Final published version
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -