An Approach to Representing Heterogeneous Non-Uniform Rational B-Spline Objects

The representation method of heterogeneous material information is one of the key technologies of heterogeneous object modeling, but almost all the existing methods cannot represent non-uniform rational B-spline （NURBS） entity. According to the characteristics of NURBS, a novel data structure, named NURBS material data structure, is proposed, in which the geometrical coordinates, weights and material coordinates of NURBS heterogene- ous objects can be represented simultaneously. Based on this data structure, both direct representation method and inverse construction method of heterogeneous NURBS objects are introduced. In the direct representation method, three forms of NURBS heterogeneous objects are introduced by giving the geometry and material information of con- trol points, among which the homogeneous coordinates form is employed for its brevity and easy programming. In the inverse construction method, continuous heterogeneous curves and surfaces can he obtained by interpolating discrete points and curves with specified material information. Some examples are given to show the effectiveness of the pro- posed methods.

Extraction of Feature Points for Non-Uniform Rational B-Splines(NURBS)-Based Modeling of Human Legs

Methods of digital human modeling have been developed and utilized to reflect human shape features.However,most of published works focused on dynamic visualization or fashion design,instead of high-accuracy modeling,which was strongly demanded by medical or rehabilitation scenarios.Prior to a high-accuracy modeling of human legs based on non-uniform rational B-splines(NURBS),the method of extracting the required quasi-grid network of feature points for human legs is presented in this work.Given the 3 D scanned human body,the leg is firstly segmented and put in standardized position.Then re-sampling of the leg is conducted via a set of equidistant cross sections.Through analysis of leg circumferences and circumferential curvature,the characteristic sections of the leg as well as the characteristic points on the sections are then identified according to the human anatomy and shape features.The obtained collection can be arranged to form a grid of data points for knots calculation and high-accuracy shape reconstruction in future work.

RATIONAL FUNCTIONS OF BEST UNIFORM APPROXIMATION AND HOLOMORPHIC CONTINUATION OF FUNCTIONS

Let f be a function, continuous and real valued on the segment △,△ (-∞,∞) and {Rn} be the sequence of the rational functions of best uniform approximation to fon △ of order (n,n). In the present work, the convergence of {Rn} in the complex plane is considered for the special caseswhen the poles (or the zeros, respectively) of {Rn} accumulate in the terms of weak convergence of measures to acompact set of zera capacity.As a consequence, sufficient conditions for the holomorphic and the meromorphic continuability of fare given.

THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

Abstract For two rational quadratic B spline curves with same control vertexes, the cross ratio of four collinear points are represented: which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the two curves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Bézier curves, the value is generally related with the location of the ray, and the necessary and sufficient condition of the ratio being independent of the ray's location is showed. Also another cross ratio of the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initial vertex intersects respectively with the curve segment, the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only with the ray's location, but not with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.

Shape Control and Modification of Rational Cubic B-Spline Curves

This paper considers the construction of a rational cubic B-spline curve that willinterpolate a sequence of data points x'+ith specified tangent directions at those points. It is emphasisedthat the constraints are purely geometrical and that the pararnetric tangent magnitudes are notassigned as in many' curl'e manipulation methods. The knot vector is fixed and the unknowns are thecontrol points and x'eightsf in this respect the technique is fundamentally different from otherswhere knot insertion is allowed.First. the theoretical result3 for the uniform rational cubic B-spline are presented. Then. in theplanar case. the effect of changes to the tangent at a single point and the acceptable bounds for thechange are established so that all the weights and tangent magnitUdes remain positive. Finally, aninteractive procedure for controlling the shape of a planar rational cubic B-spline curve is presented.

使用Rational Rose实现对基于Web的应用的OO设计

本文深讨了利用 OO的开发工具以及基于 OO的开发流程完成基于 WEB的应用的流程。并提出了开发基于 WEB的应用的一种新的开发过程。最后给出了一个具体的实现。

A New Isogeometric Finite Element Method for Analyzing Structures

High-performance finite element research has always been a major focus of finite element method studies.This article introduces isogeometric analysis into the finite element method and proposes a new isogeometric finite element method.Firstly,the physical field is approximated by uniform B-spline interpolation,while geometry is represented by non-uniform rational B-spline interpolation.By introducing a transformation matrix,elements of types C^(0)and C^(1)are constructed in the isogeometric finite element method.Subsequently,the corresponding calculation formats for one-dimensional bars,beams,and two-dimensional linear elasticity in the isogeometric finite element method are derived through variational principles and parameter mapping.The proposed method combines element construction techniques of the finite element method with geometric construction techniques of isogeometric analysis,eliminating the need for mesh generation and maintaining flexibility in element construction.Two elements with interpolation characteristics are constructed in the method so that boundary conditions and connections between elements can be processed like the finite element method.Finally,the test results of several examples show that:(1)Under the same degree and element node numbers,the constructed elements are almost consistent with the results obtained by traditional finite element method;(2)For bar problems with large local field variations and beam problems with variable cross-sections,high-degree and multi-nodes elements constructed can achieve high computational accuracy with fewer degrees of freedom than finite element method;(3)The computational efficiency of isogeometric finite element method is higher than finite element method under similar degrees of freedom,while as degrees of freedom increase,the computational efficiency between the two is similar.

An adaptive generation method for free curve trajectory based on NURBS

To realize the high precision and real-time interpolation of the NURBS （non-uniform rational B-spline） curve, a kinetic model based on the modified sigmoid function is proposed. The constraints of maximum feed rate, chord error, curvature radius and interpolator cycle are discussed. This kinetic model reduces the cubic polynomial S-shape model and the trigonometry function S-shape model from 15 sections into 3 sections under the precondition of jerk, acceleration and feedrate continuity. Then an optimized Adams algorithm using the difference quotient to replace the derivative is presented to calculate the interpolator cycle parameters. The higher-order derivation in the Taylor expansion algorithm can be avoided by this algorithm. Finally, the simplified design is analyzed by reducing the times of computing the low-degree zero-value B-spline basis function and the simplified De Boor-Cox recursive algorithm is proposed. The simulation analysis indicates that by these algorithms, the feed rate is effectively controlled according to tool path. The calculated amount is decreased and the calculated speed is increased while the machining precision is ensured. The experimental results show that the target parameter can be correctly calculated and these algorithms can be applied to actual systems.

眼镜镜片尖边轮廓的五轴数控加工

为了改善和优化眼镜镜片的加工流程,避免镜片尖边加工过程中刀轴矢量变化剧烈、影响工件表面的加工质量,提出了一种基于UG NX的五轴数控加工路径。利用智能镜框扫描仪对镜框边缘进行扫描,获得镜框凹槽点云数据文件,编写相应程序对符合眼镜片加工标准的OMA文件中的球坐标数据进行坐标及格式转换等处理。基于NURBS曲线拟合算法,实现刀路轨迹的连续性并保证拟合曲线的精度。设计和建立一种控制刀轴矢量平滑变化的刀轴驱动约束方法,依靠曲线驱动刀轴及镜片曲面法向量约束刀轴使刀头平滑进给,并将刀轨文件经过后处理转换为NC文件。最后,对加工后的镜片进行误差测量,结果表明,通过点云数据拟合刀路曲线的方法提高了加工面的精确度和光滑性,有效缩减了加工流程,提高了加工效率。

Methods of configuration test and deformation analysis for large airship

In recent years, high-altitude aerostats have been increasingly developed in the direction of multi-functionality and large size. Due to the large size and the high flexibility, new challenges for large aerostats have appeared in the configuration test and the deformation analysis. The methods of the configuration test and the deformation analysis for large airship have been researched and discussed. A tested method of the configuration,named internal scanning, is established to quickly obtain the spatial information of all surfaces for the large airship by the three-dimensional(3D) laser scanning technology. By using the surface wrap method, the configuration parameters of the large airship are calculated. According to the test data of the configuration, the structural dimensions such as the distances between the characteristic sections are measured. The method of the deformation analysis for the airship contains the algorithm of nonuniform rational B-splines(NURBS) and the finite element(FE)method. The algorithm of NURBS is used to obtain the reconfiguration model of the large airship. The seams are considered and the seam areas are divided. The FE model of the middle part of the large airship is established. The distributions of the stress and the strain for the large airship are obtained by the FE method. The position of the larger deformation for the airship is found.

基于等几何分析的风力机叶片PHT样条细分研究

等几何分析方法作为一种新型数值分析方法得到了广泛关注。针对传统等几何分析过程中,非均匀有理B样条(NURBS)曲线建模存在控制点较多、局部细化薄弱以及多面片拼接导致模型空间连续性较差等问题,提出一种基于PHT样条分层细分的等几何分析(IGA)方法。以某型风力机叶片为研究对象,分析了PHT样条细分对风力机叶片模型求解精度的影响,并通过有限元仿真结果进行对比分析。结果表明:细分前基于NURBS的风力机叶片模型等几何分析结果与有限元结果的相对误差为5.9%,细分后IGA结果与有限元结果的相对误差为3.7%,证明了经过PHT样条细分,风力机叶片的等几何分析求解精度得到了有效提高。提出的方法对后续风力机叶片的数值仿真和优化设计具有一定的参考意义。

基于LMS滤波算法优化数控加工速度误差的应用

针对数控加工过程中速度误差导致加工精度低的问题,研究所加工零件的加工精度、切削加减速误差和切削加速度变化规律等,提出基于LMS滤波算法的数控加工速度误差优化。通过对非均匀有理B样条(NURBS)曲线进行仿真加工,对数控机床加工速度进行自适应控制。通过引入最小均方算法进行误差分析,从而提高插补速度精度,使数控机床加工误差降低、效率提高。通过实验测试对所提误差控制方法进行验证。结果表明:基于LMS滤波算法优化数控加工误差控制,不仅使数控机床加工速度得到提高,还有效解决了数控机床加工运动过程中存在的加工误差问题,使加工精度得到有效提升,证明所提加工误差控制方法具有一定可行性。

复杂型腔类零件电火花加工电极运动轨迹搜索算法研究

针对复杂型腔类零件电火花加工中电极无干涉运动路径难规划的问题,提出一种电极运动轨迹搜索算法。使用NURBS参数化曲线曲面建模方法拟合叶片型面,建立叶片精确数学模型并计算流道中心线,基于流道中心线表达式提出轨迹搜索算法,开发了复杂型腔类零件多轴联动电火花加工专用CAM系统,成功实现4轴、5轴、6轴复杂型腔类零件的电极运动路径规划和无干涉加工过程仿真。进行整体带叶冠涡轮盘的加工试验,结果表明,叶形加工精度≤0.03 mm,总耗时249.3 h,满足闭式整体叶盘类零件指标要求。试验证明该算法可以快速搜索电极无干涉运动轨迹,有效避免电极干涉,从而提高轨迹搜索效率,工况适应能力强,可用于4~6轴各种工况下叶轮、叶盘等复杂型腔类零件的电极运动轨迹搜索。

Spline-based automatic path generation of welding robot

This paper presents a flexible method for the representation of welded seam based on spline interpolation. In this method, the tool path of welding robot can be generated automatically from a 3D CAD model. This technique has been implemented and demonstrated in the FANUC Arc Welding Robot Workstation. According to the method, a software system is developed using VBA of SolidWorks 2006. It offers an interface between SolidWorks and ROBOGUIDE, the off-line programming software of FANUC robot. It combines the strong modeling function of the former and the simulating function of the latter. It also has the capability of with on-line robot. The result data have shown its high accuracy and strong reliability in experiments. This method will improve the intelligence and the flexibility of the welding robot workstation.

Numerical Solution of Obstacle Problems by B-Spline Functions

In this study, we use B-spline functions to solve the linear and nonlinear special systems of differential equations associated with the category of obstacle, unilateral, and contact problems. The problem can easily convert to an optimal control problem. Then a convergent approximate solution is constructed such that the exact boundary conditions are satisfied. The numerical examples and computational results illustrate and guarantee a higher accuracy for this technique.

涡扇叶片在机测量自适应采样方法

涡扇叶片的加工和检测精度直接影响到涡扇的结构强度和气动性能。为提高叶片的在机测量精度和效率,提出一种基于弯矩理论的自适应曲面采样方法,以解决叶片曲面在前缘和后缘位置处曲率急剧变化以及轮廓面的全局采样问题。根据曲面的几何特征变化,自适应确定检测点的分布密度和数量。仿真和在机测量实验验证了该方法的有效性和可行性。通过与双向等参数法、改进的分区等参数法和Hammersley序列法的采样结果对比表明,基于弯矩理论的自适应采样方法实现了对采样点位置及数量的微细精准调整,采样误差小,重构表面精度高,满足在机测量对时间和精度的要求。

一种并联机器人轨迹规划算法研究

针对并联机器人工作空间微小线段间拐角处产生的冲击与振动问题,提出一种基于笛卡尔空间与关节空间相结合的机器人联合空间轨迹规划方法。在笛卡尔空间中采用三次非均匀有理B样条曲线对机器人末端执行器复杂的加工轨迹进行插补。为解决笛卡尔空间微小线段间拐角处的切向不连续导致轨迹突变的问题,基于并联机器人逆运动学模型,将笛卡尔空间轨迹规划算法所得插补点映射到关节空间,采取五次均匀B样条曲线进行第二次轨迹插补,平滑并联机器人运动过程中加速度及加加速度突变曲线。并在动力学层面验证所提算法的有效性。仿真结果表明:联合空间轨迹规划策略能使机器人末端执行器较好地改善连续高阶曲率导数的轨迹平滑问题,提高末端跟踪精度。实验结果表明:末端跟踪误差值最大减少21.12%,力矩最大值减少11.65%。

基于原子轨道搜索算法的6自由度装配机器人轨迹规划

针对6自由度装配机器人多目标优化和轨迹规划问题,首先,将原子轨道搜索(Atomic Orbit Search,AOS)算法融入到多目标优化中,构建了时间、能耗和冲击的多目标优化函数;其次,轨迹规划采用路径点插值非均匀有理B样条曲线的方法,使用AOS算法测定原子的结合态和结合能,并确定原子中能级最低的候选解,输出最优的电子位置,优化了Pareto取值集合空间,获得多目标优化后的轨迹曲线;最后,通过Matlab仿真验证了所提方法的有效性。结果表明,结合AOS算法优化后的轨迹规划方法能保证装配机器人按最优路线运行,具有一定的工程应用价值。

结合互相关和B样条插值的激光三角光斑定位

激光三角光斑定位通常受到像点光斑偏态的影响,为提高激光三角位移传感器的测量精度和物面适应性,在分析激光三角光斑的偏态特征的基础上,针对偏态特性提出了一种基于互相关和非均匀有理B样条插值的光斑定位算法。对光斑信号采取时域和空域相结合的滤波处理方法,降低外部噪声干扰。引入邻域标定光斑进行互相关运算,充分利用光斑偏态分布的灰度和位置相似性约束,确定像素级相关系数分布。最后,对相关系数序列进行三次非均匀有理B样条插值细分,实现亚像素级光斑质心定位。在激光三角位移传感器中验证算法,实验结果表明:该算法通过结合互相关和非均匀有理B样条插值细分,将测量重复性误差降低至0.4μm,精度相对于传统定位算法显著提高;同时,在互相关算法中采用的邻域标定光斑模板不仅容易获取,几何相似度更高,而且对不同物面特性的适应性更强。本文方法精度高、适应性强,为有效提升激光三角位移传感器的性能提供了新的技术路径。

渐进多焦点自由曲面镜片优化重构

渐进多焦点自由曲面镜片的后表面由多个曲面拟合而成,其衔接处曲率变化较大且不连续,初始的自由曲面镜片往往需要通过局部或者全局优化来改善其光学性能以及表面光顺性。提出基于NURBS曲线和最小二乘曲线的全局拟合方法来对渐进多焦点自由曲面镜片后表面进行优化重构。介绍了最小二乘曲线拟合的算法原理,在相同参数下对两组光焦度不同的镜片后表面进行重构,并进行仿真分析和测量分析,对其光学性能进行评价。实验结果表明:两组镜片最大像散分别减小了0.61 D和0.45 D,远用区像散分别减小了0.15 D和0.16 D,中间通道(Y=0 mm处)宽度增加超过1.8 mm。重构后的曲面能够在保持光焦度基本不变的情况下,提高了后表面的光滑性,有效减小了渐进片的最大像散,同时渐变通道的宽度也有一定程度的改善。