International Journal of CAD/CAM

한국CDE학회 (Society for Computational Design and Engineering)
권호 표지

[ $C^1$ ] Continuous Piecewise Rational Re-parameterization

  • Liang, Xiuxia (College of Computer Science and Technology, Shandong University) ;
  • Zhang, Caiming (College of Computer Science and Technology, Shandong University) ;
  • Zhong, Li (College of Computer Science and Technology, Yantai normal University) ;
  • Liu, Yi (College of Computer Science and Technology, Shandong University)
  • 발행 : 2006.12.31
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초록

A new method to obtain explicit re-parameterization that preserves the curve degree and parametric domain is presented in this paper. The re-parameterization brings a curve very close to the arc length parameterization under $L_2$ norm but with less segmentation. The re-parameterization functions we used are $C^1$ continuous piecewise rational linear functions, which provide more flexibility and can be easily identified by solving a quadratic equation. Based on the outstanding performance of Mobius transformation on modifying pieces with monotonic parametric speed, we first create a partition of the original curve, in which the parametric speed of each segment is of monotonic variation. The values of new parameters corresponding to the subdivision points are specified a priori as the ratio of its cumulative arc length and its total arc length. $C^1$ continuity conditions are imposed to each segment, thus, with respect to the new parameters, the objective function is linear and admits a closed-form optimization. Illustrative examples are also given to assess the performance of our new method.

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참고문헌

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