Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results - Archive ouverte HAL Access content directly
Journal Articles Journal of Symbolic Computation Year : 2024

Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results

Abstract

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.
Fichier principal
Vignette du fichier
rmconnect.pdf (3.49 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03508000 , version 1 (03-01-2022)
hal-03508000 , version 2 (07-03-2022)
hal-03508000 , version 3 (07-06-2023)

Identifiers

Cite

Rémi Prébet, Mohab Safey El Din, Éric Schost. Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results. Journal of Symbolic Computation, 2024, 120, pp.102234. ⟨10.1016/j.jsc.2023.102234⟩. ⟨hal-03508000v3⟩
214 View
120 Download

Altmetric

Share

Gmail Facebook X LinkedIn More