Mathematical Sciences: Spline Tools and Applications

数学科学：样条工具和应用

• 批准号: 9500643
• 负责人: Larry Schumaker
• 金额: $ 10.8万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-15 至 1999-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500643&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Spline; Tools; Applications

9500643 Schumaker The objectives of this project are to develop new classes of splines defined on the sphere and on sphere-like surfaces, to develop explicit numerical algorithms tailored to the sphere, and to explore their applications. Other research to be performed involves wavelets for trigonometric splines and for splines on triangulations, quasi-interpolation by trigonometric splines, splines on quadrangulations, adaptive knot removal and insertion for bivariate splines, and fitting of data in many variables. In the past 30 years, spline functions have become a well-established computational tool, and are now widely used by scientists and engineers. They are used for a variety of purposes, including approximating complicated curves and surfaces, fitting data, computer-aided geometric design (CAGD), computer-aided manufacturing (CAM), solution of differential equations, image processing, etc. The aim of this research is to develop new spline tools, and to create algorithms for solving some specific applications problems, especially problems arising in CAGD, CAM, geology, geophysics, and meteorology.

9500643 Schumaker 该项目的目标是开发在球体和类球体表面上定义的新样条类型，开发适合球体的显式数值算法，并探索它们的应用。需要进行的其他研究涉及三角样条和三角剖分样条的小波、三角样条的准插值、四边形样条的准插值、二元样条的自适应节点移除和插入以及许多变量中的数据拟合。 在过去的 30 年里，样条函数已经成为一种成熟的计算工具，现在被科学家和工程师广泛使用。它们用于多种用途，包括近似复杂曲线和曲面、拟合数据、计算机辅助几何设计（CAGD）、计算机辅助制造（CAM）、微分方程求解、图像处理等。本研究的目的是开发新的样条工具，并创建解决一些特定应用问题的算法，特别是 CAGD、CAM、地质学、地球物理学和气象学中出现的问题。