过渡面生成算法及曲面光顺技术研究

【作者】 陈亚娟；

【导师】 刘旭敏；

【作者基本信息】 首都师范大学 ， 计算机应用技术， 2009， 硕士

【摘要】 过渡曲面生成是计算机辅助几何设计和计算机图形学的一项重要课题,主要研究在计算机图形系统的环境下对曲面的表示、设计、显示和分析。随着CAD/CAM技术的迅猛发展,曲面造型技术在产品设计中的应用日益广泛,与此同时过渡曲面的构造理论与方法是当前的研究热点之一。曲面光顺也是CAGD中的重要课题,在航空、宇航、汽车和船舶等设计制造业中有着重要的应用,因此受到普遍重视。但由于光顺处理的复杂性,直到现在,此问题还没有得到彻底的解决,对它的研究仍在进行中。本文首先对典型过渡曲面生成算法的原理、特点、应用范围、优缺点,如滚球法、偏微分方程法、能量法、基于脊线、裁剪线的过渡等进行了研究和分析,探讨了过渡面设计中存在的问题。重点研究了基于偏微分方程法构造过渡曲面,从传统静态PDE和动态PDE两个方面来系统研究了过渡面的构造。利用Pseudo-Navier法实现了构造C~1连续过渡面。针对传统静态偏微分方程构造过渡面存在的不足,提出基于动态偏微分方程构造C~1连续的过渡面,并用迭代有限差分法求解PDE的数值解,讨论了形状控制因子、密度、阻尼系数等物理参数的变化对曲面形状的影响,使过渡面构造具有更高的灵活性,大大提高了工业几何设计的交互性。此外,本文总结介绍了曲面光顺的原理,曲面光顺的检查准则,以及实现曲面光顺的几种比较常用的方法,如小波分析法、能量法。比较了各种方法的特点、优缺点及适用场合。将非均匀B样条小波分解用于曲面光顺,根据整体光顺度量确定NURBS曲面整体光顺时的光顺方向。根据曲面在节点对处的光顺性选择曲面上的坏点,通过局部小波分解实现曲面的局部光顺。该方法有效可行,能较好的实现对曲面的光顺处理。更多还原

【Abstract】 Blending surfaces generation is an extremely important part in Computer Aided Geometric Design and Computer Graphics.It’s primary research objects are surfaces expression,design,display and analyze under Computer Graphics system.With the rapid development of CAD/CAM,technology of surface modeling has been used in more and more products design.At the same time,the theory and methods of blending surfaces generation is one of attractive fields.Surface fairing is also one of important topics in CAGD research.Because of its significant application in CAD/CAM domains such as aviation,space navigation,autos and shipping,this issue become a research focus.The research on surface fairing has been continued to the present because of the complexity.In this paper,firstly,we research blending surfaces generation methods,analyzed and compared all these methods on the aspects of their theories,characteristics,scope,advantages and disadvantages.The research focus on generating blending surfaces base on partial differential equations.From traditional static PDE-based and dynamic PDE-based,analyzed their theory and methods.We generated blending surface with C’continuity using Pseudo-Navier method.To solve the shortage that traditional static PDE method has,proposes dynamic PDE to generate blending surfaces.It uses iterative finite difference algorithm to solve dynamic PDE, and investigates how different user handles affect dynamic deformations of surfaces,such as parametric variables,density and damping coefficient on.The modeling samples illustrate that the new dynamic PDE method brings more and better flexibility.It is very valuable for aided geometric design.Finally,we research the theory and rule of surface fairing and several classical faring methods,moreover analyze their advantage and disadvantage.In this paper,non-uniform B-spline multi-resolution wavelet decomposition was applied to the fairing of NURBS surface. The global faring direction was determined by global faring measure of two parametrical directions,and then the global fairing of surface was realized though global decomposition of surface.This algorithm is effective,and it will be one of research focuses in the future.更多还原