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A Discussion to Dimensions of Spline Spaces Over Unconstricted Triangulations  

Yi, Na (Department of Mathematics, Shanghai University)
Liu, Huan-Wen (School of Mathematics and Computer Science, Guangxi University for Nationalities)
Publication Information
International Journal of CAD/CAM / v.9, no.1, 2010 , pp. 25-29 More about this Journal
Abstract
Let $S_n^r(\Omega)$ be the spline space of degree n and smoothness r with respect to $\Omega$ where $\Omega$ is a triangulation of a planner polygonal domain. Dimensions of $S_n^r(\Omega)$ over the so-called unconstricted triangulation were given by Farin in [J. Comput. Appl. Math. 192(2006), 320-327]. In this paper, a counter example is given to show that the condition used in the main result in Farins paper is not correct, and then an improved necessary and sufficient condition is presented.
Keywords
Bezier-net technique; Unconstricted triangulation; Bivariate spline space; Minimaldetermining set; Dimension;
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