This short contribution presents a method for generating $N$-point spherical configurations with low mesh ratios. The method extends Caspar-Klug icosahedral point-grids to non-icosahedral nets through the use of planar barycentric coordinates, which are subsequently interpreted as spherical area coordinates for spherical point sets. The proposed procedure may be applied iteratively and is parameterised by a sequence of integer pairs. For well-chosen input parameters, the proposed method is able to generate point sets with mesh ratios that are lower than previously reported for $N<10^6$.

中文翻译：

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使用球面坐标生成具有低网格比的 $N$ 点球面配置

这个简短的贡献提出了一种生成具有低网格比的 $N$ 点球形配置的方法。该方法通过使用平面重心坐标将 Caspar-Klug 二十面体点网格扩展到非二十面体网络，随后将其解释为球面点集的球面坐标。所提出的程序可以迭代地应用并且由整数对序列参数化。对于精心选择的输入参数，所提出的方法能够生成网格比低于先前报告的 $N<10^6$ 的点集。