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The hyperbolic Voronoi diagram in arbitr...

Nielsen, Frank...

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The hyperbolic Voronoi diagram in arbitrary dimension by Nielsen, Frank ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	01-08-2023
Summary	We show that in the Klein projective ball model of hyperbolic space, the hyperbolic Voronoi diagram is affine and amounts to clip a corresponding power diagram, requiring however algebraic arithmetic. By considering the lesser-known Beltrami hemisphere model of hyperbolic geometry, we overcome the arithmetic limitations of Klein construction. Finally, we characterize the bisectors and geodesics in the other Poincar\' e upper half-space, the Poincar\'e ball, and the Lorentz hyperboloid models, and discusses on degenerate cases for which the dual hyperbolic Delaunay complex is not a triangulation.
ISBN	-
Item Type	Article
File Type	pdf
File Size	30.00 KB
Language	English
Subjects	-
Charge Per Copy	MYR 0.01
Available copies	1
Total read	-
URL	http://arxiv.org/abs/1210.8234

Citation

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AMA 11th EditionReferences

Nielsen, Frank. The hyperbolic Voronoi diagram in arbitrary dimension. Australian National University. August 01, 2023. Accessed August 11, 2025. https://online.provdatabase.com/cite/9743

APA 7th EditionReferences

Nielsen, Frank. (2023). The hyperbolic Voronoi diagram in arbitrary dimension. Australian National University. https://online.provdatabase.com/cite/9743

Chicago 17th EditionReferences

Nielsen, Frank. The hyperbolic Voronoi diagram in arbitrary dimension. Australian National University. 2023. https://online.provdatabase.com/cite/9743

HarvardReferences

Nielsen, Frank. (2023). The hyperbolic Voronoi diagram in arbitrary dimension. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/9743. (Accessed 11 August 2025).

Harvard AustraliaReferences

Nielsen, Frank, 2023, The hyperbolic Voronoi diagram in arbitrary dimension, Australian National University, viewed 11 August 2025, <https://online.provdatabase.com/cite/9743>

MLA 9th EditionWorks Cited

Nielsen, Frank. The hyperbolic Voronoi diagram in arbitrary dimension. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/9743.

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