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Article overview
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Further results on the hyperbolic Voronoi diagrams | Frank Nielsen
; Richard Nock
; | Date: |
4 Oct 2014 | Abstract: | In Euclidean geometry, it is well-known that the $k$-order Voronoi diagram in
$mathbb{R}^d$ can be computed from the vertical projection of the $k$-level of
an arrangement of hyperplanes tangent to a convex potential function in
$mathbb{R}^{d+1}$: the paraboloid. Similarly, we report for the Klein ball
model of hyperbolic geometry such a {em concave} potential function: the
northern hemisphere. Furthermore, we also show how to build the hyperbolic
$k$-order diagrams as equivalent clipped power diagrams in $mathbb{R}^d$. We
investigate the hyperbolic Voronoi diagram in the hyperboloid model and show
how it reduces to a Klein-type model using central projections. | Source: | arXiv, 1410.1036 | Services: | Forum | Review | PDF | Favorites |
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