论文标题
衣架配件和几何赫米特细分
Clothoid Fitting and Geometric Hermite Subdivision
论文作者
论文摘要
我们考虑了平面曲线的几何图形细分，即，迭代地精炼了输入多边形，并在顶点中使用其他切线或正常矢量信息。我们提出的（非线性）细分方案的构件基于服装平均，即平均W.R.T.局部插值衣服，是线性曲率的曲线。为了定义服装平均，我们得出了一种新的策略，以近似于Hermite插值衣服。我们采用了建议的方法来定义著名的车道 - 雷森菲尔德和四点方案的几何赫米特类似物。我们介绍了拟议方案产生的结果并讨论其特征。特别是，我们证明所提出的方案产生了视觉上令人信服的曲线。
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 define clothoidal averaging, 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 results produced by the proposed schemes and discuss their features. In particular, we demonstrate that the proposed schemes yield visually convincing curves.
