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<p>Fair curves are widely used in geometric design, modeling, and industrial manufacturing. This paper proposes a new curve fairing algorithm based on the smoothed target curvature normal. To accomplish this, the problem of constructing the target curve is converted into solving a second-order differential equation with boundary value constraints, which is then solved through the Rayleigh–Ritz method. The effectiveness of this approach is demonstrated through several illustrative examples.</p>

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Fairing B-Spline Curves Via Smoothing Curvature

  • 期刊论文

  • 发表日期：

    2026年6月2日

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  • Zhenglong Wu,
  • Xuhui Wang,
  • Qian Ni,
  • Xiaoyan Zhang,
  • Yuhao Han

摘要

Fair curves are widely used in geometric design, modeling, and industrial manufacturing. This paper proposes a new curve fairing algorithm based on the smoothed target curvature normal. To accomplish this, the problem of constructing the target curve is converted into solving a second-order differential equation with boundary value constraints, which is then solved through the Rayleigh–Ritz method. The effectiveness of this approach is demonstrated through several illustrative examples.