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球形表面上定义的新类样条纹，以开发针对球体量身定制的显式数值算法，并探索其应用。进行的其他研究涉及三角样条和三角剖分的细条，三角样条的准插入，对二次旋转的花键，自适应结的插入，自适应结和插入双变量光泽以及在许多变量中的拟合数据。 在过去的30年中，样条函数已成为一种完善的计算工具，现在被科学家和工程师广泛使用。 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.