具有分片有理等距面的自由曲面造型方法

项目名称： 具有分片有理等距面的自由曲面造型方法

项目编号： No.61202275

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： 伯彭波

作者单位： 哈尔滨工业大学

项目金额： 25万元

中文摘要： 带几何约束的自由曲面造型问题有着重要的应用背景。本项目研究具有精确分片有理等距面的自由曲面造型问题。我们使用Dupin四次圆纹曲面片拼接构成 G1连续的自由曲面，我们称这种曲面为圆纹样条曲面。Dupin四次圆纹曲面片的等距面具有理二次形式，与CAD领域的行业标准NURBS形式兼容；圆纹样条曲面由圆弧构成，曲面上的曲率线是圆弧样条曲线。以前的方法无法构造具有复杂形状的圆纹样条曲面。我们提出整体优化的方法：通过允许顶点位置移动，增加曲面表达的自由度；把曲面支撑网格的所有顶点和顶点上的标架作为优化的变量，对曲面的整体形状进行控制，构造出形状复杂的圆纹样条曲面。在该整体优化的框架下，我们针对高质量的圆纹样条曲面的拟合和圆纹样条曲面的交互设计和修改这两方面，研究其中的一些关键问题，为圆纹样条曲面造型系统提供技术和理论支持。

中文关键词： 几何造型；圆纹曲面；可展曲面；曲面拟合；等距曲面

英文摘要： Freeform surface modeling with some geometric constraints is an important problem in a lot of applications. We study the problem of freeform surface modeling using surface patches from Dupin cyclide which is called the cyclide spline surface. By relaxing the vertex positions in the supporting mesh of a cyclide spline surface, we employ a global optimization method for computing a cyclide spline surface. In contrast to all existing approaches to this problem which are based on a strategy of vertex frame propagation, our approach treats all vertex positions and all surface frames attached to vertices as variables in a minimization problem. Using this method, we have a global control on the surface shape as well as the fairness of a surface. The two problems we consider are cyclide spline surface fitting and interactive shape design and modification with cyclide spline surfaces. We study some techniques for obtaining a cyclide spline surface fitting to a reference surface with high quality. We study the approximation degree of a cyclide spline surface. We employ a strategy of normal interpolation as an additional constraint to improve the approximation accuracy of a cyclide spline surface. We study the rules of local refinement,the handling of T-joints and umbilical points. We also propose methods to improve s

英文关键词： surface modeling；Dupin cyclide；developable surface；surface fitting；offset surface