CATIA AIDED RADOME ANALYSIS USING GEOMETRIC OPTICS METHOD

In this paper, the Geometric Optics (GO) method using the approximate ray paths coupled with the Computer Aided Tri-dimensional Interface Application (CATIA) meshing modeling are implemented to analyze the performance of electric large three-dimensional dielectric radome-enclosed antenna of arbitrary contour shape. The surfaces of the radome are approximated by planar triangular patches, the influences of various number of patches on power transmission coefficient and Insertion Phase Delay (IPD) via an ogive and a conical radome are discussed by the hybrid method. The simulation results indicate that computational error from planar triangular patches can limit in one percent, meeting the engineering application requirements.

A NEW SYSTEM FOR COMPUTER AIDED PATTERN DESIGN——CAPDS

This paper proposes a new computer aided pattern design system(CAPDS)in which a uniformmathematical expression is used to construct different objects. In the geometric model, 3 B-splineis adopted as a line model. The new system with uniform mathematical expression has the distin-guishing features: curve smoothness and fidelity, convenience to process graphic data in thedatabase and etc.. This paper presents the data structure, the program structure and also the implementation.

REFINED HYBRID MINDLIN PLATE ELEMENT FOR GEOMETRICALLY NON LINEAR ANALYSIS

Based upon a generalized variational principle, which relaxed the inter element continuity requirements, a novel refined hybrid Mindlin plate element is developed, its non linear element stiffness matrices are decomposed into a series of matrices with respect to the assumed strain modes. The formulation presented in this paper is different from any other non linear mixed/hybrid element formulation all successful experience of linear hybrid formulation is absorbed into the formulation(adding non conforming modes and realizing orthogonalization) Numerical results show that the present approach is more effective than any other non linear hybrid element formulation over the accuracy and computational efficiency. In addition, non conforming modes can also overcome the shear locking effect.

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.

THE CONCEPT OF PROBE DETECTOR AND ITS APPLICATION IN GEOMETRIC MODELING

The concept of′Probe detector′is introduced in this paper with its application in geometricmodeling and graphics.In terms of the concept,the authors derive edge data from the CSG datarepresentation and establish a wireframe model.

A 3D GIS spatial data model based on conformal geometric algebra

We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresponding basic elements (blades) in Clifford algebra, and the expressions of multi-dimensional objects are unified without losing their geometric meaning. Geometric and topologic computations are also processed in a clear and coordinates-free way. Under the CGA framework, basic geometrics are constructed and expressed by the inner and outer operators. This expression combined geometrics of different dimensions and metric relations. We present the structure of the framework, data structure design, and the data storage, editing and updating mechanisms of the proposed 3D GIS data model. 3D GIS geometric and topological analyses are performed by CGA metric, geometric and topological operators using an object-oriented approach. Demonstrations with 3D residence district data suggest that our 3D data model expresses effectively geometric objects in different dimensions, which supports computation of both geometric and topological relations. The clear and effective expression and computation structure has the potential to support complex 3D GIS analysis, and spatio-temporal analysis.

Current status and challenges of using geometric tolerance information in intelligent manufacturing systems

Recent development in computer-based manufacturing and inspection has necessitated extended knowledge and usage of geometric tolerances as carriers of design intent. The aim of applying geometrical tolerances in design is to provide function-oriented precise description of part geometry where the conventional size tolerance system fails to address. In view of the current development of computer-aided systems, applying geometric tolerances opens a new research front. This article examines the challenges in applying geometric tolerance information to carry the design intent to other downstream manufacturing processes and intelligently integrate the whole system. Based on the observed practical capabilities and literature studies, it is concluded that the current computer-aided design （CAD） systems cannot effectively provide the appropriate use of geometric tolerances. This article highlights the existing challenges and proposes a scheme of algorithm development for appropriate use of tolerance symbols and conditions at the design specification stage. This, in the long run, enables the CAD model to carry the design intent and opens a window of opportunity for intelligently integrating manufacturing systems.

三角B样条函数研究及超越曲线曲面绘制

在函数空间中构造了一类具备形状可调性、高阶连续性、变差缩减性等性质的三角B样条曲线和曲面。研究定义了三角B样条基函数,分析参数对三角B样条曲线形状的调节作用,并精确地绘制出由三角B样条构造的摆线、螺旋线、椭圆等超越曲线,最后基于张量积形式构造了三角B样条曲面。实例表明,构造的三角B样条曲面在计算机辅助几何设计几何造型中具有实用性和有效性。

LINEAR AND GEOMETRICALLY NONLINEAR ANALYSIS WITH 4-NODE PLANE QUASI-CONFORMING ELEMENT WITH INTERNAL PARAMETERS

A linear 4-node quadrilateral quasi-conforming plane element with internal parameters is proposed. The element preserves advantages of the quasi-conforming technique, including an explicit stiffness matrix, which can be applied to nonlinear problems. The weak patch test guarantees the convergence of the element. Then the linear element is extended to the geometri- cally nonlinear analysis in the framework of Total Lagrangian （TL） formulation. The numerical tests indicate that the present element is accurate and insensitive to mesh distortion.

基于共形几何代数的工业机器人运动学分析

为解决工业机器人运动学求解复杂程度高、运算量大的问题,将共形几何代数(Confor-mal Geometric Algebra,CGA)方法引入到工业机器人运动学模型构建中。在正运动学求解过程中,利用CGA中平移算子和旋转算子列出各关节的运动表达式,求出机器人末端执行器的位姿;在逆运动学求解过程中,将构造的基本几何体进行外积计算,求得各关节点的位置,然后构造过关节点的线和面,并在CGA框架内做内积,得到所有关节角的余弦表达,求解得到机器人逆运动学的全部解;最后,以MOTOMAN-HP20D型6自由度工业机器人为例进行计算,并通过Matlab/Simulink软件验证了算法的准确性和有效性,为机器人后续的运动控制奠定了基础。

Global Continuity Adjustment and Local Shape Optimization Technique for Complex Trimmed Surface Model

Smoothly stitching multiple surfaces mainly represented by B-spline or NURBS together is an extremely important issue in complex surfaces modeling and reverse engineering. In recent years, a lot of progress has been made in smooth join of non-trimmed surface patches, while there has been seldom research on smoothly stitching trimmed surface patches together. This paper studies the problem of global continuity adjustment, damaged hole repair and local shape optimization for complex trimmed surface model, and presents a uniform scheme to deal with continuity adjustment of trimmed surfaces and geometric repair of local broken region. Constrained B-spline surface refitting technique and trim calculation are first utilized to achieve global G^1 continuity, and then local shape optimization functional is adopted to reduce fitting error and improve local quality of refitted surface patch. The proposed approach is applied to a discontinuity ship hull surface model with an irregular hole, and the result demonstrates the validation of our method. Furthermore, on the premise of global continuity, the proposed locally repairing damaged surface model provides a better foundation for following research work, such as topology recovery technique for complex surface model after geometric repair.

OBJECT ORIENTED DATA MODELLING WITH APPLICATIONS TO CAD

An object oriented data modelling in computer aided design (CAD) databases is focused. Starting with the discussion of data modelling requirements for CAD applications, appropriate data modelling features are introduced herewith. A feasible approach to select the “best” data model for an application is to analyze the data which has to be stored in the database. A data model is appropriate for modelling a given task if the information of the application environment can be easily mapped to the data model. Thus, the involved data are analyzed and then object oriented data model appropriate for CAD applications are derived. Based on the reviewed object oriented techniques applied in CAD, object oriented data modelling in CAD is addressed in details. At last 3D geometrical data models and implementation of their data model using the object oriented method are presented.

GFFD： Generalized free-form deformation with scalar fields

The novel free-form deformation (FFD) technique presented in the paper uses scalar fields definedby skeletons with arbitrary topology. The technique embeds objects into the scalar field by assigning a field value to each point of the objects. When the space of the skeleton is changed, the distribution of the scalar field changes accordingly, which implicitly defines a deformation of the space. The generality of skeletons assures that the technique can freely define deformable regions to produce a broader range of shape deformations.

基于共形几何代数的并联机器人逆运动学分析方法

运动学分析是并联机器人运动学性能评估和结构尺寸优化的基础。现有并联机器人运动学分析方法存在几何建模与几何计算相分离的问题,本文利用共形几何代数(Conformal geometric algebra, CGA)集几何表示和计算为一体的优势,提出一种并联机器人逆运动学分析方法。根据动平台位姿参数给出动平台刚体运动算子,通过共形几何代数框架下的几何积实现动平台上任意点的刚体变换,得到任意点在运动过程中的共形几何表达式;结合机构中尺寸、几何约束,利用内积运算,建立机构运动学方程;根据运动学方程,进行运动学反解计算和速度分析。以3自由度的3-RPS并联机器人和6自由度6-UPS并联机器人为例,对所提方法进行验证,并将逆运动学推导结果与仿真软件所得结果进行了对比,验证了本文提出方法的正确性。该方法将空间向量和旋转表示等几何对象与矩阵乘法、矢量外积等计算方式相结合,使得并联机器人空间几何问题统一在一个代数系统中进行处理,因此分析过程几何直观性较强,简化了运动学逆解分析计算过程。

G^0 and G^1 connection between two adjacent B-spline surfaces

In this paper, the smooth connection between two B-spline surfaces is discussed. First, a brief proof of some simple sufficient conditions of Go and G1 continuity is given. On this basis, a novel method for Go or G1 connection between two adjacent B-spline surfaces is presented. A reparameterization step is firstly taken for one of the surfaces such that they have the same parameterization in v direction, then, adjust their boundary control vertices to make them Go or Gl connected. The GI connection parameter is determined by an optimization problem. Compared with the existed methods, our method is simple and easy to be used in practice.

Implementation of a Sketch Based Approach to Conceptual Aircraft Design Synthesis and Modeling

In the context of applying computer aided design tools to aircraft conceptualdesign, a sketch based approach is proposed to help designers turn their original concepts intocomplex numerical models that are usable for further analysis and optimization. This approachemphasizes the integration of general configuration and the layout of such components as engines,payloads, fuel tanks and landing gears, and the representation of a design scheme as uniform planesketches and three dimensional models. This paper presents the measures adopted to implement theapproach in a prototype system, including the object-oriented data structure, friendly graphicaluser interfaces and basic features of relevant modules. Several examples generated in the prototypeand applications of the results are finally outlined to illustrate the effectiveness of theapproach.

G^2 Continuity Algorithms between Adjacent NURBS Patches along Common Cubic Boundary Curve

Non-uniform rational B-spline (NURBS) curves and surfaces are becoming increasingly widespread. The author have explored G^1 continuity condition between adjacent NURBS surface patches along common cubic boundary curve. On the basis of the research performed, this paper presents a G^2 continuity condition between adjacent NURBS patches along common cubic boundary curve and deduces a specific algorithm for contro1 points and weights of NURBS patch. For making another NURBS patch and one given NURBS patch to attain G^2, according to algorithm condition, one can adjust another patch control points and weights. It is much more convenient for engineers to apply.

Approximate merging of B-spline curves and surfaces

Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.

Computation of lower derivatives of rational triangular Bézier surfaces and their bounds estimation

By introducing the homogenous coordinates, degree elevation formulas and combinatorial identities, also by using multiplication of Bernstein polynomials and identity transformation on equations, this paper presents some explicit formulas of the first and second derivatives of rational triangular Bézier surface with respect to each variable (including the mixed derivative) and derives some estimations of bound both on the direction and magnitude of the corresponding derivatives. All the results above have value not only in surface theory but also in practice.