We propose and analyze a global search algorithm for the computation of the minimum zone sphericity (circularity) error of a given set. The formulation is valid in any dimension and covers both finite sets of data points as well as infinite sets like polygonal chains or triangulations of surfaces. We derive theoretical estimates for the cost to reach a desired accuracy, and validate the performance of the algorithm with various numerical experiments.

中文翻译：

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经认证的高效全球圆度评估

我们提出并分析了一种全局搜索算法，用于计算给定集合的最小区域球度（圆度）误差。该公式在任何维度上都有效，并涵盖有限数据点集以及无限集，如多边形链或曲面三角剖分。我们推导出达到所需精度的成本的理论估计，并通过各种数值实验验证算法的性能。