论文标题
计算无界平滑真实代数集I的计算路线图I：连接结果
Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results
论文作者
论文摘要
在实际代数集中回答连接性查询是有效的实际代数几何形状中的一个基本问题，它在例如运动计划问题是主题的机器人技术。通过计算所谓的路线图来解决这个计算问题，这些路线图是所研究集合V的真实代数子集，最多是一个尺寸，并且它们与V.算法的所有半代数相互连接的组件具有连接的相互作用。 在本文中，我们通过删除V上的界定假设来扩展此类连通性声明。这利用了所谓的广义极性品种的性质，对于某些精心选择的多项式图，它们是V的关键基因座。
Answering connectivity queries in real algebraic sets is a fundamental problem in effective real algebraic geometry that finds many applications in e.g. robotics where motion planning issues are topical. This computational problem is tackled through the computation of so-called roadmaps which are real algebraic subsets of the set V under study, of dimension at most one, and which have a connected intersection with all semi-algebraically connected components of V. Algorithms for computing roadmaps rely on statements establishing connectivity properties of some well-chosen subsets of V , assuming that V is bounded. In this paper, we extend such connectivity statements by dropping the boundedness assumption on V. This exploits properties of so-called generalized polar varieties, which are critical loci of V for some well-chosen polynomial maps.
