Point-hyperplane frameworks, slider joints, and rigidity preserving transformations

Eftekhari, Yaser and Jackson, Bill and Nixon, Anthony Keith and Schulze, Bernd and Tanigawa, Shin-ichi and Whiteley, Walter (2019) Point-hyperplane frameworks, slider joints, and rigidity preserving transformations. Journal of Combinatorial Theory, Series B, 135. pp. 44-74. ISSN 0095-8956

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A one-to-one correspondence between the infinitesimal motions of bar-joint frameworks in Rd and those in Sd is a classical observation by Pogorelov, and further connections among different rigidity models in various different spaces have been extensively studied. In this paper, we shall extend this line of research to include the infinitesimal rigidity of frameworks consisting of points and hyperplanes. This enables us to understand correspondences between point-hyperplane rigidity, classical bar-joint rigidity, and scene analysis. Among other results, we derive a combinatorial characterization of graphs that can be realized as infinitesimally rigid frameworks in the plane with a given set of points collinear. This extends a result by Jackson and Jordán, which deals with the case when three points are collinear.

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Journal Article
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Journal of Combinatorial Theory, Series B
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26 Jul 2018 12:48
Last Modified:
22 Nov 2022 06:09