Matches in SemOpenAlex for { <https://semopenalex.org/work/W2964388618> ?p ?o ?g. }
Showing items 1 to 82 of
82
with 100 items per page.
- W2964388618 endingPage "349" @default.
- W2964388618 startingPage "335" @default.
- W2964388618 abstract "An order-k univariate B-spline is a parametric curve defined over a set S of at least $$k+2$$ real parameters, called knots. Such a B-spline can be obtained as a linear combination of basic B-splines, each of them being defined over a subset of $$k+2$$ consecutive knots of S, called a configuration of S. In the bivariate setting, knots are pairs of reals and basic B-splines are defined over configurations of $$k+3$$ knots. Among these configurations, the Delaunay configurations introduced by Neamtu in 2001 gave rise to the first bivariate B-splines that retain the fundamental properties of univariate B-splines. An order-k Delaunay configuration is characterized by a circle that passes through three knots and contains k knots in its interior. In order to construct a wider variety of bivariate B-splines satisfying the same fundamental properties, Liu and Snoeyink proposed, in 2007, an algorithm to generate configurations. Even if experimental results indicate that their algorithm generates indeed valid configurations, they only succeeded in proving it up to $$k=3$$. Until now, no proof has been given for greater k. In this paper we first show that, if we replace the circles in Neamtu’s definition by maximal families of convex pseudo-circles, then we obtain configurations that satisfy the same fundamental properties as Delaunay configurations. We then prove that these configurations are precisely the ones generated by the algorithm of Liu and Snoeyink, establishing thereby the validity of their algorithm for all k." @default.
- W2964388618 created "2019-08-13" @default.
- W2964388618 creator A5033062463 @default.
- W2964388618 date "2019-01-01" @default.
- W2964388618 modified "2023-09-28" @default.
- W2964388618 title "Bivariate B-Splines from Convex Pseudo-circle Configurations" @default.
- W2964388618 cites W1539645382 @default.
- W2964388618 cites W2021326615 @default.
- W2964388618 cites W2039170720 @default.
- W2964388618 cites W2039820941 @default.
- W2964388618 cites W2103777374 @default.
- W2964388618 cites W2106906788 @default.
- W2964388618 cites W2108724379 @default.
- W2964388618 cites W2111335529 @default.
- W2964388618 cites W2120590198 @default.
- W2964388618 cites W2137563517 @default.
- W2964388618 cites W2168397817 @default.
- W2964388618 cites W2585421008 @default.
- W2964388618 cites W3101503192 @default.
- W2964388618 doi "https://doi.org/10.1007/978-3-030-25027-0_23" @default.
- W2964388618 hasPublicationYear "2019" @default.
- W2964388618 type Work @default.
- W2964388618 sameAs 2964388618 @default.
- W2964388618 citedByCount "3" @default.
- W2964388618 countsByYear W29643886182020 @default.
- W2964388618 countsByYear W29643886182022 @default.
- W2964388618 crossrefType "book-chapter" @default.
- W2964388618 hasAuthorship W2964388618A5033062463 @default.
- W2964388618 hasConcept C105795698 @default.
- W2964388618 hasConcept C112680207 @default.
- W2964388618 hasConcept C11413529 @default.
- W2964388618 hasConcept C114614502 @default.
- W2964388618 hasConcept C117251300 @default.
- W2964388618 hasConcept C118615104 @default.
- W2964388618 hasConcept C127413603 @default.
- W2964388618 hasConcept C134306372 @default.
- W2964388618 hasConcept C15945459 @default.
- W2964388618 hasConcept C161584116 @default.
- W2964388618 hasConcept C199163554 @default.
- W2964388618 hasConcept C2524010 @default.
- W2964388618 hasConcept C2779863119 @default.
- W2964388618 hasConcept C33923547 @default.
- W2964388618 hasConcept C42360764 @default.
- W2964388618 hasConcept C64341305 @default.
- W2964388618 hasConcept C68010082 @default.
- W2964388618 hasConceptScore W2964388618C105795698 @default.
- W2964388618 hasConceptScore W2964388618C112680207 @default.
- W2964388618 hasConceptScore W2964388618C11413529 @default.
- W2964388618 hasConceptScore W2964388618C114614502 @default.
- W2964388618 hasConceptScore W2964388618C117251300 @default.
- W2964388618 hasConceptScore W2964388618C118615104 @default.
- W2964388618 hasConceptScore W2964388618C127413603 @default.
- W2964388618 hasConceptScore W2964388618C134306372 @default.
- W2964388618 hasConceptScore W2964388618C15945459 @default.
- W2964388618 hasConceptScore W2964388618C161584116 @default.
- W2964388618 hasConceptScore W2964388618C199163554 @default.
- W2964388618 hasConceptScore W2964388618C2524010 @default.
- W2964388618 hasConceptScore W2964388618C2779863119 @default.
- W2964388618 hasConceptScore W2964388618C33923547 @default.
- W2964388618 hasConceptScore W2964388618C42360764 @default.
- W2964388618 hasConceptScore W2964388618C64341305 @default.
- W2964388618 hasConceptScore W2964388618C68010082 @default.
- W2964388618 hasLocation W29643886181 @default.
- W2964388618 hasLocation W29643886182 @default.
- W2964388618 hasOpenAccess W2964388618 @default.
- W2964388618 hasPrimaryLocation W29643886181 @default.
- W2964388618 hasRelatedWork W1524808628 @default.
- W2964388618 hasRelatedWork W1835213773 @default.
- W2964388618 hasRelatedWork W1982612683 @default.
- W2964388618 hasRelatedWork W1994222927 @default.
- W2964388618 hasRelatedWork W2110584579 @default.
- W2964388618 hasRelatedWork W2364528848 @default.
- W2964388618 hasRelatedWork W2964926980 @default.
- W2964388618 hasRelatedWork W3122371356 @default.
- W2964388618 hasRelatedWork W3137081315 @default.
- W2964388618 hasRelatedWork W4379258846 @default.
- W2964388618 isParatext "false" @default.
- W2964388618 isRetracted "false" @default.
- W2964388618 magId "2964388618" @default.
- W2964388618 workType "book-chapter" @default.