Matches in SemOpenAlex for { <https://semopenalex.org/work/W4298861454> ?p ?o ?g. }
Showing items 1 to 63 of
63
with 100 items per page.
- W4298861454 abstract "Higher order Delaunay triangulations are a generalization of the Delaunay triangulation which provides a class of well-shaped triangulations, over which extra criteria can be optimized. A triangulation is order-$k$ Delaunay if the circumcircle of each triangle of the triangulation contains at most $k$ points. In this paper we study lower and upper bounds on the number of higher order Delaunay triangulations, as well as their expected number for randomly distributed points. We show that arbitrarily large point sets can have a single higher order Delaunay triangulation, even for large orders, whereas for first order Delaunay triangulations, the maximum number is $2^{n-3}$. Next we show that uniformly distributed points have an expected number of at least $2^{rho_1 n(1+o(1))}$ first order Delaunay triangulations, where $rho_1$ is an analytically defined constant ($rho_1 approx 0.525785$), and for $k > 1$, the expected number of order-$k$ Delaunay triangulations (which are not order-$i$ for any $i < k$) is at least $2^{rho_k n(1+o(1))}$, where $rho_k$ can be calculated numerically." @default.
- W4298861454 created "2022-10-02" @default.
- W4298861454 creator A5009125793 @default.
- W4298861454 creator A5047854337 @default.
- W4298861454 creator A5074443763 @default.
- W4298861454 date "2010-02-23" @default.
- W4298861454 modified "2023-09-30" @default.
- W4298861454 title "On the Number of Higher Order Delaunay Triangulations" @default.
- W4298861454 hasPublicationYear "2010" @default.
- W4298861454 type Work @default.
- W4298861454 citedByCount "0" @default.
- W4298861454 crossrefType "posted-content" @default.
- W4298861454 hasAuthorship W4298861454A5009125793 @default.
- W4298861454 hasAuthorship W4298861454A5047854337 @default.
- W4298861454 hasAuthorship W4298861454A5074443763 @default.
- W4298861454 hasBestOaLocation W42988614541 @default.
- W4298861454 hasConcept C10138342 @default.
- W4298861454 hasConcept C114614502 @default.
- W4298861454 hasConcept C121198538 @default.
- W4298861454 hasConcept C128321387 @default.
- W4298861454 hasConcept C134306372 @default.
- W4298861454 hasConcept C162324750 @default.
- W4298861454 hasConcept C167117609 @default.
- W4298861454 hasConcept C177148314 @default.
- W4298861454 hasConcept C178609930 @default.
- W4298861454 hasConcept C182306322 @default.
- W4298861454 hasConcept C183342303 @default.
- W4298861454 hasConcept C33923547 @default.
- W4298861454 hasConcept C68010082 @default.
- W4298861454 hasConcept C99886907 @default.
- W4298861454 hasConceptScore W4298861454C10138342 @default.
- W4298861454 hasConceptScore W4298861454C114614502 @default.
- W4298861454 hasConceptScore W4298861454C121198538 @default.
- W4298861454 hasConceptScore W4298861454C128321387 @default.
- W4298861454 hasConceptScore W4298861454C134306372 @default.
- W4298861454 hasConceptScore W4298861454C162324750 @default.
- W4298861454 hasConceptScore W4298861454C167117609 @default.
- W4298861454 hasConceptScore W4298861454C177148314 @default.
- W4298861454 hasConceptScore W4298861454C178609930 @default.
- W4298861454 hasConceptScore W4298861454C182306322 @default.
- W4298861454 hasConceptScore W4298861454C183342303 @default.
- W4298861454 hasConceptScore W4298861454C33923547 @default.
- W4298861454 hasConceptScore W4298861454C68010082 @default.
- W4298861454 hasConceptScore W4298861454C99886907 @default.
- W4298861454 hasLocation W42988614541 @default.
- W4298861454 hasLocation W42988614542 @default.
- W4298861454 hasLocation W42988614543 @default.
- W4298861454 hasLocation W42988614544 @default.
- W4298861454 hasOpenAccess W4298861454 @default.
- W4298861454 hasPrimaryLocation W42988614541 @default.
- W4298861454 hasRelatedWork W1648170231 @default.
- W4298861454 hasRelatedWork W1964815690 @default.
- W4298861454 hasRelatedWork W1979362696 @default.
- W4298861454 hasRelatedWork W2001351033 @default.
- W4298861454 hasRelatedWork W2149044706 @default.
- W4298861454 hasRelatedWork W2168284009 @default.
- W4298861454 hasRelatedWork W2172589357 @default.
- W4298861454 hasRelatedWork W2359979928 @default.
- W4298861454 hasRelatedWork W2361950850 @default.
- W4298861454 hasRelatedWork W2953026322 @default.
- W4298861454 isParatext "false" @default.
- W4298861454 isRetracted "false" @default.
- W4298861454 workType "article" @default.