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Home > Archive>Volume 13, Issue 11, 2002 >2176-2182
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Approximate Degree Reduction of Interval Triangular Bézier Surfaces
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    Abstract:

    An efficient algorithm of bounding interval triangular B-B (Bernstein-Béier) surfaces with lower degree interval triangular B-B surfaces is presented. The algorithm is based on linear programming techniques. An analytical method is also given for degree reduction of one order. The result of degree reduction approximation can be used for the purpose of data transmission among various CAD systems, as well as for the saving of computation time for some geometric operations.

    Reference
    [1] Brunnet, G., Schreiber, T., Braun, J. The geometry of optimal degree reduction of Bézier curves. Computer Aided Geometric Design, 1996,13(8):773～788.
    [2] Hu, Shi-min, Zuo, Zheng, Sun, Jia-guang. Approximate degree reduction of triangular Bézier surfaces. Tsinghua Science and Technology, 1998,3(2):1001～1004.
    [3] Sederberg, T.W., Farouki, R.T. Approximation by interval Bézier curves. IEEE Computer Graphics and Applications, 1992,15(2): 87～95.
    [4] Hu, Chun-yi, Maekawa, T., Patrikalakis, N.M., et al. Robust interval algorithm for Surface intersections. Computer Aided Design, 1997,29(9):617～627.
    [5] Tuohy, S.T., Maekawa, T., Shen, G., et al. Approximation of measured data with interval B-splines. Computer Aided Design, 1997,29(11):791～799.
    [6] Chen, Fa-lai, Lou, Wen-ping. Degree reduction of interval Bézier curves. Computer Aided Design, 2000,32(10):571～582.
    [7] Farin, G. Triangular Bernstein-Bézier patches. Computer Aided Geometric Design, 1986,3(8):773～788.
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杨勤民,杨勋年,汪国昭.区间三角Bézier曲面的降阶逼近.软件学报,2002,13(11):2176-2182

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History
  • Received:March 07,2001
  • Revised:May 15,2001
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