A Geometric Duality for Two Metrics for the Co-Ordinate Plane

1970 ◽  
Vol 54 (387) ◽  
pp. 19 ◽  
Author(s):  
Frank Rhodes
Keyword(s):  
Geometric Duality

scholarly journals The Delaunay tessellation in hyperbolic space

2016 ◽  
Vol 164 (1) ◽  
pp. 15-46 ◽  
Author(s):  
JASON DEBLOIS
Keyword(s):  
Hyperbolic Space ◽  
Finite Subset ◽  
Voronoi Tessellation ◽  
Invariant Sets ◽  
Convex Hulls ◽  
Delaunay Tessellation ◽  
Locally Finite ◽  
Euclidean Setting ◽  
Geometric Duality

AbstractThe Delaunay tessellation of a locally finite subset of the hyperbolic space ℍnis constructed via convex hulls in ℝn+1. For finite and lattice-invariant sets it is proven to be a polyhedral decomposition, and versions (necessarily modified from the Euclidean setting) of the empty circumspheres condition and geometric duality with the Voronoi tessellation are proved. Some pathological examples of infinite, non lattice-invariant sets are exhibited.

Polemics in Public: Poncelet, Gergonne, Plücker, and the Duality Controversy

2015 ◽  
Vol 28 (4) ◽  
pp. 545-585 ◽  
Author(s):  
Jemma Lorenat
Keyword(s):  
Public Controversy ◽  
Textual Study ◽  
Historical Literature ◽  
Principle Of Duality ◽  
Geometric Duality

ArgumentA plagiarism charge in 1827 sparked a public controversy centered between Jean-Victor Poncelet (1788–1867) and Joseph-Diez Gergonne (1771–1859) over the origin and applications of the principle of duality in geometry. Over the next three years and through the pages of various journals, monographs, letters, reviews, reports, and footnotes, vitriol between the antagonists increased as their potential publicity grew. While the historical literature offers valuable resources toward understanding the development, content, and applications of geometric duality, the hostile nature of the exchange seems to have deterred an in-depth textual study of the explicitly polemical writings. We argue that the necessary collective endeavor of beginning and ending this controversy constitutes a case study in the circulation of geometry. In particular, we consider how the duality controversy functioned as a medium of communicating new fundamental principles to a wider audience of practitioners.

Demosaicking using geometric duality and dilated directional differentiation

2014 ◽  
Vol 324 ◽  
pp. 194-201 ◽  
Author(s):  
Joohyeok Kim ◽  
Gwanggil Jeon ◽  
Jechang Jeong
Keyword(s):  
Geometric Duality

The Side-Force Problem for Shallow Helicoidal Shells

1969 ◽  
Vol 36 (2) ◽  
pp. 292-295 ◽  
Author(s):  
F. Y. M. Wan
Keyword(s):  
Computer Program ◽  
Numerical Results ◽  
Elementary Functions ◽  
Pure Bending ◽  
Side Force ◽  
Force Problem ◽  
Geometric Duality

The side-force problem for a shallow helicoidal shell is shown to be the complete static-geometric analog of the pure bending problem for the same shell. The solution of the former in terms of elementary functions is obtained, without another set of independent calculations, simply by applying the rules of the static-geometric duality to that of the latter. The analogy also enables us to use the same computer program developed for the pure bending problem (without any modification) to generate numerical results for the side-force problem.

Single Image Super-Resolution Using Local Geometric Duality and Non-Local Similarity

2016 ◽  
Vol 25 (5) ◽  
pp. 2168-2183 ◽  
Author(s):  
Chao Ren ◽  
Xiaohai He ◽  
Qizhi Teng ◽  
Yuanyuan Wu ◽  
Truong Q. Nguyen
Keyword(s):  
Super Resolution ◽  
Local Similarity ◽  
Single Image ◽  
Non Local ◽  
Image Super Resolution ◽  
Single Image Super Resolution ◽  
Geometric Duality
Sign in / Sign up

Export Citation Format

Share Document