Multiresolution Framework for B-Splines

The piecewise polynomial B-spline representation is a flexible tool in CAGD for representing and designing geometric objects. In the field of computer graphics (CG), computer-aided design (CAD), or computer-aided engineering (CAE), a very useful property for a given spline model is to have locally supported basis functions. This allows localized modification of the shape. Unfortunately this property can also become a serious disadvantage when the user wishes to edit the global shape of a complex object. Multiresolution representation is proposed as a solution to alleviate this problem. Various multiresolution methods are described for different B-spline models.

Keywords

Control Point Computer Graphic Comput Graphic Spline Model Global Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bartels, R.H., and Samavati, F.F. (2000), Reversing subdivision rules: local linear conditions and observations on inner products, J Computational Appl Math 119(1-2), 29-67.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Celniker, G., and Gossard, D. (1991), Deformable curve and surface finite elements for freeform shape design, Comput Graphics 25(4).Google Scholar
  3. 3.
    Chughtai, M.S.A. (1999), ANURBS: An Alternative to the NURBS of Degree Three, MS Thesis, King Fahd University of Petroleum & Minerals, Dhahran Saudi Arabia.Google Scholar
  4. 4.
    Cobb, E. (1984), Design of Sculptured Surfaces Using the B-spline Representation, Ph.D. Thesis, University of Utah, Utah.Google Scholar
  5. 5.
    Conner, D., Snibble, S., Herndon, K., Robins, D., Zeleznic, R., and Van-Dam, A. (1992), Three-dimensional widgets, Proceeding of the Symposium on Interactive 3D Graphics.Google Scholar
  6. 6.
    Elber, G., and Gotsman, C. (1995), Multiresolution control for nonuniform B-spline curve editing, Pacific Graphics ’95.Google Scholar
  7. 7.
    Farin, G. (1990), ACurves and Surfaces for Computer-Aided Geometric Design A Prac- tical Guide, Academic Press, New York.Google Scholar
  8. 8.
    Farin, G. (1992), NURB Curves and Surfaces: From Projective Geometry to Practical Use, AK Peters Ltd.Google Scholar
  9. 9.
    Finkelstein, A., and Salesin, D.H. (1994), Multiresolution curves, Proceedings of SIG- GRAPH, ACM, New York, pp. 261-268,Google Scholar
  10. 10.
    Foley, V.D., Feiner, H. (1994), Computer Graphics, Prentice-Hall, Englewood Cliffs NJ.MATHGoogle Scholar
  11. 11.
    Gregory, J.A., Sarfraz, M., and Yuen, P.K. (1994), Interactive curve design using C 2 rational splines, Comput Graphics 18(2), 153-159.CrossRefGoogle Scholar
  12. 12.
    Grisoni L., Schlick C., and Blanc, C. (1997), An Hermitian Approach for Multiresolu-tion Splines, Technical Report no. 1192-97, LaBRI.Google Scholar
  13. 13.
    Rogers, D.F., and Adams A.J., (1990), Mathematical Elements for Computer Graphics, 2nd Edition, McGraw-Hill, New York.Google Scholar
  14. 14.
    Sarfraz, M., and Raheem A. (2000), Curve designing using a rational cubic spline with point and interval shape control, The Proceedings of IEEE International Conference on Information Visualization-IV, IEEE Computer Society Press, pp. 63-68Google Scholar
  15. 15.
    Sarfraz, M. (1999), Designing of objects using rational quadratic spline with interval shape control, Proc. International Conference on Imaging Science, Systems, and Tech-nology (CISST’99), Las Vegas, NV, CSREA Press, pp. 558-564.Google Scholar
  16. 16.
    Sarfraz, M. (1995), Curves and surfaces for CAD using C 2 rational cubic splines, Eng Comput 11(2), 94-102.CrossRefGoogle Scholar
  17. 17.
    Sarfraz, M (1994), Cubic spline curves with shape control, Comput Graphics 18(5), 707-713.CrossRefGoogle Scholar
  18. 18.
    Sarfraz, M. (1994), Generalized geometric interpolation for rational cubic splines, Comput Graphics 18(1), 61-72.CrossRefGoogle Scholar
  19. 19.
    Stollnitz, E.J., DeRose T.D., and Salesin D.H. (1995), Wavelets for computer graphics: a primer, part-1, IEEE Comput Graphics Appl 15(3), 76-84.CrossRefGoogle Scholar
  20. 20.
    Stollnitz, E.J., DeRose T.D., and Salesin D.H. (1995), Wavelets for computer graphics: a primer, part-2, IEEE Comput Graphics Appl 15(4), 75-85.CrossRefGoogle Scholar
  21. 21.
    Stollnitz, E.J., DeRose, T.D., and Salesin, D.H. (1996), Wavelets for Computer Graph- ics: Theory and Applications, Morgan Kaufman Publishers, San Francisco, CA.Google Scholar
  22. 22.
    Welch, W., and Witkin, A. (1992), Variational surface modeling, Comput Graphics 26(2).Google Scholar

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