Bivariate Simplex B-Splines A New Paradigm
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 generaliza...
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| Veröffentlicht in: | Proceedings of the 17th Spring Conference on Computer Graphics S. 71 |
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| Format: | Tagungsbericht |
| Sprache: | Englisch |
| Veröffentlicht: |
Washington, DC, USA
IEEE Computer Society
25.04.2001
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| Schriftenreihe: | ACM Conferences |
| Schlagworte: | |
| ISBN: | 9780769512150, 0769512151 |
| Online-Zugang: | Volltext |
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| 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. |
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| AbstractList | 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. |
| Author | Neamtu, Marian |
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| Copyright | Copyright (c) 2001 Institute of Electrical and Electronics Engineers, Inc. All rights reserved. |
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| Keywords | Higher Order Voronoi Diagrams Delaunay Configurations Bivariate Simplex B-Splines |
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| SubjectTerms | Computing methodologies Computing methodologies -- Computer graphics Computing methodologies -- Computer graphics -- Shape modeling Mathematics of computing Mathematics of computing -- Mathematical analysis Mathematics of computing -- Mathematical analysis -- Functional analysis Mathematics of computing -- Mathematical analysis -- Functional analysis -- Approximation Mathematics of computing -- Mathematical analysis -- Numerical analysis Mathematics of computing -- Mathematical analysis -- Numerical analysis -- Computations on polynomials Mathematics of computing -- Mathematical analysis -- Numerical analysis -- Interpolation |
| Subtitle | A New Paradigm |
| Title | Bivariate Simplex B-Splines |
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