Dimensions of spline spaces over unconstricted triangulations

Gerald Farin

doi:10.1016/j.cam.2005.05.010

Dimensions of spline spaces over unconstricted triangulations

Gerald Farin

Computing, Informatics and Decision Systems Engineering, School of (CIDSE)

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

One of the puzzlingly hard problems in Computer Aided Geometric Design and Approximation Theory is that of finding the dimension of the spline space of C^r piecewise degree n polynomials over a 2D triangulation Ω. We denote such spaces by S_n^r ( Ω ). In this note, we restrict Ω to have a special structure, namely to be unconstricted. This will allow for several exact dimension formulas.

Original language	English (US)
Pages (from-to)	320-327
Number of pages	8
Journal	Journal of Computational and Applied Mathematics
Volume	192
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2005.05.010
State	Published - Aug 1 2006

Keywords

Bernstein-Bézier form
Bivariate spline spaces
Dimensions
Minimal determining sets
Unconstricted triangulations

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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AB - One of the puzzlingly hard problems in Computer Aided Geometric Design and Approximation Theory is that of finding the dimension of the spline space of Cr piecewise degree n polynomials over a 2D triangulation Ω. We denote such spaces by Snr ( Ω ). In this note, we restrict Ω to have a special structure, namely to be unconstricted. This will allow for several exact dimension formulas.

KW - Bernstein-Bézier form

KW - Bivariate spline spaces

KW - Dimensions

KW - Minimal determining sets

KW - Unconstricted triangulations

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