Differential Geometry of Curves and Surfaces with Singularities
Differential Geometry of Curves and Surfaces with Singularities
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DOI：
10.1142/12284
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发表时间：
2021-02
期刊：
影响因子：
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通讯作者：
M. Umehara;K. Saji;Kotaro Yamada;W. Rossman
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文献类型：
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作者：
M. Umehara;K. Saji;Kotaro Yamada;W. Rossman
正则平面曲线是没有奇异点的曲线。我们将其视为（一维）波前，并将平行曲线族视为给定曲线的时间演化。在这些平行曲线中看到的最常见的奇点类型是所谓的尖点奇点。与曲面的情况相比，平面曲线，无论是通过方程描述还是通过几何描述，都是非常容易理解的对象，正因为如此，本章在阅读时基本上是独立的。
A regular planar curve is a curve without singular points. We will regard it as a (one-dimensional) wave front, and consider the family of parallel curves as a time evolution of the given curve. The most common type of singularity that one sees in these parallel curves is what is called a cusp singularity. More so than with the case of surfaces, the planar curves, whether described via equations or described geometrically, are remarkably accessible objects—and because of this, this chapter in particular is essentially self-contained upon reading.