基于有向超图的参数化表示模型及其实现

本文提出了一种基于有向超图的参数化图表表示模型。它不仅能够表示图形的尺寸约束和几何约束，而且能够支持图形拓扑结构变化和工程设计约束的表示，在交互绘制图形对象的同时直接建立参数化图形约束模型。由于在图形构造的每一步都保证约束的一致性，因此，不会出现过约束或欠约束的情况。经实践表明，该模型具有实用方便、高效可行的特点，适合于系列化产品的参数化ＣＡＤ系统建模和绘图。     

AutoCAD环境下面向对象参数化设计的实现

文章论述了一种面向对象的参数化设计方法。采用基于有向无环超图的约束表示，完整的建立参数化模型，不仅可以表示简单约束关系，还可以方便的表示元素间的双向约束。在交互绘图的过程中获取约束关系并保存，实现参数驱动。利用功能强大的0bjectARX[1]进行AutoCAD上的二次开发，采用面向对象的技术，充分利用0bjectARX的类库，有效发挥其封装性和扩展性，在Windows环境下和VC 结合编程，实现参数化设计。     

满足多向驱动自动匹配的图形与尺寸约束自组织*

本文通过对图形约束的描述，约束识别与尺寸匹配的自组织．有效地建立了图形尺寸参数、零件图、装配圈之间的多向驱动机制.该方法具有通用性，使得参数化CAD支撑软件能满足整个产品设计的要求．     

一种适用于特征造型的参数化设计方法

本文提出了一种面向特征造型的参数化设计方法，该方法对三维几何约束在初始设计阶段采用高层表示，并基于面向特征造型的高层几何约束模型与约束传播实现尺寸驱动几何，从而能够有效地支持特征设计，初始设计。     

参数化设计中的对象约束模型及反向约束的研究

应用图论方法,建立了基于有向超图的对象约束模型,提出了压缩十字链表形式的网状存储结构,能够完整,准确地记录设计者的设计意图,实现尺寸及参数驱动图形的功能清晰地表示约束间的双向约束关系,有效地实现了约束的传播与救解,其完备的表不方式可方便地实现反向约束求解。同时利用面向对象技术,高效地实现了实体及约束建模,采用相应的类层次结构,充分发挥对象的封装性和扩展性,提出了一种方便灵活的参数化设计方法。     

一种基于几何推理的参数化设计方法

本文提出一种基于几何推理的参数化设计方法，该方法引入了已知元素，已知约束等新概念；通过扩展一般的图形数据结构统一表示几何元素与几何约束；基于普通算法而不是专家系统实现几何推理，并采用一个更适合地几何推理策略；基于几何推理实现参数化设计。     

基于图形数据库的变量化设计方法

文章针对参数化技术中过约束和欠约束的求解和图形设计问题,提出了一种新的基于图形数据库的变量化设计方法。该方法依据一组变量化基本规则,采用人工智能方法,对过约束与大约束问题判断、求解,扩大了模型图的自由度,提高了图形设计的效率和可靠性。     

参数化的图形建库工具

本文介绍了基于约束网络图的参数化图形建库方法，它是利用几何构型建立的约束模型，通过求解约束模型实现尺寸变量驱动图形，用该方法能简便快速地建立标准件、通用件图形库，所建图形库占用空间少，调用方便，因此该建库方法可广泛应用于机械行业。     

基于尺寸约束离线形成的参数化驱动方法

本文提出了实现了基于尺寸约束离线形成的参数化驱动方法，即通过对尺寸的识别理解，自动形成尺寸对图形的约束及尺寸之间的相互约束，达到尺寸约束的自动组织，从而实现参数化尺寸驱动图形。     

图形输入与图库建立的参数化编码方法及其实现软件PCTS

本文介绍一种参数化编码方法，所提出的轮廓描述表及其约束关系表，用以描述零件形状基本元素之间的拓扑、几何信息及表达其约束关系．对闭合轮廓及非闭合轮廓均适用，并实现了轮廓描述表及约束关系表的交互与自动建立．这种参数化编码方法对图形输入、模具标准零件及非标准零件形状的设计及其图形绘制与修改，具有较大的实用性，所建立的图库具有柔性和扩充性．用该方法实现的参数化编码工具系统ＰＣＴＳ，应用于华中理工大学模具技术国家重点实验室开发的冲裁模ＣＡＤ／ＣＡＭ（ＨＰＣ２．０）系统之中，效果良好     

Free-form geometric modeling by integrating parametric and implicit PDEs

Parametric PDE techniques, which use partial differential equations (PDEs) defined over a 2D or 3D parametric domain to model graphical objects and processes, can unify geometric attributes and functional constraints of the models. PDEs can also model implicit shapes defined by level sets of scalar intensity fields. In this paper, we present an approach that integrates parametric and implicit trivariate PDEs to define geometric solid models containing both geometric information and intensity distribution subject to flexible boundary conditions. The integrated formulation of second-order or fourth-order elliptic PDEs permits designers to manipulate PDE objects of complex geometry and/or arbitrary topology through direct sculpting and free-form modeling. We developed a PDE-based geometric modeling system for shape design and manipulation of PDE objects. The integration of implicit PDEs with parametric geometry offers more general and arbitrary shape blending and free-form modeling for objects with intensity attributes than pure geometric models     

Formulating and solving parametric design problems involving non-interference constraints

Improvements in computer-aided design (CAD) tools can significantly increase designer productivity, since the ability to explore a variety of possible designs quickly and effectively is essential for a designer. Using an optimization tool, systematic exploration of design spaces can be achieved readily. The general goal of the work presented here is to aid design by combining the strengths of optimization techniques with those of CAD systems. The specific objective of this paper is to introduce goal directed geometry (GDG) as a computational framework for parametric design, aiding the formulation of engineering problems with geometric considerations and their solution with a multi-objective optimization package. Using GDG, What if questions can be posed and answered in a systematic fashion. Specific issues to be addressed include the development of a general parametric design problem formulation, development of static and dynamic geometric non-interference constraints for use in this formulation, and investigation of the efficacy of the adaptive linear programming (ALP) multiobjective optimization algorithm in solving such problems. Two examples are presented, one each to illustrate the use of the static and dynamic non-interference constraints. Results demonstrate that the GDG formulation can be applied readily to a wide variety of parametric design problems. Additionally, the ALP algorithm successfully navigates around geometric constraints, although care must be taken when linearizing highly non-linear design spaces.     

基于参数化设计的三维桥梁模型构建

参数化设计是几何体建模的重要手段,而桥梁的三维可视化是当今桥梁信 息化的发展趋势。论文针对桥梁外观参数化模型可视化的需要,对几何体参数化建模的原理 和方法进行了深入探讨。结合桥梁结构特点,分析了主要桥梁组件结构（如T 梁、盖梁柱 式墩、轻型桥台等）构件图的几何和拓扑关系,对组件进行了参数化设计,实现组件的三维 建模;并对组件中特殊图元（如圆弧倒角形墩柱、桥台近似锥面护坡）的绘制算法进行详细 研究;根据各组件间空间位置的拓扑关系,利用参数化变量驱动计算各组件空间位置坐标, 进行桥梁的快速拼接。完成的桥梁三维参数化建模以参数为驱动,用户可以对设计结果进行 可视化修改。所实现的三维参数桥梁可视化系统具有模型构建精致,参数化建模彻底、建模 速度快,参数分类清晰,可视化效果好的特点。     

基于活动约束系统的变量化设计

在变量化设计过程中设计对象可以看作是一个几何约束系统,这个系统由几何元素以及作用于几何元素之间的各种约束关系构成。一个复杂的设计对象所对应的几何约束系统往往包含大量几何元素和约束关系,如果不加区别地把所有的几何元素和约束关系纳入变量化求解的范围,则很难满足交互设计的需要。而另一方面几何约束系统又往往是稀疏系统：（1）作用于任一几何元素的约束很少;（2）与任一约束相关的几何元素很少。基于这一事实给出了一种预处理策略从原始几何约束系统中搜索得到一个规模较小的活动约束系统,变量化求解在活动约束系统上进行。该方法已在自行研制的参数化造型系统GEMS5．0中实现。     

A shape design system using volumetric implicit PDEs

Solid modeling based on partial differential equations (PDEs) can potentially unify both geometric constraints and functional requirements within a single design framework to model real-world objects via its explicit, direct integration with parametric geometry. In contrast, implicit functions indirectly define geometric objects as the level-set of underlying scalar fields. To maximize the modeling potential of PDE-based methodology, in this paper we tightly couple PDEs with volumetric implicit functions in order to achieve interactive, intuitive shape representation, manipulation, and deformation. In particular, the unified approach can reconstruct the PDE geometry of arbitrary topology from scattered data points or a set of sketch curves. We make use of elliptic PDEs for boundary value problems to define the volumetric implicit function. The proposed implicit PDE model has the capability to reconstruct a complete solid model from partial information and facilitates the direct manipulation of underlying volumetric datasets via sketch curves and iso-surface sculpting, deformation of arbitrary interior regions, as well as a set of CSG operations inside the working space. The prototype system that we have developed allows designers to interactively sketch the curve outlines of the object, define intensity values and gradient directions, and specify interpolatory points in the 3D working space. The governing implicit PDE treats these constraints as generalized boundary conditions to determine the unknown scalar intensity values over the entire working space. The implicit shape is reconstructed with specified intensity value accordingly and can be deformed using a set of sculpting toolkits. We use the finite-difference discretization and variational interpolating approach with the localized iterative solver for the numerical integration of our PDEs in order to accommodate the diversity of generalized boundary and additional constraints.     

装配位置约束建模及求解

以基本几何约束组合统一表达装配约束,为提高求解效率,研究了姿态约束和位置约束的可解耦情况下位置约束的解析求解.将基本位置约束映射为移动空间并以参数方程表达,通过移动空间的增量解析求交,满足约束;在姿态约束和位置约束的不可解耦情况,联立基本约束进行整体数值法求解.文中方法保持了基本约束表达的独立性,适合于欠约束系统和完整约束系统.     

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     

参数化设计系统中约束的层次结构

介绍了一种参数化设计系统中约束的层次结构。该结构具有３层约束：工程约束、适配约束和几何约束。适配约束用于将工程约束转换为几何约束,从而实现工程约束对参数化几何图形变动的控制,而整个约束系统的求解也能够通过多个子系统的分别求解来完成。     

Solving Interval Constraints by Linearization in Computer-Aided Design

Current parametric CAD systems require geometric parameters to have fixed values. Specifying fixed parameter values implicitly adds rigid constraints on the geometry, which have the potential to introduce conflicts during the design process. This paper presents a soft constraint representation scheme based on nominal interval. Interval geometric parameters capture inexactness of conceptual and embodiment design, uncertainty in detail design, as well as boundary information for design optimization. To accommodate under-constrained and over-constrained design problems, a double-loop Gauss-Seidel method is developed to solve linear constraints. A symbolic preconditioning procedure transforms nonlinear equations to separable form. Inequalities are also transformed and integrated with equalities. Nonlinear constraints can be bounded by piecewise linear enclosures and solved by linear methods iteratively. A sensitivity analysis method that differentiates active and inactive constraints is presented for design refinement.