Equivalent Graphical Conditions for Angle Rigidity and Angle-Based Network Localization
Abstract
Angle rigidity theory provides a theoretical basis for characterizing the geometric shape of graphs embedded in the plane under angle constraints, and establishing global convergence of angle-based network localization algorithms. The related references, however, are largely restricted to graphs generated by triangulation or bilateration ordering, which are sufficient but not necessary for angle rigidity. This paper addresses this challenge by focusing on establishing the equivalence between angle constraints and bearing constraints. The conditions for cycle compatible frameworks (with possibly non-generic configurations) to be angle fixable are provided. Moreover, it is shown for the first time that Laman graphs equivalently characterize minimally globally angle rigid graphs, implying that a Laman graph is the simplest graph that allows a generic embedding in the plane to be uniquely determined by subtended angles. As an application, a distributed algorithm for angle-based sensor network localization is proposed, which guarantees global convergence under a much milder network topology condition than those in the literature.
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BibTeX
@misc{huang2026equivalent,
title = {{Equivalent Graphical Conditions for Angle Rigidity and Angle-Based Network Localization}},
author = {Jinpeng Huang and Gangshan Jing and Kai Zhao and Yongduan Song},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02764},
eprint = {2611.02764},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02764},
}
RIS
TY - UNPB
TI - Equivalent Graphical Conditions for Angle Rigidity and Angle-Based Network Localization
AU - Jinpeng Huang
AU - Gangshan Jing
AU - Kai Zhao
AU - Yongduan Song
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02764
UR - https://arxiv.org/abs/2611.02764
AB - Angle rigidity theory provides a theoretical basis for characterizing the geometric shape of graphs embedded in the plane under angle constraints, and establishing global convergence of angle-based network localization algorithms. The related references, however, are largely restricted to graphs generated by triangulation or bilateration ordering, which are sufficient but not necessary for angle rigidity. This paper addresses this challenge by focusing on establishing the equivalence between angle constraints and bearing constraints. The conditions for cycle compatible frameworks (with possibly non-generic configurations) to be angle fixable are provided. Moreover, it is shown for the first time that Laman graphs equivalently characterize minimally globally angle rigid graphs, implying that a Laman graph is the simplest graph that allows a generic embedding in the plane to be uniquely determined by subtended angles. As an application, a distributed algorithm for angle-based sensor network localization is proposed, which guarantees global convergence under a much milder network topology condition than those in the literature.
ER -