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

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Point-hyperplane frameworks, slider joints, and rigidity preserving transformations. / Eftekhari, Yaser; Jackson, Bill; Nixon, Anthony Keith; Schulze, Bernd; Tanigawa, Shin-ichi; Whiteley, Walter.

In: Journal of Combinatorial Theory, Series B, Vol. 135, 03.2019, p. 44-74.

Research output: Contribution to journalJournal article

Harvard

Eftekhari, Y, Jackson, B, Nixon, AK, Schulze, B, Tanigawa, S & Whiteley, W 2019, 'Point-hyperplane frameworks, slider joints, and rigidity preserving transformations', Journal of Combinatorial Theory, Series B, vol. 135, pp. 44-74. https://doi.org/10.1016/j.jctb.2018.07.008

APA

Eftekhari, Y., Jackson, B., Nixon, A. K., Schulze, B., Tanigawa, S., & Whiteley, W. (2019). Point-hyperplane frameworks, slider joints, and rigidity preserving transformations. Journal of Combinatorial Theory, Series B, 135, 44-74. https://doi.org/10.1016/j.jctb.2018.07.008

Vancouver

Eftekhari Y, Jackson B, Nixon AK, Schulze B, Tanigawa S, Whiteley W. Point-hyperplane frameworks, slider joints, and rigidity preserving transformations. Journal of Combinatorial Theory, Series B. 2019 Mar;135:44-74. https://doi.org/10.1016/j.jctb.2018.07.008

Author

Eftekhari, Yaser ; Jackson, Bill ; Nixon, Anthony Keith ; Schulze, Bernd ; Tanigawa, Shin-ichi ; Whiteley, Walter. / Point-hyperplane frameworks, slider joints, and rigidity preserving transformations. In: Journal of Combinatorial Theory, Series B. 2019 ; Vol. 135. pp. 44-74.

Bibtex

@article{3d7db9b5828b49b8a92c57f3de4020ae,
title = "Point-hyperplane frameworks, slider joints, and rigidity preserving transformations",
abstract = "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 Jord{\'a}n, which deals with the case when three points are collinear.",
keywords = "Infinitesimal rigidity, Bar-joint framework, Point-hyperplane framework, Spherical framework, Slider constraints",
author = "Yaser Eftekhari and Bill Jackson and Nixon, {Anthony Keith} and Bernd Schulze and Shin-ichi Tanigawa and Walter Whiteley",
year = "2019",
month = "3",
doi = "10.1016/j.jctb.2018.07.008",
language = "English",
volume = "135",
pages = "44--74",
journal = "Journal of Combinatorial Theory, Series B",
issn = "0095-8956",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Point-hyperplane frameworks, slider joints, and rigidity preserving transformations

AU - Eftekhari, Yaser

AU - Jackson, Bill

AU - Nixon, Anthony Keith

AU - Schulze, Bernd

AU - Tanigawa, Shin-ichi

AU - Whiteley, Walter

PY - 2019/3

Y1 - 2019/3

N2 - 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.

AB - 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.

KW - Infinitesimal rigidity

KW - Bar-joint framework

KW - Point-hyperplane framework

KW - Spherical framework

KW - Slider constraints

U2 - 10.1016/j.jctb.2018.07.008

DO - 10.1016/j.jctb.2018.07.008

M3 - Journal article

VL - 135

SP - 44

EP - 74

JO - Journal of Combinatorial Theory, Series B

JF - Journal of Combinatorial Theory, Series B

SN - 0095-8956

ER -