We define general geometric subdivision schemes generating curves on the 2-dimensional unit sphere by using geodesic polygons and the spherical distance. We show that a spherical interpolatory geometric subdivision scheme is convergent if the sequence of maximum edge lengths is summable and the limit curve is $G^1$-continuous if in addition the sequence of maximum angular defects is summable. In particular, we study the case of bisector interpolatory schemes. Some experimental examples are given to demonstrate the excellent properties of these schemes.

中文翻译：

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球面插值几何细分方案

我们定义了一般的几何细分方案，通过使用测地线多边形和球面距离在二维单位球面上生成曲线。我们证明，如果最大边缘长度的序列是可加的并且极限曲线是，则球面插值几何细分方案是收敛的。$G^{\mathrm{1个}}$-连续，如果最大角度缺陷的序列是可累加的。特别是，我们研究了平分插值方案的情况。给出了一些实验示例，以证明这些方案的出色性能。