用有效配置空间刻画1-Dof Henneberg-I图
Characterizing 1-Dof Henneberg-I graphs with efficient configuration spaces
摘要：
我们定义和研究的实现空间的一个自然类的欠约束的二维欧氏距离约束系统（EDCS）或框架的基础上1-dof Henneberg-I图的精确，有效的表示。每个表示对应于一个参数的选择，并产生一个不同的参数化配置空间。我们的概念的效率是基于采样的配置空间，并获得一个实现的样本（参数化）配置的代数复杂性。值得注意的是，我们给出了纯粹的组合特征，捕获（i）具有有效配置空间的图类和（ii）为给定图产生有效配置空间的表示参数的可能选择。我们的研究结果自动产生一个有效的算法采样实现，而不会错过极端或边界实现。此外，我们的结果正式表明，我们的有效配置空间的定义是强大的，我们的特征是紧密的。我们选择类的1-dof Henneberg-I图，以采取下一步的系统和分级程序的组合特征的有效配置空间。特别是，这里提出的结果是第一个特征，超越了图，有连接和凸配置空间。
英文摘要：
We define and study exact, efficient representations of realization spaces of a natural class of underconstrained 2D Euclidean Distance Constraint Systems(EDCS) or Frameworks based on 1-dof Henneberg-I graphs. Each representation corresponds to a choice of parameters and yields a different parametrized configuration space. Our notion of efficiency is based on the algebraic complexities of sampling the configuration space and of obtaining a realization from the sample (parametrized) configuration. Significantly, we give purely combinatorial characterizations that capture (i) the class of graphs that have efficient configuration spaces and (ii) the possible choices of representation parameters that yield efficient configuration spaces for a given graph. Our results automatically yield an efficient algorithm for sampling realizations, without missing extreme or boundary realizations. In addition, our results formally show that our definition of efficient configuration space is robust and that our characterizations are tight. We choose the class of 1-dof Henneberg-I graphs in order to take the next step in a systematic and graded program of combinatorial characterizations of efficient configuration spaces. In particular, the results presented here are the first characterizations that go beyond graphs that have connected and convex configuration spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
