基于几何体代数结构的Minkowski和计算方法建模与分析

发布时间：2018-02-28 20:51

本文关键词： Minkowski和碰撞干涉检测代数结构凸多面体类环状凹多面体　出处：《燕山大学》2016年博士论文　论文类型：学位论文

【摘要】：智能制造作为国内外研究的一大热点,日益成为未来制造业发展的重大趋势和核心内容。碰撞干涉检测的精度和效率是衡量智能制造水平的一个重要指标,是促进该行业发展的关键技术之一。Minkowski和作为计算几何的一个重要分支,是一种研究几何模型间精确相对位置关系的工具。然而,现有Minkowski和算法复杂度均较高,很大程度上限制了其应用范围。为了进一步提高Minkowski和构造效率,提升其应用价值,本文直接从几何模型的拓扑结构着手,构建其代数结构,并依此对Minkowski和的计算方法进行建模与分析。首先,依多面体及多边形拓扑结构,探究其代数表达,提出几何模型代数结构的概念,并分析其上各顶点极点区域的结构。其次,对两凸多面体Minkowski和计算方法进行建模与分析。该模型主要包括一种更加直接的Minkowski和边界平移小面集解法模型及一种快速精确的平移小面集上“洞”的修补方法模型。模型的有效性、稳定性及高效性从理论及实验两个角度进行了分析。再次,采用卷积的思想对涉及凹多面体及凹多边形Minkowski和计算方法进行建模与分析。其中,类环状凹多面体与凸多面体Minkowski和计算方法模型主要包括两步:首先,基于多面体的代数结构,得到类环状凹多面体与凸多面体的简化卷积;其次,采用平面扫描法对简化卷积内部面信息进行裁剪,将散乱空间平面片间的求交过程简化为平面有序线段间的求交过程,以提取精确的Minkowski和边界。两凹多边形Minkowski和计算方法模型包括如下三步:首先,基于多边形代数结构,计算其简化卷积;其次,将简化卷积分为内部折线类及边界折线类,并依多边形代数结构对边界折线类的邻接顺序进行判定;最后,相邻边界折线类依次求交,直接提取精确的Minkowski和边界。所构建模型的有效性、稳定性从理论及实验两个角度进行了分析。最后,为了验证基于多面体代数结构的Minkowski和计算方法模型的实用性,对模型在一类特殊机械部件虚拟装配过程中的应用进行研究。首先,结合Minkowski和计算方法模型的特点,对装配部件Minkowski和的构造性质进行分析;其次,鉴于装配部件Minkowski和特性,探究基于Minkowski和的机械虚拟装配检测算法;最后,通过理论分析及仿真实验对模型的实用性及算法的有效性、稳定性进行验证。
[Abstract]:As a hot topic in intelligent manufacturing research at home and abroad, has become the core content and the major development trends of the manufacturing industry in the future. Collision detection accuracy and efficiency is an important index to measure the level of intelligent manufacturing, promoting the development of the industry is one of the key technologies of.Minkowski and as an important branch of computational geometry, is a a geometric model of the precise relative position between the tools. However, the existing Minkowski and the complexity of the algorithm are high, largely limits the scope of its application. In order to further improve the efficiency of Minkowski and structure, improve its application value, this paper starts directly from the topology of geometric model, construct its algebraic structure, and so on Modeling and analysis of calculation method and Minkowski. Firstly, according to the polyhedron and polygon topology, explore the algebraic expression, the geometric model of algebraic structure The concept and the structure analysis of the vertices on the pole region. Secondly, the modeling and analysis of two convex polyhedral Minkowski and calculation method. This model includes a more direct translation set method Minkowski and boundary facet model and a fast and accurate translation facet set the "hole" model. The effective method for repairing the model, stability and efficiency are analyzed from two aspects of theory and experiment. Thirdly, the modeling and analysis of concave polyhedron and concave polygon Minkowski and computational methods of convolution thought. Among them, the ring concave polyhedron and a convex polyhedron and Minkowski model calculation method includes two steps: first, algebraic structure based on the simplified polyhedron, convolution ring concave polyhedron and a convex polyhedron; secondly, cut to simplify convolution internal face information by using the plane sweep method, the scattered The space between the film plane intersection is simplified to the ordered plane intersection of lines, in order to extract accurate Minkowski and boundary. The model two concave polygon Minkowski and calculation method comprises the following three steps: first, based on the calculation of the polygon algebraic structure, simplify convolution; secondly, will simplify the volume integral internal and boundary line line, and according to the sequence adjacent to boundary line polygon algebra class are determined; finally, the adjacent boundary line in class intersection, direct extraction of accurate Minkowski and boundary. The effectiveness of the proposed model, the stability is analyzed from two aspects of theory and experiment. Finally, in order to verify the practicability of the model Minkowski and the calculation method of polyhedral algebra structure based on the research on Application of the model in a special class of mechanical parts in virtual assembly process. First, the combination of Minkowski and calculation method of die The characteristics of the type of structure, properties of assembly parts Minkowski and analyzed; secondly, in view of the assembly parts of Minkowski and explore characteristics of virtual assembly of mechanical detection algorithm based on Minkowski and; finally, the effectiveness and practicability of the algorithm model of theoretical analysis and simulation experiment, the stability is verified.

【学位授予单位】：燕山大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TH16

【相似文献】