| 罗钟铉,刘凤山,施锡泉.Morgan-Scott型剖分上的样条空间的奇异性[J].数学研究及应用,2010,30(1):1~16 |
| Morgan-Scott型剖分上的样条空间的奇异性 |
| On Singularity of Spline Space Over Morgan-Scott's Type Partition |
| 投稿时间：2008-06-17 修订日期：2008-10-08 |
| DOI：10.3770/j.issn:1000-341X.2010.01.001 |
| 中文关键词: 样条空间奇异性 Morgan-Scott剖分 平面代数曲线 特征比 特征映射 特征数. |
| 英文关键词:singularity of spline space Morgan-Scott's partition planar algebraic curve characteristic ratio characteristic mapping characteristic number. |
| 基金项目:国家自然科学基金资助项目（Grant Nos.10771028;?60533060）；新世纪优秀人才资助项目；DoD基金资助项目（Grant No.DAAD19-03-1-0375） |
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| 中文摘要: |
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| 英文摘要: |
| Multivariate spline function is an important research object and tool in Computational Geometry. The singularity of multivariate spline spaces is a difficult problem that is ineritable in the research of the structure of multivariate spline spaces. The aim of this paper is to reveal the geometric significance of the singularity of bivariate spline space over Morgan-Scott type triangulation by using some new concepts proposed by the first author such as characteristic ratio, characteristic mapping of lines (or ponits), and characteristic number of algebraic curve. With these concepts and the relevant results, a polished necessary and sufficient conditions for the singularity of spline space $S_{\mu 1}^\mu(\Delta_{MS}^\mu)$ are geometrically given for any smoothness $\mu$ by recursion. Moreover, the famous Pascal's theorem is generalized to algebraic plane curves of degree $n\geq 3$. |
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