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Angular constraints on planar frameworks.

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Title: Angular constraints on planar frameworks.
Authors: Dewar, Sean1 (AUTHOR), Grasegger, Georg2 (AUTHOR), Nixon, Anthony3 (AUTHOR) a.nixon@lancaster.ac.uk, Rosen, Zvi4 (AUTHOR), Sims, William5 (AUTHOR), Sitharam, Meera6 (AUTHOR), Urizar, David7 (AUTHOR)
Source: Discrete Applied Mathematics. Sep2026, Vol. 390, p151-166. 16p.
Subjects: Matroids, Matrices (Mathematics), Graph theory, Planar graphs, Combinatorics
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. [ABSTRACT FROM AUTHOR]
Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 193680364
AccessLevel: 6
PubType: Academic Journal
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  Data: Angular constraints on planar frameworks.
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  Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Sep2026, Vol. 390, p151-166. 16p.
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.dam.2026.03.009
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      – Code: eng
        Text: English
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        PageCount: 16
        StartPage: 151
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      – SubjectFull: Matroids
        Type: general
      – SubjectFull: Matrices (Mathematics)
        Type: general
      – SubjectFull: Graph theory
        Type: general
      – SubjectFull: Planar graphs
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      – SubjectFull: Combinatorics
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      – TitleFull: Angular constraints on planar frameworks.
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            – D: 15
              M: 09
              Text: Sep2026
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              Y: 2026
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              Value: 390
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