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.

小行星9500643 这个项目的目标是开发新的类样条定义的领域 和类球体表面，开发显式的数值算法， 领域，并探讨其应用。其他研究涉及 三角样条和三角剖分样条的小波、准插值 三角样条，四边形样条，自适应节点删除和 二元样条的插入，以及许多变量的数据拟合。 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。它们用于各种 目的，包括逼近复杂的曲线和曲面，拟合数据， 计算机辅助几何设计（CAGD），计算机辅助制造（CAM）， 微分方程的解，图像处理等。本研究的目的是 开发新的样条工具，并创建用于解决某些特定应用的算法 问题，特别是CAGD、CAM、地质学、地球物理学中出现的问题， 气象学