Rigidity of polyhedral surfaces, II
Rigidity of polyhedral surfaces, II
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DOI：
10.2140/gt.2009.13.1265
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发表时间：
2006-12
影响因子：
2.5
通讯作者：
Ren Guo;Feng Luo
中科院分区：
文献类型：
--
作者：
Ren Guo;Feng Luo
我们用变分原理研究了多面体曲面的刚性。作用泛函是由余弦定律导出的。本文主要研究由三条可能不相交的测地线限定的非三角形区域的余弦律。这些余弦定律中的几个最先被芬切尔和尼尔森发现并使用。通过研究余弦定律的导数，我们发现了多面体曲面上有边界或无边界的几个变分原理的统一方法。因此，Penner，Bobenko和SpringBorn和瑟斯顿关于多面体曲面和圆图案的刚性的工作被扩展到非常一般的背景下。
We study the rigidity of polyhedral surfaces using variational principles. The action functionals are derived from the cosine laws. The main focus of this paper is on the cosine law for a nontriangular region bounded by three possibly disjoint geodesics. Several of these cosine laws were first discovered and used by Fenchel and Nielsen. By studying the derivative of the cosine laws, we discover a uniform approach to several variational principles on polyhedral surfaces with or without boundary. As a consequence, the work of Penner, Bobenko and Springborn and Thurston on rigidity of polyhedral surfaces and circle patterns are extended to a very general context.