论文标题
链接的对称配置空间
Symmetric Configuration spaces of linkages
论文作者
论文摘要
链接$γ$的A $配置$是$ \ Mathbb {r}^d $中的$γ$，以及所有此类形式的集合$ \ MATHCAL {c}（c}（γ）$ $γ$。我们在这里介绍了链接的$对称配置空间$的概念，在该链接中，我们确定了几何无法区分的配置。我们表明，平面多边形的对称配置空间具有常规的单元结构，提供了一些用于计算此结构的原理，并提供了所有四边形和等边五角大楼的对称配置空间的完整描述。
A $configuration$ of a linkage $Γ$ is a possible positioning of $Γ$ in $\mathbb{R}^d$ and the collection of all such forms the configuration space $\mathcal{C}(Γ)$ of $Γ$. We here introduce the notion of the $symmetric configuration space$ of a linkage, in which we identify configurations which are geometrically indistinguishable. We show that the symmetric configuration space of a planar polygon has a regular cell structure, provide some principles for calculating this structure, and give a complete description of the symmetric configuration space of all quadrilaterals and of the equilateral pentagon.
