Abstract Voronoi diagrams revisited

“…Given a set of primitives, the Voronoi diagram partitions space into regions, where each region consists of all points that are closer to one primitive than to any other. The Voronoi diagrams have important applications in many sciences, including visualization of medical datasets, proximity queries, spatial data manipulation, shape analysis, computer animation, robot motion planning, modeling spatial structures and processes, pattern recognition, locational optimization and selection in user-interfaces [30,31]. A concept of the Centroidal Voronoi tessellation was presented in the form of graphs in [32].…”

Section: The Related Workmentioning

confidence: 99%

Visualization of cracks by using the local Voronoi decompositions and distributed software

Pacevič

Kačeniauskas

Markauskas

2015

Advances in Engineering Software

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“…[15,16,66]). Bisectors of Minkowski spaces have, in general, a complicated topological and geometric structure (cf.…”

Section: Bisectors In a Minkowski Plane The Bisectormentioning

confidence: 99%

On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces

2011

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We survey mainly recent results on the two most important orthogonality types in normed linear spaces, namely on Birkhoff orthogonality and on isosceles (or James) orthogonality. We lay special emphasis on their fundamental properties, on their differences and connections, and on geometric results and problems inspired by the respective theoretical framework. At the beginning we also present other interesting types of orthogonality. This survey can also be taken as an update of existing related representations. Mathematics Subject Classification (2000). 46B20, 46C15, 52A21.

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Abstract Voronoi diagrams revisited

Cited by 49 publications

References 19 publications

Abstract Voronoi Diagrams

Abstract Voronoi Diagrams

Visualization of cracks by using the local Voronoi decompositions and distributed software

On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces

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