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 Cr piecewise degree n polynomials over a 2D triangulation Ω. We denote such spaces by Sn 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 | |
| State | Published - Aug 1 2006 |
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Keywords
- Bernstein-Bézier form
- Bivariate spline spaces
- Dimensions
- Minimal determining sets
- Unconstricted triangulations
ASJC Scopus subject areas
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis
Cite this
Dimensions of spline spaces over unconstricted triangulations. / Farin, Gerald.
In: Journal of Computational and Applied Mathematics, Vol. 192, No. 2, 01.08.2006, p. 320-327.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Dimensions of spline spaces over unconstricted triangulations
AU - Farin, Gerald
PY - 2006/8/1
Y1 - 2006/8/1
N2 - 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 Sn 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.
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 Sn 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.
KW - Bernstein-Bézier form
KW - Bivariate spline spaces
KW - Dimensions
KW - Minimal determining sets
KW - Unconstricted triangulations
UR - http://www.scopus.com/inward/record.url?scp=33646117019&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33646117019&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2005.05.010
DO - 10.1016/j.cam.2005.05.010
M3 - Article
AN - SCOPUS:33646117019
VL - 192
SP - 320
EP - 327
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 2
ER -