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<p>For rational parameterization of curves, it is desirable that the angular speed is made as uniform as possible. When the rational parameterization of a curve is given, the uniformity of its angular speed may be enhanced by finding a <i>re</i>-parameterization that achieves better uniformity, where one natural approach is to use <i>piecewise</i> rational reparameterization. However, this approach does <i>not</i> improve the situation when the angular speed of the original rational parameterization is zero at certain points on the curve. In this paper, we demonstrate that the challenge may be tackled by utilizing piecewise <i>radical</i> reparameterization.</p>

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Improving angular speed uniformity of rational parameterization using piecewise radical reparameterization

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Hoon Hong,
  • Dongming Wang,
  • Jing Yang

摘要

For rational parameterization of curves, it is desirable that the angular speed is made as uniform as possible. When the rational parameterization of a curve is given, the uniformity of its angular speed may be enhanced by finding a re-parameterization that achieves better uniformity, where one natural approach is to use piecewise rational reparameterization. However, this approach does not improve the situation when the angular speed of the original rational parameterization is zero at certain points on the curve. In this paper, we demonstrate that the challenge may be tackled by utilizing piecewise radical reparameterization.