Integration of CAD and boundary element analysis through subdivision methods

Subdivision methods have been mainly used in computer graphics. This paper extends their applications to mechanical design and boundary element analysis (BEA), and fulfills the seamless integration of CAD and BEA in the model and representation.Traditionally, geometric design and BEA are treated as separate modules requiring different representations and models, which include continuous parametric models and discrete models. Due to the incompatibility of the involved representations and models, the post-processing in geometric design or the pre-processing in BEA is essential. The transition from geometric design to BEA requires substantial effort and errors are inevitably introduced during the transition. In this paper, a framework of realizing the integration of CAD and BEA was first presented based on subdivision methods. A common model or a unified representation for geometric design and BEA was created with subdivision surfaces. For general 3D structures, automatic mesh generation for geometric design and BEA was fulfilled through subdivision methods. The seamless integration improves the accuracy of numerical analysis and shortens the cycle of geometric design and BEA.     

Cyclides in surface and solid modeling

It is shown that Dupin cyclides (C.P. Dupin, 1822), as surfaces in computer-aided geometric design (CAGD), have attractive properties such as low algebraic degree, rational parametric forms, and an easily comprehensible geometric representation using simple and intuitive geometric parameters. Their alternative representations permit the transition between forms when one or the other is more convenient for a specific purpose. Cyclides provide is useful extension of geometric coverage in solid modeling, primarily as blending surfaces for many commonly occurring situations. The geometry, properties, and uses of the Dupin cyclide in free-form surface modeling and blending are discussed     

Generative geometric design

Boundary solid grammars use design rules that express complex geometric conditions and operations using a logical reasoning mechanism, allowing one to construct powerful rules and describe appropriate grammars for the generation of solid models for a variety of design domains. The formalism I present in this article is not sufficient for all engineering and architectural domains (e.g., polyhedral solids are not adequate geometric abstractions for mechanical design). The boundary solid grammar formalism is, however, well suited to extensions for the representation of nonlinear geometry and mixed-dimensional modeling. Design in these domains will require additional representations, such as electrical and hydraulic schematics, structural and aerodynamic meshes, kinematics, and assemblies. These representations and their analysis techniques will need to be integrated into a common framework to permit interdependent design analysis and generation     

有理曲线的均匀区间隐式化

参数式曲线与隐式曲线是CAGD中常用的两种曲线形式,因此需要建立起二者之间相互转换的体制.长期以来,许多工作都集中在利用结式思想,将一个参数式曲线精确转化为一个隐式曲线上,而事实上用隐式曲线精确表示一条参数式曲线不仅非常麻烦,而且往往也没有必要.故此提出了参数式有理曲线均匀区间隐式化的一种新方法,利用区间算术和空间重心坐标的定义,可以用一个低阶区间多项式隐式曲线来逼近所给的参数式有理曲线,同时使一些目标函数最小化,达到用隐式多项式曲线来逼近参数式有理曲线的很好效果,并提供了一些算法和实例.     

Fast generation of 3-D deformable moving surfaces

Dynamic surface modeling is an important subject of geometric modeling due to their extensive applications in engineering design, entertainment and medical visualization. Many deformable objects in the real world are dynamic objects as their shapes change over time. Traditional geometric modeling methods are mainly concerned with static problems, therefore unsuitable for the representation of dynamic objects. Apart from the definition of a dynamic modeling problem, another key issue is how to solve the problem. Because of the complexity of the representations, currently the finite element method or finite difference method is usually used. Their major shortcoming is the excessive computational cost, hence not ideal for applications requiring real-time performance. We propose a representation of dynamic surface modeling with a set of fourth order dynamic partial differential equations (PDEs). To solve these dynamic PDEs accurately and efficiently, we also develop an effective resolution method. This method is further extended to achieve local deformation and produce n-sided patches. It is demonstrated that this new method is almost as fast and accurate as the analytical closed form resolution method and much more efficient and accurate than the numerical methods.     

ORICRETE: Modeling support for design and manufacturing of folded concrete structures

The paper presents a flexible and efficient modeling approach to the simulation of the folding process of general crease patterns. The development of the model has been motivated by the need to provide support for targeted design and efficient manufacturing of shell structures inspired by the origami technique. This type of structures is becoming increasingly popular in many engineering disciplines and has been referred to as origamics. In the present work the folding technique is used to produce spatial structures from continuously reinforced thin-walled cementitious composite plates without the need to construct curved spatial formworks. In order to support the targetted design and manufacturing of folded concrete (oricrete) structures numerical model has been formulated as an optimization framework with several types of optimality conditions and equality constraints. The model is used both for form-finding of the spatial structure and for the realization of the manufacturing process.     

An integrated method of multi-objective optimization for complex mechanical structure

An integrated method of multi-objective optimization for complex mechanical structures is presented, which integrates prototype modeling, FEM analysis and optimization. To explore its advantages over traditional methods, optimization of a manipulator in hybrid mode aerial working vehicle (HMAWV) is adopted. The objective is to increase its working domain and decrease the cost under the constraint of enough strength, and the design variables are geometric dimensions. NLPQL and NSGA-II are synthesized to achieve optimal solutions. The results indicated that this integrated method was more efficient than enumerative search algorithm. NSGA-II could approximate the global Pareto front precisely, and the relative error between NLPQL and NSGA-II is trivial. Therefore, this integrated method is effective and shows a potential in engineering applications.     

Computing general geometric structures on surfaces using Ricci flow

Systematically generalizing planar geometric algorithms to manifold domains is of fundamental importance in computer aided design field. This paper proposes a novel theoretic framework, geometric structure, to conquer this problem. In order to discover the intrinsic geometric structures of general surfaces, we developed a theoretic rigorous and practical efficient method, Discrete Variational Ricci flow.Different geometries study the invariants under the corresponding transformation groups. The same geometry can be defined on various manifolds, whereas the same manifold allows different geometries. Geometric structures allow different geometries to be defined on various manifolds, therefore algorithms based on the corresponding geometric invariants can be applied on the manifold domains directly.Surfaces have natural geometric structures, such as spherical structure, affine structure, projective structure, hyperbolic structure and conformal structure. Therefore planar algorithms based on these geometries can be defined on surfaces straightforwardly.Computing the general geometric structures on surfaces has been a long lasting open problem. We solve the problem by introducing a novel method based on discrete variational Ricci flow.We thoroughly explain both theoretical and practical aspects of the computational methodology for geometric structures based on Ricci flow, and demonstrate several important applications of geometric structures: generalizing Voronoi diagram algorithms to surfaces via Euclidean structure, cross global parametrization between high genus surfaces via hyperbolic structure, generalizing planar splines to manifolds via affine structure. The experimental results show that our method is rigorous and efficient and the framework of geometric structures is general and powerful.     

基于几何法表示的曲面实体的分割算法

分割是实体造型的重要步骤,而边界问题是影响分割算法效率和稳定性的主要因素。工程中常用的二次曲面有自封闭的特性,在相交时交线会出现退化和自交等情况,给拓扑表示和帝体重建带来困难,另外,边界重合也是实体分割时经常要遇到的问题,该文在二次曲面几何法表示的基础上,针对二次曲面相交时交线的特性,设计了合理的分割策略,提出了有效的分割算法,并对边界重合等问题做了很好的处理,同时用实例验证了本文算法的有效性。     

Fast character modeling with sketch-based PDE surfaces

Virtual characters are 3D geometric models of characters. They have a lot of applications in multimedia. In this paper, we propose a new physics-based deformation method and efficient character modelling framework for creation of detailed 3D virtual character models. Our proposed physics-based deformation method uses PDE surfaces. Here PDE is the abbreviation of Partial Differential Equation, and PDE surfaces are defined as sculpting force-driven shape representations of interpolation surfaces. Interpolation surfaces are obtained by interpolating key cross-section profile curves and the sculpting force-driven shape representation uses an analytical solution to a vector-valued partial differential equation involving sculpting forces to quickly obtain deformed shapes. Our proposed character modelling framework consists of global modeling and local modeling. The global modeling is also called model building, which is a process of creating a whole character model quickly with sketch-guided and template-based modeling techniques. The local modeling produces local details efficiently to improve the realism of the created character model with four shape manipulation techniques. The sketch-guided global modeling generates a character model from three different levels of sketched profile curves called primary, secondary and key cross-section curves in three orthographic views. The template-based global modeling obtains a new character model by deforming a template model to match the three different levels of profile curves. Four shape manipulation techniques for local modeling are investigated and integrated into the new modelling framework. They include: partial differential equation-based shape manipulation, generalized elliptic curve-driven shape manipulation, sketch assisted shape manipulation, and template-based shape manipulation. These new local modeling techniques have both global and local shape control functions and are efficient in local shape manipulation. The final character models are represented with a collection of surfaces, which are modeled with two types of geometric entities: generalized elliptic curves (GECs) and partial differential equation-based surfaces. Our experiments indicate that the proposed modeling approach can build detailed and realistic character models easily and quickly.

     

新一代几何造型系统—GEMS4.0

ＧＥＭＳ４．０是清华大学ＣＡＤ中心在工作站上用Ｃ语言开发的新一代几何造型系统。和９０年代初问世的第三代几何造型系统相比，它具有如下特点：基于线框，表面，实体和特征表示的非流形造型；具有参数化设计，变量几何，尺寸驱动；扫描面，自由曲面和雕塑面用非均匀有理Ｂ样条（ＮＵＲＢＳ）表示，几何数据及属性的文件传送和数据库存取基于国际标准ＳＴＥＰ；基于窗口环境，面向对象的事件驱动和数据表格驱动的系统结构有利于开     

A stiffness modeling methodology for simulation-driven design of haptic devices

Efficient development and engineering of high performing interactive devices, such as haptic robots for surgical training benefits from model-based and simulation-driven design. The complexity of the design space and the multi-domain and multi-physics character of the behavior of such a product ask for a systematic methodology for creating and validating compact and computationally efficient simulation models to be used in the design process. Modeling the quasi-static stiffness is an important first step before optimizing the mechanical structure, engineering the control system, and performing hardware in the loop tests. The stiffness depends not only on the stiffness of the links, but also on the contact stiffness in each joint. A fine-granular Finite element method (FEM) model, which is the most straightforward approach, cannot, due to the model size and simulation complexity, efficiently be used to address such tasks. In this work, a new methodology for creating an analytical and compact model of the quasi-static stiffness of a haptic device is proposed, which considers the stiffness of actuation systems, flexible links and passive joints. For the modeling of passive joints, a hertzian contact model is introduced for both spherical and universal joints, and a simply supported beam model for universal joints. The validation process is presented as a systematic guideline to evaluate the stiffness parameters both using parametric FEM modeling and physical experiments. Preloading has been used to consider the clearances and possible assembling errors during manufacturing. A modified JP Merlet kinematic structure is used to exemplify the modeling and validation methodology.     

Dynamic PDE-based surface design using geometric and physical constraints

PDE surfaces, which are defined as solutions of partial differential equations (PDEs), offer many modeling advantages in surface blending, free-form surface modeling, and specifying surface’s aesthetic or functional requirements. Despite the earlier advances of PDE surfaces, previous PDE-based techniques exhibit certain difficulties such as lack of interactive sculpting capabilities and restrained topological structure of modeled objects. This paper presents an integrated approach that can incorporate PDE surfaces into the powerful physics-based modeling framework, to realize the full potential of PDE methodology. We have developed a prototype system that allows interactive design of flexible topological surfaces as PDE surfaces and displacements using generalized boundary conditions as well as a variety of geometric and physical constraints, hence supporting various interactive techniques beyond the conventional boundary control. The system offers a set of sculpting toolkits that allow users to interactively modify arbitrary points, curve spans, and/or regions of interest across the entire PDE surfaces and displacements in an intuitive and physically meaningful way. To achieve real-time performance, we employ several simple, yet efficient numerical techniques, including the finite-difference discretization, the multigrid-like subdivision, and the mass-spring approximation of elastic PDE surfaces and displacements. In addition, we present the standard bivariant B-spline finite element approximations of dynamic PDEs, which can subsequently be sculpted and deformed directly in real-time subject to the intrinsic PDE constraints. Our experiments demonstrate many attractive advantages of the physics-based PDE formulation such as intuitive control, real-time feedback, and usability to both professional and common users.     

Parameterization in Finite Precision

Certain classes of algebraic curves and surfaces admit both parametric and implicit representations. Such dual forms are highly useful in geometric modeling since they combine the strengths of the two representations. We consider the problem of computing the rational parameterization of an implicit curve or surface in a finite precision domain. Known algorithms for this problem are based on classical algebraic geometry, and assume exact arithmetic involving algebraic numbers. In this work we investigate the behavior of published parameterization algorithms in a finite precision domain and derive succinct algebraic and geometric error characterizations. We then indicate numerically robust methods for parameterizing curves and surfaces which yield no error in extended finite precision arithmetic and, alternatively, minimize the output error under fixed finite precision calculations. Received January 8, 1997; revised August 27, 1998.     

基于参数化造型设计及表达的工程制图国际化教学实践

论文介绍了北京理工大学机械工程专业国际化班工程制图课程的教学设计 和实践。在教学设计和实践中,面向课程目标,引入参数化造型设计所具有的参数化、变量 化、几何约束等概念及设计理念;压缩画法几何及视图基础知识,加强以三维造型软件为工 具的设计及表达能力培养;引入基于装配的零件设计理念,使学生快速掌握凑配设计技术; 全英文教学,使用一套标准打通课程,同时通过对比分析加深学生对国标的理解。学生经过 本门课程的学习,在造型设计和工程图表达等专业基础方面,达到或接近传统教学计划经过 课程设计训练才具备的水平,并具备一定的国际交流专业基础。     

Symbolic modeling in robotics: Genesis,applicaton, and future prospects

This survey article gives an overview of software packages for generating numerically efficient manipulator models in symbolic form, i.e. as computer programs written in a high-level language such as C or FORTRAN. We chronicle the history of computational robot dynamics and, to some extent, multibody systems dynamics. We survey several mechanical computer-aided engineering software packages because they have charted the course for symbolic robot modeling software. The attractive features of various programs regarding areas of application (vehicles, robots, satellites, etc.) and design possibilities (kinematic and dynamic analysis, modal analysis, optimization of mechanical design, numerical efficiency of generated symbolic models, etc.) are emphasized. Finally, as an example, we present the SYM program package in more detail and point out the new strategic area of robotics which has emerged during the last two years: computer-aided generation of control laws.     

Agent UML notation for multiagent system design

From the earliest days of multiagent system development, the need has existed for both a methodology and a modeling notation that assist in design. The agent UML community has responded by developing the AUML notation - a UML profile dedicated to agents that tries to simplify the transition from software engineering to multiagent system engineering. The idea behind AUML is to exploit UML extension capabilities such as stereotypes and constraints. AUML crystallizes a growing concern for agent-based modeling representations and lets designers move smoothly from software development to agent development.     

Rational Beta-splines for representing curves and surfaces

The rational Beta-spline representation, which offers the features of the rational form as well as those of the Beta-spline, is discussed. The rational form provides a unified representation for conventional free-form curves and surfaces along with conic sections and quadratic surfaces, is invariant under projective transformation, and possesses weights, which can be used to control shape in a manner similar to shape parameters. Shape parameters are an inherent property of the Beta-spline and provide intuitive and natural control over shape. The Beta-spline is based on geometric continuity, which provides an appropriate measure of smoothness in computer-aided geometric design. The Beta-spline has local control with respect to vertex movement, is affine invariant, and satisfies the convex hull property. The rational Beta-spline enjoys the benefit of all these attributes. The result is a general, flexible representation, which is amenable to implementation in modern geometric modeling systems