[2403.16145] Angular constraints on planar frameworks Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2403.16145 (math) [Submitted on 24 Mar 2024 ( v1 ), last revised 24 Apr 2026 (this version, v2)] Title: Angular constraints on planar frameworks Authors: Sean Dewar , Georg Grasegger , Anthony Nixon , Zvi Rosen , William Sims , Meera Sitharam , David Urizar View a PDF of the paper titled Angular constraints on planar frameworks, by Sean Dewar and 6 other authors View PDF HTML (experimental) Abstract: Consider a collection of points in the plane and the sets of slopes or directions of the lines between pairs of points. It is known that the algebraic matroid on the set of direction constraints between the points is equivalent to the algebraic matroid on the set of distances between the points. This is the well-studied generic 2-dimensional rigidity matroid of a graph. This article studies a higher-level construction built on the slope data: an angle constraint system obtained by prescribing relationships between pairs of slopes. The central question we analyze is: when is an angle system rigid, in the sense that every nontrivial motion alters one of the fixed angles? We formulate the problem in matricial terms for certain edge-colored graphs, finding precise necessary conditions for when such edge-colored graphs are rigid, and a combinatorial characterization of generic rigidity for a special case. We also prove the validity of an equivalent formulation of the angle matroid as the algebraic matroid of a field extension. Comments: 22 pages, 8 figures, 3 tables Subjects: Combinatorics (math.CO) ; Metric Geometry (math.MG) MSC classes: 52C25 (Primary) 05C10, 52C35 (Secondary) Cite as: arXiv:2403.16145 [math.CO] (or arXiv:2403.16145v2 [math.CO] for this version) https://doi.org/10.48550/arXiv.2403.16145 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sean Dewar PhD [ view email ] [v1] Sun, 24 Mar 2024 13:35:40 UTC (30 KB) [v2] Fri, 24 Apr 2026 12:52:14 UTC (28 KB) Full-text links: Access Paper: View a PDF of the paper titled Angular constraints on planar frameworks, by Sean Dewar and 6 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2024-03 Change to browse by: math math.MG References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from