International Journal of CAD/CAM

Society for Computational Design and Engineering (한국CDE학회)
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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)
  • Published : 2010.04.01
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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.

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References

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