Most genuine multi-sided surface representations depend on a 2D domain that enables a mapping between local parameters and global coordinates. The shape of this domain ranges from regular polygons to curved configurations, but the simple circular domain - to the best of our knowledge - has not been investigated yet. Here we fill this gap, and introduce a parameter mapping ideal for use with periodic boundaries. It is based on circular arcs and satisfies constraints often needed in actual surface formulations. The proposed method is demonstrated through a corner-based variant of Generalized B\'ezier patches.

翻译：大多数真正的多边曲面表示依赖于一个二维域，该域实现了局部参数与全局坐标之间的映射。该域的形状范围从正多边形到曲线配置，但据我们所知，简单的圆形域尚未被研究。本文填补了这一空白，并引入了一种适用于周期边界的参数映射。它基于圆弧，并满足了实际曲面公式中经常需要的约束条件。所提出的方法通过基于角点的广义贝塞尔曲面片变体进行了演示。