Approximation algorithms for developable surfaces

Computer Aided Geometric Design

Volumn 16, Issue 6, 1999, Pages 539-556

  Pottmann, Helmut ^a   Wallner, Johannes ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; MATRIX ALGEBRA; POLYNOMIALS; VECTORS;

COMPUTER AIDED GEOMETRIC DESIGN; DEVELOPABLE SURFACE; DUAL REPRESENTATION; RATIONAL B-SPLINES; SURFACE APPROXIMATION;

COMPUTER AIDED DESIGN;

EID: 0033165273     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8396(99)00012-6     Document Type: Article

References (25)

1. Aumann, G. (1991), Interpolation with developable Bézier patches, Computer Aided Geometric Design 8, 409-420.
2. SR Aumann, G. (1994), A closer look at developable Bézier surfaces, J. Theoret. Graphics and Computing 7, 12-26.
3. SR Bodduluri, R.M.C. and Ravani, B. (1992), Geometric design and fabrication of developable surfaces, ASME Adv. Design Autom. 2, 243-250.
4. SR Bodduluri, R.M.C. and Ravani, B. (1993), Design of developable surfaces using duality between plane and point geometries, Computer-Aided Design 25, 621-632.
5. Chalfant, J. and Maekawa, T. (1997a), Design for manufacturing using B-spline developable surfaces, Preprint, MIT.
6. Chalfant, J. and Maekawa, T. (1997b), Computation of inflection lines and geodesics on developable surfaces, Preprint, MIT.
7. Farin, G. (1992), Curves and Surfaces for Computer Aided Geometric design, Academic Press, Boston.
8. Frey, W.H. and Bindschadler, D. (1993), Computer aided design of a class of developable Bézier surfaces, General Motors R&D Publication 8057.
9. Hoschek, J. (1983), Dual Bézier curves and surfaces, in: Barnhill, R.E. and Boehm, W., eds., Surfaces in Computer Aided Geometric Design, North-Holland, 147-156.
10. Hoschek, J. and Lasser, D. (1993), Fundamentals of Computer Aided Geometric Design, A.K. Peters, Wellesley, MA.
11. Hoschek, J. and Pottmann, H. (1995), Interpolation and approximation with developable B-spline surfaces, in: Dæhlen, M., Lyche, T. and Schumaker, L.L., eds., Mathematical Methods for Curves and Surfaces, Vanderbilt University Press, NA, 255-264.
12. Hoschek, J. and Schneider, M. (1997), Interpolation and approximation with developable surfaces, in: Le Méhauté, A., Rabut, C. and Schumaker, L.L., eds., Curves and Surfaces with Applications in CAGD, Vanderbilt University Press, NA, 185-202.
13. Hoschek, J. and Schwanecke, U. (1998), Interpolation and approximation with ruled surfaces, in: Cripps, R., ed., The Mathematics of Surfaces VIII, Information Geometers, 213-231.
14. Lang, J. and Röschel, O. (1992), Developable (1, n)-Bézier surfaces, Computer Aided Geometric Design 9, 291-298.
15. Lyche, T. and Schumaker, L.L. (1994), L-spline wavelets, in: Chui, C. Montefusco, L. and Puccio, L., eds., Wavelets: Theory, Algorithms, and Applications, Academic Press, 197-212.
16. Neamtu, M., Pottmann, H. and Schumaker, L.L., Dual focal splines and rational curves with rational offsets, Mathematical Engineering in Industry, to appear.
17. Nesterov, Yu. and Nemirovskii, A. (1994), Interior-Point Polynomial Algorithms in Convex Programming, SIAM.
18. Piegl, L. and Tiller, W. (1995), The NURBS Book, Springer, Berlin.
19. Pottmann, H. (1995), Studying NURBS curves and surfaces with classical geometry, in: Dæhlen, M., Lyche, T. and Schumaker, L.L., eds., Mathematical Methods for Curves and Surfaces, Vanderbilt University Press, NA, 413-438.
20. Pottmann, H. and Farin, G. (1995), Developable rational Bezier and B-spline surfaces, Computer Aided Geometric Design 12, 513-531.
21. Randrup, T. (1998), Approximation of surfaces by cylinders, Computer-Aided Design 30, 807-812.
22. Schneider, M. (1996), Approximation von Blechhalterflächen mit Torsen in B-spline Darstellung, Diplomarbeit, TH Darmstadt.
23. Stollnitz, E., DeRose, T. and Salesin, H. (1996), Wavelets for Computer Graphics, Morgan Kaufmann, San Francisco, CA.
24. Vatter, R. (1996), Approximation von Datenpunkten mit Torsen in B-spline Darstellung, Diplomarbeit, TH Darmstadt.
25. Wallner, J. (1998), Generalized multiresolution analysis for arc splines, in: Dæhlen, M., Lyche, T. and Schumaker, L.L., eds., Mathematical Methods for Curves and Surfaces II, Vanderbilt University Press, 537-544.