论文标题
Epsilon局部刚性和数值代数几何形状
Epsilon local rigidity and numerical algebraic geometry
论文作者
论文摘要
众所周知的组合算法可以通过确定图表是否为Pollaczek-Geiringer-Laman类型来确定平面中的通用刚度。在通用配置的假设下，来自Matroid理论的方法已被用来证明其他有趣的结果。但是，应用程序中出现的配置可能不是通用的。我们介绍定理5及其相应的算法1，该算法1决定配置是否为Epsilon-locigid（我们定义的概念）。 Epsilon-Locigin刚性的配置可能是局部刚性或灵活的，但是在配置空间中，任何连续变形都保留在Radius Epsilon的球体内。对于光滑或奇异，通用或非传统的配置，可以决定epsilon-local僵化。我们还提出了使用数值代数几何形状来计算连续flex的离散时间样本的算法2和3，为科学家提供了有用的视觉信息。
A well-known combinatorial algorithm can decide generic rigidity in the plane by determining if the graph is of Pollaczek-Geiringer-Laman type. Methods from matroid theory have been used to prove other interesting results, again under the assumption of generic configurations. However, configurations arising in applications may not be generic. We present Theorem 5 and its corresponding Algorithm 1 which decide if a configuration is epsilon-locally rigid, a notion we define. A configuration which is epsilon-locally rigid may be locally rigid or flexible, but any continuous deformations remain within a sphere of radius epsilon in configuration space. Deciding epsilon-local rigidity is possible for configurations which are smooth or singular, generic or non-generic. We also present Algorithms 2 and 3 which use numerical algebraic geometry to compute a discrete-time sample of a continuous flex, providing useful visual information for the scientist.
