• Article
  • | |
  • Metrics
  • |
  • Reference [21]
  • |
  • Related [20]
  • | | |
  • Comments
    Abstract:

    The V-system is a new class of complete orthogonal functions system in L2[0,1], which is composed of piecewise kth-order polynomials. There are continuous functions as well as discontinuous functions in V-system. It can be used for signal processing and global expression of a geometric graph group. Moreover, the information of geometric modeling in CAGD can be reconstructed precisely by finite terms of V-system without Gibbs phenomenon, so global feature analysis of the complicated modeling can be implemented. This paper shows that 3-dimension complicated geometric model can be reconstructed by the V-system over triangulated domain. The experiment results indicate that V-system is an effective tool used to reconstruct complicated geometric information with both continuous and discontinuous signals. This is the essential difference among V-system, the classical complete orthogonal system with continuous functions and Walsh and Haar system which include intense discontinuous functions.

    Reference
    [1] Tang RX, Wang JY, Peng QS, Wang GZ, et al. Course of Computer Graphics. Beijing: Science Press, 2000. 56-115 (in Chinese).
    [2] Peng QS, Bao HJ, Jin XG. Fundamental Algorithms for Realistic Image Synthesis. Beijing: Science Press, 1999 (in Chinese).
    [3] Foley JD, van Dam A, Feiner SK, Hughes JF. Computer Graphics. Principles and Practice. 2nd Edition, New York: Addison-Wesley Professional, 1995.
    [4] Wang GJ, Wang GZ, Zheng JM. Computer Aided Geometric Design. Beijing: China Higher Education Press; Berlin: Springer-Verlag, 2001 (in Chinese).
    [5] Li HG. Hyperbolic conformal geometry with Clifford algebra. Int'l Journal of Theoretical Physics, 2001,40(1):79-91.
    [6] Jerri AJ. The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Applications in the Mathematics and Its Applications. New York: Springer-Verlag, 2006.
    [7] Peter DL. Gibbs phenomena. Journal of Scientific Computing, 2006,28(2-3):445-449.
    [8] Gilbert GW, Shen XP. Wavelets and Other Orthogonal Systems. 2nd Edition, Boca Raton Florida: Chapman & Hall/CRC, 2001.
    [9] Yves M. Wavelets: Algorithms and applications. Philadelphia: SIAM, 1993.
    [10] Henning FH. Sequency Theory—Foundations and Applications. New York: Academic Press, 1977.
    [11] Zhang QS, Zhang YG. Theory and Application of Bridge Function. Beijing: National Defense Industry Press, 1992 (in Chinese).
    [12] Feng YY, Qi DX. A sequence of piecewise orthogonal polynomials. SIAM Journal of Mathematical Analysis, 1984,15(4):834-844.
    [13] Song RX, Ma H, Wang TJ, Qi DX. Complete orthogonal V-system and its applications. Communications on Pure and Applied Analysis, 2007,6(3):853-871.
    [14] Song RX, Wang XC, Ou MF, Li J. The structure of V-system over triangulated domains. In: Chen FL, Bert J, eds. Advances in Geometric Modeling and Processing LNCS 4975, Springer-Verlag, 2008.563-569.
    [15] Song RX. The Construction of a new class of orthogonal function over triangular domain. Journal of Systems Science and Mathematical Sciences, 2008,28(8):949-960 (in Chinese with English abstract).
    [16] Song RX, Wang XC, Ma H, Qi DX. V-Descriptor and shape similarity measurement between B-spline curves. In: Proc. of the 1st Int'l Symp. on Pervasive Computing and Application. Beijing: IEEE Press, 2006. 486-490.
    [17] Liang YY, Song RX, Qi DX. Complete orthogonal function system V and points cloud fitting. Journal of System Simulation, 2006,18(8):2109-2113 (in Chinese with English abstract).
    [18] Liang YY, Song RX, Wang XC, Qi DX. Application of a new class of orthogonal function system in geometrical information. Journal of Computer-Aided Design & Computer Graphics, 2007,19(7):871-875 (in Chinese with English abstract).
    [19] Song RX, Liang YY, Wang XC, Qi DX. Elimination of Gibbs phenomenon in computational information based on the V-system. In: Proc. of the 2nd Int'l Conf. on Pervasive Computing and Applications. 2007. 337-341.
    [20] Wang XC, Liang YY, Ou MF, Song RX. Application of complete orthogonal V-system. In: Proc. of The 2008 Int'l Congress on Image and Signal Processing, 2008,2:694-698.
    [21] Song RX, Ou MF. The application of V-system in the digital image transform. In: Proc. of the IEEE Int'l Conf. on Information Acquisition 2008 (ICIA 2008). 2008. 296-301.
    Cited by
Get Citation

李 坚,宋瑞霞,叶梦杰,梁延研,齐东旭. V-系统与几何群组信息的频域表达.软件学报,2008,19(zk):41-51

Copy
Share
Article Metrics
  • Abstract:3473
  • PDF: 5993
  • HTML: 0
  • Cited by: 0
History
  • Received:May 03,2008
  • Revised:November 14,2008
You are the firstVisitors
Copyright: Institute of Software, Chinese Academy of Sciences Beijing ICP No. 05046678-4
Address:4# South Fourth Street, Zhong Guan Cun, Beijing 100190,Postal Code:100190
Phone:010-62562563 Fax:010-62562533 Email:jos@iscas.ac.cn
Technical Support:Beijing Qinyun Technology Development Co., Ltd.

Beijing Public Network Security No. 11040202500063