Mathematical Sciences: Computational Aspects of MultivariateSplines

数学科学：多元样条的计算方面

• 批准号: 8701190
• 负责人: Charles Chui
• 金额: $ 6万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-15 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701190&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Computational; Aspects; MultivariateSplines

This research effort is designed to go hand in hand with the theoretical work being carried out under NSF GRANT DMS-8602337, entitled "Theory and Applications of Multivariate Splines". The aim of this research is twofold. We propose 1) to translate the theoretical results obtained under the earlier grant into practical computational algorithms. In particular, software will be developed for triangulation and tesselation, for storing and evaluating piecewise polynomial surfaces efficiently, for contouring, for surface-surface intersection, for interpolation (with and without shape control), for quasi-interpolation, for fitting surfaces on surfaces, for computer-aided design schemes, for least squares fitting of scatted data, for evaluation of simplex splines and for solving boundary-value problems. Secondly, we propose 2) to develop computational tools which can be used to support our theoretical work on the dimension, the construction of locally supported bases, and the poisedness of interpolation problems for multivariate splines.

这项研究工作旨在与 在NSF GRANT DMS-8602337下进行的理论工作， 《多元样条的理论与应用》 这项研究的目的有两个。 我们建议1）翻译 根据早期赠款获得的理论结果， 实用的计算算法 特别是，软件将 开发用于三角测量和镶嵌，用于存储和 有效地评估分段多项式曲面， 轮廓绘制，用于曲面-曲面相交，用于插值 (with没有形状控制），对于准插值，对于 曲面上的拟合曲面，用于计算机辅助设计方案， 用于散点数据的最小二乘拟合，用于评估 单纯形样条和解决边值问题。 其次，我们建议2）开发计算工具， 可以用来支持我们的理论工作的维度， 局部支持基地的建设，以及 多元样条插值问题。