两空间三角形的退化关系研究

通过对两空间三角形关系的分类,讨论了几何退化对几何计算的稳健性的影响力。解决一个问题的第一步是描述这个问题,空间几何退化的完整表述是稳健几何计算算法的设计、改进以及测试的重要基础和保障。首次对空间三角形对的退化进行了深入的研究、全面的梳理。基于投影降维原理,抽取繁杂的空间两三角形关系的规律,分离出完整的空间三角形对的退化样本模型。基本策略是建立计算坐标系,通过投影降维,将空间三角形对的位置关系变成一个固定,只有一个变化的平面位置关系。以相离、接触、相交、内含的线索改变另一三角形的位置和大小,分类出空间三角形对的位置关系,检索出两者的所有退化状态。该方法可以推广到其他三维几何间的退化状态分类和几何计算算法的稳健性设计中。     

视锥体裁剪几何算法研究

从几何角度出发,以投影理论为指导,设计了一种降维投影的视锥体裁剪几何算法。基本思想是基于视锥体构建计算坐标系,在计算坐标系下,向两个投影平面做正投影。空间中被裁剪线段与视锥体的位置关系被简化为投影平面内线段与等腰梯形的关系。这种几何化的降维方法有利于解决空间几何奇异问题。构建了空间视锥体裁剪中线段与视锥体的各种位置关系的测试样本,特别是78种处于几何奇异状态的位置关系,用于综合评估算法的速度和稳定性。用C语言在VC++平台上分别实现了投影降维的视锥体裁剪几何算法、经典的Liang-Barsky算法和与6个面分别求交的一般算法。在定性分析基础上,利用测试样本对3种算法做了计算速度与稳定性方面的测试对比。     

面向对象的铁路超限货物轮廓计算方法

准确计算铁路超限货物轮廓有力保障货物运输安全、提高运输效率,是日常运输管理中一项必不可少的基础性工作。从微观角度入手,结合面向对象思想,提出以三维实体对象描述、投影和综合为核心的超限货物轮廓计算方法。将超限货物视为独立对象,结合对象特征构造以基本体素分解和几何运算相结合的实体对象描述方法;投影对象后以纵横交替扫描方法对投影进行预处理;通过定义交点序列、内外边等概念,设计了以交点确定和边属性判断为主体的投影综合算法。面向对象的超限货物轮廓计算方法在理论上有保证,拟合实际,有效避免遗漏隐藏超限点,准确反映货物的空间几何形态。算例证实了方法的有效性。     

基于对象的直线上区段综合限界计算方法

从微观角度入手,结合面向对象思想,提出以三维实体对象描述、投影和综合为核心的直线上区段综合限界计算方法。将桥梁、隧道、其他建筑物或设备等控制物视为独立对象,结合对象特征构造以基本体素分解与几何运算相结合的实体对象描述方法;沿线路纵向投影对象,并以纵横交替扫描对投影进行预处理,刻画对象对综合限界的控制形态;通过定义交点序列、内外边等概念,设计了以交点确定和边属性判断为主体的投影对象综合算法。面向对象区段综合限界计算方法在理论上与实际拟合准确,有效地避免了遗漏隐藏控制点,准确反映控制物的空间几何形态。算例证实了方法的有效性。     

三维几何约束求解的自由度归约算法

三维几何约束求解在装配设计、几何造型和动力学分析等领域有着广泛的应用．在分析基本几何元素间的约束关系对刚体自由度状态影响的基础上,提出刚体自由度的归约算法,以求得满足约束后刚体的自由度状态空间;以刚体自由度状态空间分析为基础,实现对合理约束的推理求解和约束一致性维护,该算法解决了三维几何约束求解中自由度计算问题,同时避免了一些推理求解算法中出现的“组合爆炸”问题．     

V-型皱褶结构的设计及优化

对V-型皱褶结构的设计及优化进行研究,给出平面构型与空间构型的几何参数转换公式。编写了快速设计和成型模拟的C程序及参数化建模和有限元分析前、后处理的Python程序。使用C+OpenGL+GLUT实现V-型皱褶结构的成型过程,改变C程序中的几何参数可以实现V-型皱褶结构的快速设计和成型过程。使用Python+Abaqus+modeFRONTIER对V-型皱褶结构的几何参数进行优化,得到了满足约束条件的优化结果。     

协作机器人的构型分析研究

针对协作机器人的构型分析研究,得出了偏置是影响机器人构型的一个重要因素。首先,对现有典型协作机器人的构型进行分析,通过构型间的内在联系与演化过程得到构型之间的差异。然后利用构型之间的差异引出了偏置的定义,并通过偏置对关节运动范围的影响将其分为S型偏置和Y型偏置。最后以全局性能指标、工作空间体积指标和灵活工作空间指标为性能评价标准,对iiwa、Sawyer、Yumi三种典型构型的性能进行了仿真。通过对比分析可知,偏置的存在使构型的全局性能和工作空间体积性能降低,但对灵活工作空间性能有提高作用。结果表明偏置是影响机器人性能的重要因素,该分析研究为协作机器人的构型设计提供了理论依据。     

低轨四星时差定位技术研究

文章重点分析影响低轨四星时差定位系统精度的主要因素;首先,从四星时差定位的基本原理出发,对四星时差定位的模型和几何精度因子进行了详细的推导,并通过仿真分析了四星构型、时差测量精度、卫星位置误差、基线长度、星座投影面积等对四星时差定位系统精度的影响;通过比较可知,在相同参数条件下,采用Y形构形,减小时差测量误差、提高卫星定位精度、增加基线长度,增大星座投影面积均等均能够提高该系统的定位精度;在低轨四星定位系统应用场景中,四星构型、卫星绝对位置测量精度、基线长度以及星座投影面积对四星时差定位系统精度影响较大,时差测量精度和卫星相对位置测量精度对四星时差定位系统精度影响较小;而在实际任务中应权衡各因素的效费比,来保证定位精度。     

基于投影特征识别的斜截切二次曲面重建算法

平面与二次曲面的截切组合是机械零件常用的设计手段.在分析斜截切二次曲面在三视图中的投影特性的基础上,提出识别和重建这类曲面的算法.首先根据曲面的投影特性在三视图中检索斜截切曲面的投影痕迹;然后以其作为引导,初步判定曲面类型,深度优先搜索进一步识别斜截切二次曲面;再根据投影边的二维信息计算未截切曲面的几何参数,并通过未截切曲面与截平面求交获取截切曲线;最后构造斜截切曲面的拓扑结构,生成三维曲面.该算法可以识别和重建空间任意位置的斜截切二次曲面,拓展了重建算法的形体覆盖域.文中算法目前已运用到形体重建原型系统中,实验结果证明了其有效性.     

通用几何约束系统统一建模研究

在几何约束和几何实体的基本约束和欧拉参数表达的基础上,研究了通用几何约束系统的统一建模问题。通过对三维几何实体姿态约束和位置约束解耦性的分析,抽象出球实体、盒体和球盒体三种基本几何实体表达空间几何实体,并以基本约束的组合表达几何约束,形成几何约束模型特有的层次结构;并以有向图管理几何约束系统,可以清晰地反映姿态约束和位置约束的解耦性,实现约束系统的细粒度分解,得到规模更小的求解序列,实现高效求解。方法实现于原型系统WhutVAS中。     

Simple methods for computing the least squares line in three dimensions

Simple non-iterative linear procedures for finding the least squares line in three dimensions are presented. The more rigorous minimizes the sum of the squared perpendicular distances between the data points and the fitted line. It involves the solution to an eigensystem and is an example of the well known method from classical mechanics of finding the principal axes and moments of inertia of an anisotropic object. In addition to determining the best fitted line to the data according to the least squares criterion, the eigensystem solution produces the best fitted plane. This is useful in cases where the data display curvature, for the best fitted plane is the plane of curvature. The less rigorous solution is an approximation that minimizes the sum of squared lengths of the bases of isosceles triangles. The arms of the triangles are the lines from the origin, which is placed at the centroid of the data, to the data point and the line of the same length from the origin along the fitted line. The approximate procedure is three to four times faster than the rigorous one and gives virtually identical results as long as the data do not deviate extensively from linearity.     

An application of fuzzy sets to the classification of geometric figures and chromosome images

The concept of a fuzzy set is applied to the classification of geometric figures and chromosome images through the use of shape-oriented angular and dimensional proximity measures. Various properties of approximate isosceles, approximate equilateral, approximate right, and approximate isosceles right triangles are investigated. A method for classifying a triangle as an “approximate right triangle,” “approximate isosceles triangle,” “approximate isosceles right triangle,” “approximate equilateral triangle,” or “ordinary triangle” is presented. A method used to classify a quadrangle as “approximate square,” “approximate rectangle,” “approximate rhombus,” “approximate parallelogram,” “approximate trapezoid,” or “ordinary quadrangle” is also presented. The measures of proximity employed for this purpose have an intuitive interpretation. The stochastic syntactic analysis technique and the “rubber-mask” technique have, in the past, been applied to the classification of chromosome images. In this paper, chromosome images are classified through the use of angular and dimensional proximity measures. The uttermost dimensional proximity and the least dimensional dissimilarity of chromosome images are defined and investigated. The results obtained in this paper may contribute to processing a picture from the polygonal approximation stage to the final classification stage in order to recognize a picture.     

Automated modular fixture planning: Geometric analysis

Attendant Processes such as fixture and die design are often a necessary but time-consuming and expensive component of a production cycle. Coupling such attendant processes to product design via feature-based CAD will lead to more responsive and affordable product design and redesign. In the context of on-going research in automating fixture configuration design, this paper presents a fundamental study of automated fixture planning with a focus on geometric analysis. The initial conditions for modular fixture assembly are established together with geometric relationships between fixture components and the workpiece to be analyzed. Of particular focus is the design of alternative locating points and components, together with examples of 3-D fixture designs.     

Automated modular fixture planning: Accuracy, clamping, and accessibility analyses

Attendant Processes such as fixture and die design are often a necessary but time-consuming and expensive component of a production cycle. Coupling such attendant processes to product design via feature-based CAD will lead to more responsive and affordable product design and redesign. In the context of on-going research in automating fixture configuration design, this paper presents a fundamental study of automated fixture planning with a focus on geometric analysis. The initial conditions for modular fixture assembly are established together with geometric relationships between fixture components and the workpiece to be analyzed. Of particular focus is the design of alternative locating points and components, together with examples of 3-D fixture designs.     

产品三维数据模型轻量化表示实现

提出一种能快速浏览的产品三维模型轻量化文件格式,文件中包含零件显示信息和几何信息·显示信息记录面的三角化模型和边的多边形模型,以加快模型的浏览速度,且按装配、零件、面、线、点层次关系进行组织;几何数据附加在显示信息上,提供几何数据的精确查询·文件大小通过数据压缩大幅度地减小,便于在网上发布·以此为基础开发了三维产品浏览系统和用于生成轻量化文件的接口程序·     

基于拟合投影的车身老鼠洞检查方法研究

汽车车身在设计制造过程中由钣金件装配焊接形成的老鼠洞,在某种程度上影响了整车的安全 性能以及空间结构。为解决老鼠洞尺寸检查步骤繁琐、检查效率低等问题,提出了一种基于拟合投影的车身老 鼠洞检查方法。首先,通过创建老鼠洞边缘轮廓截面对轮廓曲线进行直线拟合并投影至截面;其次,建立投影 轮廓范围内的等距空间网格划分机制,借鉴最小二乘法的“残差平方和最小”原理筛选网格节点;最后,运用 最佳逼近定义提取老鼠洞中心轨迹点及最大内切圆半径。利用 CATIA 软件为开发平台并结合 CAA 框架结构, 实现老鼠洞检查功能,实例分析表明,检查结果具有良好的准确性,功能运行高效、自适应性强,有效缩短了 产品研发周期。     

Geometric computation based assembly sequencing and evaluating in terms of assembly angle, direction, reorientation, and stability

Assembly sequence matters much to the performance in assembly production. Focusing on the spatial assembly sequencing and evaluating, a set of geometric computation methods and algorithms are studied systematically. A method entitled 3D geometric constraint analysis (3D-GCA) is proposed based on the planar GCA method combined with the techniques of oriental bounding boxes and the separation axis theorem. With 3D-GCA, the assembly precedence relations and the spatial geometric feasible assembly sequences can be reasoned out correctly and automatically. Furthermore, four evaluation criteria, viz. assembly angle, assembly direction, reorientation, and stability, and related algorithms are defined for evaluating the assembly’s complexity. For selecting the optimal sequence, a comprehensive evaluation function is constructed by integrating the four criteria and the weights are quantitatively allocated referring to fuzzy set theory, clustering analysis, and entropy theory. In addition, a software prototype system is developed and two case assemblies are studied. The analysis results and findings demonstrate that the proposed approaches and algorithms can provide significant assistance in the spatial assembly sequencing and the optimal sequence selection.     

图像中任意三角形检测方法

提出了一种基于加窗Hough变化的任意三角形检测方法。选择适当大小窗口在图像中滑动,以窗口中心为坐标原点对窗口内图像作Hough变换,在图像的Hough域中检测直线段,从检测出的直线段中找出满足三角形条件的线段组合,然后定位这些线段构成的三角形。实验表明该算法能够有效检测出任意三角形,改变线段的长度条件或角度条件还可以检测直角三角形、等腰三角形、等边三角形等特殊三角形。该算法还可以实现在图像中检索三角形目标的功能。     

基于自由度分析的三维几何约束推理求解

三维几何约束求解对于装配设计、装配工艺规划和并行工程等多个领域的研究具有重要意义。以自由度分析为基础，对冗余约束和约束冲突的情况进行判断。采用几何推理的方法，直接从零件上的点、线、面、圆柱面、球面等基本几何元素出发，对这些基本几何元素之间的位置关系进行分析，求解三维几何约束。避免了数值解法中对初始值的依赖和迭代过程的不稳定，提高了三维几何约束求解的速度和稳定性。