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<p>The existing curve smoothing methods frequently suffer from overcorrection and even linearization, while lacking a comprehensive and efficient framework for smoothness evaluation. To address these limitations, this paper proposes a geometric feature-driven curve smoothness evaluation and optimization method (GFD-CSEOM) for applications across multiple domains. The smoothness evaluation framework consists of three core criteria: uniformity of discrete curvature variation, uniformity of discrete torsion variation, and accumulation of neighboring differences (AND). The method explores the intrinsic relationship between microscale geometric characteristics and curve smoothness, identifying key factors influencing smoothness. In the typical defective-triangle geometric optimization model, a multilevel optimization point-solving method is introduced, and the influence of optimization point levels on computational time and optimization rate was analyzed. The smoothness of planar closed curves, convex curves, and concave-convex curves was evaluated and optimized to verify the feasibility and universality of the proposed method. The results indicate that the three criteria of the smoothness evaluation framework complement each other and can accurately evaluate curve smoothness. The optimized curves of the three types show only minor deformation, preserve the key shape information, and exhibit significantly improved uniformity of discrete curvature and torsion variations. The AND values are reduced by 95.12 %, 92.23 %, and 81.74 %, respectively.</p>

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A geometric feature-driven curve smoothness evaluation and optimization method

  • 期刊论文

  • 发表日期：

    2026年4月14日

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  • Tianze Li,
  • Pengwen Sun,
  • Lanting Zhang,
  • Si Wang,
  • Chunxiao Jia,
  • Yong Jiang,
  • Jinshun Yan

摘要

The existing curve smoothing methods frequently suffer from overcorrection and even linearization, while lacking a comprehensive and efficient framework for smoothness evaluation. To address these limitations, this paper proposes a geometric feature-driven curve smoothness evaluation and optimization method (GFD-CSEOM) for applications across multiple domains. The smoothness evaluation framework consists of three core criteria: uniformity of discrete curvature variation, uniformity of discrete torsion variation, and accumulation of neighboring differences (AND). The method explores the intrinsic relationship between microscale geometric characteristics and curve smoothness, identifying key factors influencing smoothness. In the typical defective-triangle geometric optimization model, a multilevel optimization point-solving method is introduced, and the influence of optimization point levels on computational time and optimization rate was analyzed. The smoothness of planar closed curves, convex curves, and concave-convex curves was evaluated and optimized to verify the feasibility and universality of the proposed method. The results indicate that the three criteria of the smoothness evaluation framework complement each other and can accurately evaluate curve smoothness. The optimized curves of the three types show only minor deformation, preserve the key shape information, and exhibit significantly improved uniformity of discrete curvature and torsion variations. The AND values are reduced by 95.12 %, 92.23 %, and 81.74 %, respectively.