Theoretically-based algorithms for robustly tracking intersection curves of deforming surfaces

This paper applies singularity theory of mappings of surfaces to 3-space and the generic transitions occurring in their deformations to develop algorithms for continuously and robustly tracking the intersection curves of two deforming parametric spline surfaces, when the deformation is represented as a family of generalized offset surfaces. The set of intersection curves of two deforming surfaces over all time is formulated as an implicit 2-manifold I in an augmented (by time domain) parametric space R⁵. Hyperplanes corresponding to some fixed time instants may touchI at some isolated transition points, which delineate transition events, i.e. the topological changes to the intersection curves. These transition points are the 0-dimensional solution to a rational system of five constraints in five variables, and can be computed efficiently and robustly with a rational constraint solver using subdivision and hyper-tangent bounding cones. The actual transition events are computed by contouring the local osculating paraboloids. Away from any transition points, the intersection curves do not change topology and evolve according to a simple evolution vector field that is constructed in the Euclidean space in which the surfaces are embedded.     

采用"结式法"的圆环面和球面求交算法

提出了一种不需跟踪的求交算法.通过坐标变换使圆环中心轴与球心共处在XOZ平面内,然后讨论该平面内圆环面小圆和球面截圆的位置关系,给出了圆环面和球面不相交、交线为一个或两个圆、有孤立交点的几何条件以及交线的区间.最后,将圆环面和球面求交转化为平行于XOY面的平面内的两圆交点的问题并利用"结式法"解得交点.     

A novel methodology to solve the CQLF problem for a finite set of stable second-order systems

A new methodology to provide conclusive information about the existence/non-existence of a common quadratic Lyapunov function (CQLF) for a finite set of stable second-order systems is presented. Despite the high complexity of the CQLF problem, even in the case of N second-order systems, the results presented in this paper have a very simple and intuitive theoretical support, including topics such as classical intersection of convex sets and properties of convex linear combinations. Illustrative examples to show the performance of the proposed methodology are provided.     

用前方交会进行水平位移监测的一种解算方法

根据前方交会公式导出其坐标变化量与交会角变化量之间的线性关系式,使位移量的解算变得直接、简单,在理论上便于分析。     

空间多管相贯计算机放样的新算法

以两管相贯相贯线图解法求解为基础，建立了空间多管相贯的数学模型．利用坐标变换、母线比较等方法，形成了求解空间多管相贯相贯线展开方程的新算法．该算法避免了传统算法中联立空间柱面方程求解交线和交点，以及选取由多切管所形成的各相贯线段等复杂运算．基于该算法利用AutoCAD VBA鳊程技术。实现了多管相贯相贯线的计算机自动绘图．     

远引平面交叉口中央分向岛开口位置探讨

在城市交通系统中,解决好交叉口的左转交通具有举足轻重的作用。近年来许多地方和政府考虑在中央分隔带上开口采用迂线回转来代替交叉口直接左转以减少交叉口的交通冲突。在设置中央分隔带回转路口时,其位置对回转车流的安全及其运行效率有着直接的影响。作者结合远引平面交叉口的交通特性,道路通行能力与左转车辆延误,建立了确定中央分向岛开口位置的模型。计算表明其对远引平面交叉口的运营及安全设计具有一定的指导意义。     

大屋盖网架安装检测方法及精度分析

为确保深圳市民中心大屋盖网架的安装质量,发挥结构的受力作用,运用前方交会法来确定球心节点的几何中心.对不同测量图形、不同交会点的测量精度进行分析,得出其交会角为108°00′28″时,其测量度最高.在考虑图形强度的前提下,对该工程542个节点均进行了观测,其点位误差绝大多数在1cm以下,最大为1.8cm,测量精度和安装工程质量均达到了预期目的.     

空间多管相贯计算机放样的新算法

以两管相贯相贯线图解法求解为基础,建立了空间多管相贯的数学模型.利用坐标变换、母线比较等方法,形成了求解空间多管相贯相贯线展开方程的新算法.该算法避免了传统算法中联立空间柱面方程求解交线和交点,以及选取由多切管所形成的各相贯线段等复杂运算.基于该算法利用AutoCAD VBA编程技术,实现了多管相贯相贯线的计算机自动绘图.     

应用3DSMAX制作《机械制图》多媒体课件动画素材

《机械制图》课程教学的难点是培养学生的空间想象和构思能力.掌握动画的制作方法,选择合适的动画素材制作多媒体课件,可以提高课件的主动性,使其更加新颖、形象、有吸引力.以相贯线为例说明了多媒体课件动画素材的制作方法.     

Analysis of opposing left-turn conflicts based on traffic conflict technology

The relationship between the opposing left-turn conflict and the traffic participants was analyzed in this study. Based on the traffic conflict technology, the image data were collected in a real traffic situation. The relationship was investigated under two different conditions. The number of opposing left-turn conflicts was positively correlated with the number of left-turn vehicles while the ratio of left-turn vehicles to opposing vehicles was less than 1, and showed a positive correlation with the number of opposing-through vehicles when the ratio of left-turn vehicles to opposing vehicles was more than 1. In other words, the opposing left-turn risk was positively correlated with the number of the minor traffic participants, which had a negative effect on the whole traffic system operation.