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Rigidity through a Projective Lens

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Rigidity through a Projective Lens. / Nixon, Anthony; Schulze, Bernd; Whiteley, Walter.
In: Applied Science, Vol. 11, No. 24, e11946, 15.12.2021.

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

Harvard

Nixon, A, Schulze, B & Whiteley, W 2021, 'Rigidity through a Projective Lens', Applied Science, vol. 11, no. 24, e11946. https://doi.org/https://www.researchgate.net/publication/350838924_Rigidity_Through_a_Projective_Lens, https://doi.org/10.3390/app112411946

APA

Nixon, A., Schulze, B., & Whiteley, W. (2021). Rigidity through a Projective Lens. Applied Science, 11(24), Article e11946. https://doi.org/https://www.researchgate.net/publication/350838924_Rigidity_Through_a_Projective_Lens, https://doi.org/10.3390/app112411946

Vancouver

Nixon A, Schulze B, Whiteley W. Rigidity through a Projective Lens. Applied Science. 2021 Dec 15;11(24):e11946. doi: https://www.researchgate.net/publication/350838924_Rigidity_Through_a_Projective_Lens, 10.3390/app112411946

Author

Nixon, Anthony ; Schulze, Bernd ; Whiteley, Walter. / Rigidity through a Projective Lens. In: Applied Science. 2021 ; Vol. 11, No. 24.

Bibtex

@article{a5ff696f2409407d8ab72a0434fab6f3,
title = "Rigidity through a Projective Lens",
abstract = "In this paper, we offer an overview of a number of results on the static rigidity and infinitesimal rigidity of discrete structures which are embedded in projective geometric reasoning, representations, and transformations. Part I considers the fundamental case of a bar−joint framework in projective d-space and places particular emphasis on the projective invariance of infinitesimal rigidity, coning between dimensions, transfer to the spherical metric, slide joints and pure conditions for singular configurations. Part II extends the results, tools and concepts from Part I to additional types of rigid structures including body-bar, body−hinge and rod-bar frameworks, all drawing on projective representations, transformations and insights. Part III widens the lens to include the closely related cofactor matroids arising from multivariate splines, which also exhibit the projective invariance. These are another fundamental example of abstract rigidity matroids with deep analogies to rigidity. We conclude in Part IV with commentary on some nearby areas.",
author = "Anthony Nixon and Bernd Schulze and Walter Whiteley",
year = "2021",
month = dec,
day = "15",
doi = "https://www.researchgate.net/publication/350838924_Rigidity_Through_a_Projective_Lens",
language = "English",
volume = "11",
journal = "Applied Science",
publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",
number = "24",

}

RIS

TY - JOUR

T1 - Rigidity through a Projective Lens

AU - Nixon, Anthony

AU - Schulze, Bernd

AU - Whiteley, Walter

PY - 2021/12/15

Y1 - 2021/12/15

N2 - In this paper, we offer an overview of a number of results on the static rigidity and infinitesimal rigidity of discrete structures which are embedded in projective geometric reasoning, representations, and transformations. Part I considers the fundamental case of a bar−joint framework in projective d-space and places particular emphasis on the projective invariance of infinitesimal rigidity, coning between dimensions, transfer to the spherical metric, slide joints and pure conditions for singular configurations. Part II extends the results, tools and concepts from Part I to additional types of rigid structures including body-bar, body−hinge and rod-bar frameworks, all drawing on projective representations, transformations and insights. Part III widens the lens to include the closely related cofactor matroids arising from multivariate splines, which also exhibit the projective invariance. These are another fundamental example of abstract rigidity matroids with deep analogies to rigidity. We conclude in Part IV with commentary on some nearby areas.

AB - In this paper, we offer an overview of a number of results on the static rigidity and infinitesimal rigidity of discrete structures which are embedded in projective geometric reasoning, representations, and transformations. Part I considers the fundamental case of a bar−joint framework in projective d-space and places particular emphasis on the projective invariance of infinitesimal rigidity, coning between dimensions, transfer to the spherical metric, slide joints and pure conditions for singular configurations. Part II extends the results, tools and concepts from Part I to additional types of rigid structures including body-bar, body−hinge and rod-bar frameworks, all drawing on projective representations, transformations and insights. Part III widens the lens to include the closely related cofactor matroids arising from multivariate splines, which also exhibit the projective invariance. These are another fundamental example of abstract rigidity matroids with deep analogies to rigidity. We conclude in Part IV with commentary on some nearby areas.

U2 - https://www.researchgate.net/publication/350838924_Rigidity_Through_a_Projective_Lens

DO - https://www.researchgate.net/publication/350838924_Rigidity_Through_a_Projective_Lens

M3 - Journal article

VL - 11

JO - Applied Science

JF - Applied Science

IS - 24

M1 - e11946

ER -