高精度几何近似造型的关键技术及其应用研究

项目名称： 高精度几何近似造型的关键技术及其应用研究

项目编号： No.61202201

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 计算机科学学科

项目作者： 胡倩倩

作者单位： 浙江工商大学

项目金额： 23万元

中文摘要： 当前CAD/CAM有三大矛盾亟待解决: 现代制造业对设计精度的要求日益提高, 与外形系统对多项式数模沿用不衰的矛盾; 现代设计对外形算法的高精度追求, 与现有数模工具对几何近似功能不足的矛盾; 以及等距曲线有理高精度近似引发的,近似曲线次数过高与设计系统承受力间的矛盾。为此，申请人将对高精度几何近似造型的关键技术、基础理论及其应用作深入研究: 以新颖的约束对偶基为工具，讨论圆锥曲线曲面的高精度多项式近似表示，保持几何特征，建立高效算法；设计一种全新度量来近似Hausdorff距离，探索保几何连续的有理曲线高精度多项式近似算法，并拓展到有理三角乃至NURBS曲面；创造性地引入Chebyshev有理近似方法，实现等距曲线曲面的高精度有理近似。与此同时,探索其在CAD、精密机械、数控加工和铁路工程测量等领域的应用研究。本项目将为几何造型设计提供强大理论支撑与核心算法,具有重要理论意义和应用价值。

中文关键词： 计算机辅助几何设计；近似；曲线曲面；多项式；重新参数化

英文摘要： WitIn current CAD/CAM systems, there are three contradictions needed to be solved urgently. That is, the contradiction between the increasing requirements of the design accuracy in modern manufacturing and polynomial being a main tool for shape design; the contradiction between the pursuit of high accuracy of algorithms for shape design and the shortage of approximation function for modern math modeling tools; the contradiction between the high degree of approximation rational curves for offset curves while improving the accuracy of the algorithm and the tolerance ability of design system. Therefore, we will do deep research on the key techniques, basic theory of high-accuracy geometric approximation modeling and its applications. First, based on the new tool of constrained dual Bernstein basis, to discuss polynomial approximation with high accuracy of conic sections, preserve geometric characteristics and construct efficient algorithms; Next, to design a brand-new metric to approximate Hausdorff distance, explore polynomial approximation with high accuracy of rational curves with geometric continuity and expand to rational triangular surfaces and NURBS surfaces; Third, creatively introducing Chebyshev rational approximation method, to achieve high-accuracy rational approximation of offset curves and surfaces. M

英文关键词： CAGD；approximation；curves and surfaces；polynomial；reparameterization