【作者】 赵建民；

【导师】 王敏杰；

【作者基本信息】 大连理工大学 ， 机械制造及其自动化， 2008， 硕士

【摘要】 细分方法是一种新的离散造型技术,通过定义控制网格和细分规则来表示造型曲面。它不仅具备B样条曲面的局部支承性、仿射不变性等良好性质,而且具有参数曲面所没有的任意拓扑性等特点,正逐渐成为几何造型的有力工具。曲面的细分算法采用逐次细分,从离散到离散,最终得到所需要的曲面,避免了以往样条曲面从离散到连续,再从连续到离散的过程。在诸多细分模式中,Catmull-Clark细分曲面是B样条曲面的推广,这样的细分曲面具有易于与NURBS曲面融合的特点,能更好的与数控加工相结合。细分曲面的数控加工,是细分曲面应用于工程生产的基础。而精确的刀具轨迹规划算法是数控加工的灵魂。本文就是以Catmull-Clark细分曲面为切入点,提出了一种基于Catmull-Clark模式的细分曲面NC刀具轨迹生成算法,旨在将细分曲面应用于生产加工,为细分曲面在工业领域的发展打下基础。主要工作如下:1.提出了一种基于Catmull-Clark模式的细分曲面NC刀具轨迹生成算法:首先计算Catmull-Clark细分曲面初始控制网格顶点的极限点和法矢量,然后由极限点出发,按给定精度、以球头刀半径长度沿其法矢量方向向外等距,获得等距曲面,最后在等距曲面上生成NC刀具轨迹。该算法可以将细分曲面应用于CAD/CAM系统,适用于任意拓扑的四边形网格模型。2.应用开发工具Visual C++6.0和OpenGL,对Catmull-Clark模式的细分曲面进行了实现;采用四叉树结构和翼边结构相结合的方法,对Catmull-Clark细分曲面等距面进行了实现;采用截平面法,生成了Catmull-Clark细分曲面NC刀具轨迹。3.等距曲面误差作为细分曲面等距的一个基本问题,本文对其进行了分析,提出了两种控制方法:第一种方法以相邻点法矢夹角为基准,控制等距面的精度。第二种以控制网格点与非控制网格点的等距距离差为基准,获得具有给定精度的等距面。更多还原

【Abstract】 Subdivision scheme is a new discrete modeling technology which describes the modeling surface through controlling mesh and subdivision rules. It has many advantages such as localness and affine-invariance of traditional B-spline surface and adaptability to arbitrary topology which parameter surfaces do not have, and is becoming one of the most powerful geometric modeling tools. Subdivision scheme for surface is a gradual subdivision which obtains final surface by discrete-to-discrete method, and the disadvantage of conventional method from discrete to continuous and then from continuous to discrete is avoided. The Catmull-Clark subdivision scheme is generalization of B-spline surfaces, which can be blent with NURBS surfaces easily and be unified with the NC processing commendably. Numerical Control of subdivision surface is the base of subdivision surface applied to industry manufacture. And an accurate programming method of Numerical Control tool path is a soul of Numerical Control.The paper focuses on the Catmull-Clark subdivision surfaces. Based on the Catmull-Clark subdivision scheme , a new approach to generate NC tool path for subdivision surfaces is presented. The aim is to apply subdivision surfaces to product manufacture, and to make preparations for development of subdivision surfaces in industry field. The main contents are as follows:1. Based on the Catmull-Clark subdivision scheme, a new approach to generate NC tool path for subdivision surfaces is presented: First calculate the limit points and the normal vectors at these points from the initial control mesh . Second generate offset surface with controlling accuracy by using the limit points, the normal vectors and the radius of the ball end milling cutter. Next generate NC cutting tool path from the offset subdivision surface. This method applies subdivision surfaces to CAD/ CAM system , and adapts to quadrilateral models of arbitrary topology.2. Catmull-Clark subdivision scheme is implemented by developing tool Visual C++ 6.0 and OpenGL; Offset surface of Catmull-Clark subdivision surface is implemented by combinative method of Quadtree structure and Winged Edge structure; NC tool path of Catmull-Clark subdivision surface is generated by section plane method.3. Offset error, which is a basis problem in subdivision suifaces, is also analyzed in the paper. And two methods about analysis and control are presented. The first one is to control precision of offset surfaces by criterion based on angle between normal vectors of two neighbor vertexes. The second one is to obtain offset surfaces whose precision has been given by criterion based on distance between control mesh vertexes and non-control mesh vertexes.更多还原