过网状测地线的样条曲面优化设计

项目名称： 过网状测地线的样条曲面优化设计

项目编号： No.61462036

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 计算机科学学科

项目作者： 杨火根

作者单位： 江西理工大学

项目金额： 45万元

中文摘要： 过测地线的曲面重构是计算机辅助设计领域中一项具有广泛应用性的研究课题。本项目以CAD中常用样条为工具，将局部格式与曲面能量优化技术相结合，研究过网状测地线的有理和非有理Bézier曲面、B样条曲面以及三角B-B曲面的重构问题，内容包括：（1）过非相交等参测地线的样条曲面优化设计；（2）测地三角形和四边形的几何判别及其几何优化构造；（3）过测地三角形和四边形的样条曲面优化设计；（4）过测地三角网和四边形网的组合样条曲面优化设计。 与以往基于传统Hermite方法或Coons超限插值法的过测地线的曲面重构相比，本项目考虑的测地线表示具有多样性，分布具有任意性；插值曲面次数较低，具有几何操作性和整体最优性；算法的可操作性强且与CAD有很好的兼容性等。因此该算法很容易被纳入到CAD软件系统，这对提高CAD系统的造型能力具有重要的现实意义。

中文关键词： 计算机辅助几何设计；优化设计；样条曲面；测地线网；局部格式

英文摘要： Surface reconstruction via geodesic interpolation is a wide application of research topic in the field of CAD. In this project, based on local scheme and surface energy optimization techniques, we take the splines which are used commonly in CAD as a tool and study the problem of the spline surface reconstruction through the network of geodesic. The interpolating surfaces are NURBS surface or triangular B-B surface. The research content includes: (1) Optimization design of spline surfaces through the non-intersecting isoparametric geodesics; (2) Geometric discrimination and geometric optimization construction of the geodesic triangulation and quadrilateral; (3) Optimization design of spline surface through the geodesic triangulation and quadrilateral; (4) Optimization design of composite spline surface through the network of geodesic triangulation and quadrilateral. Compared with the traditional Hermite interpolation and Coons interpolation scheme, the advantages of the method proposed in this project are: The representations of geodesic are of diversity, and the distribution of geodesics is of arbitrariness; The interpolating surfaces are of low degree, geometric operability and global optimality; The algorithm is of strong operability and good compatibility with the CAD systems. So the algorithm incorporated into the CAD systems is of great practical significance to improve its modeling ability.

英文关键词： CAGD;optimization design;spline surface;geodesic network;local scheme