Bivariate simplex B-splines: a new paradigm

Author

Neamtu, Marian

Author_Institution

Dept. of Math., Vanderbilt Univ., Nashville, TN, USA

fYear

2001

fDate

2001

Firstpage

71

Lastpage

78

Abstract

A construction of bivariate splines is described, based on a new concept of higher degree Delaunay configurations. The crux of this construction is that knot-sets for simplex B-splines are selected by considering groups of "nearby" knots. The new approach gives rise to a natural generalization of univariate splines in that the linear span of this collection of B-splines forms a space which is analogous to the classical univariate splines. This new spline space depends uniquely and in a local way on the prescribed knot locations, and there is no need to use auxiliary or perturbed knots as in some earlier constructions

Keywords

CAD; computational geometry; mesh generation; polynomials; splines (mathematics); Delaunay configurations; bivariate simplex B-splines; classical univariate splines; higher degree Delaunay configurations; higher order Voronoi diagrams; knot-sets; linear span; natural generalization; prescribed knot locations; spline space; univariate splines; Collaboration; Design engineering; Ear; Extraterrestrial measurements; Mathematical model; Mathematics; Polynomials; Solid modeling; Spline;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Graphics, Spring Conference on, 2001.

Conference_Location

Budmerice

Print_ISBN

0-7695-1215-1

Type

conf

DOI

10.1109/SCCG.2001.945339

Filename

945339