces with cone spline surfaces. Computer-Aided Design, 30(7):571-582, 1998.
15. Matlab ©, copyright 1984-2002, The Mathworks, Inc. See also http://www.mathworks.com/.
16. F. Park, J. Yu, C. Chun, and B. Ravani. Design of developable surfaces using optimal control. Journal of Mechanical Design, 124(4):602-608, December 2002.
17. M. Peternell. Developable surface fitting to point clouds. In Computer Aided Geometric Design, pages 785-803, 2004.
18. M. Peternell. Recognition and reconstruction of developable surfaces from point clouds. In GMP, pages 301-310, 2004.
19. H. Pottmann and G. E. Farin. Developable rational Bézier and B-spline surfaces. Computer Aided Geometric Design, 12(5):513-531, 1995.
20. H. Pottmann and J. Wallner. Approximation algorithms for developable surfaces. Computer Aided Geometric Design, 16(6):539-556, 1999.