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<p>We propose an algorithm to compute the <i>n</i>-arc (spline) that best approximates a spatial curve. An <i>n</i>-arc is a tangent continuous spline consisting of <i>n</i> circular or linear arcs and can be parametrized by a piecewise rational quadratic spline with control points satisfying a non-linear constraint. Using these control points, we iteratively determine a least squares approximant for any fixed segmentation and optimize the segmentation by a genetic algorithm. Furthermore, we derive all differentiable piecewise rational <i>n</i>-arc spline representations of low degree, which generalizes known results for elliptical <i>n</i>-arc splines.</p>

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Spatial arc spline approximants with fewest arcs and their smooth representations by low-degree splines

  • 期刊论文

  • 发表日期：

    2025年7月3日

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  • Stephan Alt,
  • Hartmut Prautzsch

摘要

We propose an algorithm to compute the n-arc (spline) that best approximates a spatial curve. An n-arc is a tangent continuous spline consisting of n circular or linear arcs and can be parametrized by a piecewise rational quadratic spline with control points satisfying a non-linear constraint. Using these control points, we iteratively determine a least squares approximant for any fixed segmentation and optimize the segmentation by a genetic algorithm. Furthermore, we derive all differentiable piecewise rational n-arc spline representations of low degree, which generalizes known results for elliptical n-arc splines.