Theory And Application of Splines

在过去的40年里，样条函数（以其最简单的形式，分段多项式）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，包括近似曲线和曲面，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。本研究的目的是继续发展样条的理论和应用，并创建和测试算法来解决一些具体的应用问题，特别是在inCAGD， CAM，地质学，地球物理学和气象学中出现的问题。

In the past 40 years, spline functions (in their simplest form,piecewise polynomials) have become a well-establishedcomputational tool, and are now widely used by scientistsand engineers. They are used for a variety of purposes,including approximating 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 continue to developthe theory and applications of splines,and to create and test algorithms for solving some specificapplications problems, especially problems arising inCAGD, CAM, geology, geophysics, and meteorology.