【作者】 王海霞；

【导师】 孙玉文；

【作者基本信息】 大连理工大学 ， 机械电子工程， 2005， 硕士

【摘要】 随着数字化测量技术的迅速发展,反求工程(RE)已与快速成型(RP)、多轴数控加工(NC)等先进制造技术一起成为快速产品开发(RPD)的支撑技术。面对海量的无序数据,重构其流形网格模型是最为有效的手段之一,但该种表达还不能直接用于精密加工,为此仍需要建立精确的解析表达。当前,NURBS等流行建模技术均建立在矩形拓扑上,四边形区域划分是进行流形网格上组合NURBS曲面重建的前提条件,也是其中的难点问题。 首先,针对点云数据网格不具备显式拓扑且存在冗余的特点,定义了网格的边界、星型邻域、半星型邻域、平均平面、曲率及形态因子等基本概念,提出了以综合考虑顶点曲率和到其平均平面距离为简化原则的网格简化算法,给出了保证算法实施的合理数据结构以及基于短边删除长边对分的网格优化原则。由此,在适度简化的流形网格上提出了进行四边形区域划分的映射法与匹配法。鉴于在复杂的空间网格上进行四边形区域划分需要复杂的几何操作和数学基础,映射法将空间网格模型调和映射到平面上简单拓扑区域,使得对复杂模型的操作如同对平面操作一样。为此,通过定义矩形及圆形等简单映射区域,加之以合理的区域分割模板,并采用逆向映射、短程线、追踪多边形内部三角形的算法,实现了复杂流形网格的快速四边形区域划分。同时,针对有些简化模型三角形品质较好且数量较少的特点,基于两个相邻三角形可合并得到一个四边形的简单理念,在与之相关的无向图理论指导下,建立了流形网格的匹配模型。此外,针对提出的两种算法,进行了时间和空间复杂度分析以及实例验证,表明了方法的可行性和有效性。更多还原

【Abstract】 With the development of the digital measure technology, RE( Reverse Engineering )、 RP(Rapid Prototyping) and NC(numerical control) together have become the key technologies of RPD(Rapid Product Development). Reconstructing manifold mesh model is one of valid methods for massive disheveled data. however, this method cannot still be used in precision machining directly. Therefore exact parsing method should be founded. At the present time, popular modeling technologies like NURBS are based on rectangle topology, quadrilateral region partition is a precondition of NURBS surface reconstruction based on manifold mesh, and it is also a difficulty.Firstly, for the point clouds without obvious topology and with redundancy, we defined some basal concepts including the mesh boundary, the star adjacent field, the semi-star adjacent field, the average plane, the curvature, the shape factor and so on. And we present the mesh simplification method considering the vertex curvature and the distance to the average plane and put forward the rule of optimized mesh which guarantees the reasonable data structure for the arithmetic and is based on short edge deleted and the long edge bisected. Thereout, the mapping method and matching method are presented, which are for the quadrilateral partition of the moderate manifold mesh. Due to the complicated geometrical operation and the mathematic groundwork are needed for the quadrilateral partition on the complicated spatial mesh, the mapping method makes the spatial mesh model mapped to the simple topology field on the plane by harmonic mapping, which makes us manage the complicated model like managing the plane. Therefore, the rapid quadrilateral partition of the complicated manifold mesh is implemented by the definition of the simple mapping field for rectangle and circle, the reasonable region intersected template, the reverse mapping, shortest path boundary, and the interior triangular rapid tracing arithmetic. At the same time, in view of good triangular quality and lesser amounts on some simplification models, and based on thesimple idea of two neighboring triangles combined one quadrangle, the matching model of the manifold mesh is founded, which is guided by the related theory of the undirected graph. Besides, the complexity of time and space is analyzed, and some examples areindicated feasibility and validity of the method.更多还原