# Dimensions of spline spaces over unconstricted triangulations

Gerald Farin

Research output: Contribution to journalArticle

3 Citations (Scopus)

### 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) 320-327 8 Journal of Computational and Applied Mathematics 192 2 https://doi.org/10.1016/j.cam.2005.05.010 Published - Aug 1 2006

### Fingerprint

Approximation theory
Triangulation
Splines
Spline
Computer aided design
Polynomials
Computer Aided Geometric Design
Approximation Theory
Denote
Polynomial

### 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 journalArticle

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