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<p>The paper deals with non-convexity measure calculation of a&#xa0;helix in three-dimensional space. The key calculation element is constructing the set bisector and finding the angular characteristics of the bisector points. The equation to measure non-convexity as the upper value limit the angular characteristic is derived. A theorem is proved on the conditions that a&#xa0;measure of non-convexity of a&#xa0;curve reaches the maximum possible value of <i>π</i>. The problem solution is simulated for two helices with various parameters. The results obtained are visualized.</p>

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Numerical and analytical procedures for non-convexity measure calculation of a helix

  • 期刊论文

  • 发表日期：

    2025年12月17日

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  • Pavel D. Lebedev,
  • Oleg A. Kuvshinov

摘要

The paper deals with non-convexity measure calculation of a helix in three-dimensional space. The key calculation element is constructing the set bisector and finding the angular characteristics of the bisector points. The equation to measure non-convexity as the upper value limit the angular characteristic is derived. A theorem is proved on the conditions that a measure of non-convexity of a curve reaches the maximum possible value of π. The problem solution is simulated for two helices with various parameters. The results obtained are visualized.