We consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision schemes we propose is based on clothoidal averaging, i.e., averaging w.r.t. locally interpolating clothoids, which are curves of linear curvature. To this end, we derive a new strategy to approximate Hermite interpolating clothoids. We employ the proposed approach to define the geometric Hermite analogues of the well-known Lane-Riesenfeld and four-point schemes. We present numerical results produced by the proposed schemes and discuss their features.

我们考虑平面曲线的几何 Hermite 细分，即使用位于顶点的附加切线或法线矢量信息迭代地细化输入多边形。我们提出的（非线性）细分方案的构建块基于回旋平均，即对局部内插回旋曲线求平均值，回旋曲线是线性曲率曲线。为此，我们推导出一种新的策略来近似 Hermite 插值回旋曲线。我们采用所提出的方法来定义著名的 Lane-Riesenfeld 和四点方案的几何 Hermite 类似物。我们介绍了由所提出的方案产生的数值结果并讨论了它们的特征。