Mathematical Sciences: Multivariate Splines

数学科学：多元样条

• 批准号: 8701121
• 负责人: Peter Alfeld
• 金额: $ 9.4万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-09-01 至 1991-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701121&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multivariate; Splines

This project aims at solving the outstanding problem of the dimension and basis for the multivariate spline spaces and applying the results to the most effective surface interpolation and computer representation of three dimensional objects via computer graphics. The structure of multivariate spline spaces is vastly more complex than in the univariate case and fundamental questions are still unanswered. Among these questions are the dimension, the construction of bases, existence of a local basis, and application to interpolation problems. The main tool of this research will be the symbolic manipulation language "Reduce", which will enable the investigator to solve exactly the large linear systems that arise from the smoothness conditions linking polynomials on neighboring triangles. The investigator will blend the Bezier-Bernstein techniques with the symbolic manipulation and will attempt to apply his results to surface representation problems arising in engineering.

该项目旨在解决多元样条空间的维数和基础的突出问题，并将结果应用于最有效的表面插值和通过计算机图形学表示三维物体的计算机表示。 多元样条空间的结构比单变量情况复杂得多，并且基本问题仍未得到解答。 这些问题包括维度、基的构造、局部基的存在以及插值问题的应用。 这项研究的主要工具将是符号操作语言“Reduce”，这将使研究人员能够精确地解决由连接相邻三角形上的多项式的平滑条件产生的大型线性系统。 研究人员将贝塞尔-伯恩斯坦技术与符号操作相结合，并尝试将其结果应用于工程中出现的表面表示问题。