Mathematical Sciences: Spline Tools and Applications

该项目的目标是开发在球体和类球体表面上定义的新类样条曲线，开发适合球体的显式数值算法，并探索其应用。其他需要进行的研究包括三角样条和三角样条的小波、三角样条的准插值、四边形上的样条、二元样条的自适应结去除和插入，以及多变量数据的拟合。在过去的30年里，样条函数已经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。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，并创建算法来解决一些特定的应用问题，特别是在CAGD， CAM，地质学，地球物理学和气象学中出现的问题。

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.