三维几何约束系统的等价性分析

针对过约束、完整约束和欠约束三维几何约束系统的求解问题,提出了等价性分析方法.该方法基于三维几何约束系统的内在等价性,充分挖掘几何领域知识,依据拆解约束闭环、缩减约束闭环和析出约束闭环等原则,采用等价约束替换来处理几何约束闭环问题,优化几何约束图的结构,实现几何约束系统的优化分解.最后用多个实例验证了该方法的正确性和有...     

Dealing with redundancy and inconsistency in constructive geometric constraint solving

General constructive geometric constraint solvers are pre-processed by a degree-of-freedom analysis, which enables efficient graph decomposition and recombination. However, all these methods are based on the assumption that structural rigidity automatically assures solvability. In this paper, we show that this assumption fails in numerous, even the most basic, configurations. We introduce several simple but efficient rules aimed to additionally analyse solvability in such cases. Another novelty addresses conditional constraints between three or more geometric parts, rules for their simplification and a redundancy check. All these functionalities are built into our original 2D geometric constraint solver, based on concepts of rigid clusters and constrained-angle (CA) sets.     

面向欠约束几何系统的一种同伦求解方法

针对几何约束系统的数值求解过程中，经常发生的数值不稳定性问题，构造了一种面向欠约束系统的同伦方法，并将其与现有的求解与分解方法有机地结合起来，提出了一种牛顿－同伦混合方法，在牛顿迭代失败的位置自动调用欠约束同伦法，既提高了几何约束求解器的效率，同时又保证了求解的效率。     

A constructive approach to solving 3-D geometric constraint systems using dependence analysis

Solving geometric constraint systems in 3-D is much more complicated than that in 2-D because the number of variables is larger and some of the results valid in 2-D cannot be extended for 3-D. In this paper, we propose a new DOF-based graph constructive method to geometric constraint systems solving that can efficiently handle well-, over- and under-constrained systems based on the dependence analysis. The basic idea is that the solutions of some geometric elements depend on some others because of the constraints between them. If some geometric elements depend on each other, they must be solved together. In our approach, we first identify all structurally redundant constraints, then we add some constraints to well constrain the system. And we prove that the order of a constraint system after processing under-constrained cases is not more than that of the original system multiplied by 5. After that, we apply a recursive searching process to identify all the clusters, which is shown to be capable of getting the minimum order-reduction result of a well-constrained system. We also briefly describe the constraint evaluation phase and show the implementation results of our method.     

一种基于图分解的几何约束求解方法

为了提高几何约束求解的效率和鲁棒性 ,对基于图的构造方法进行了改进 ,即加入虚约束进行扩展和过约束问题的一致性判定 ,提出了一种基于图分解的方法 ,用此方法可以处理包括完全约束、过约束和欠约束等多种情况的约束求解问题 ,另外 ,在该方法中还通过引入分解树将约束求解的范围由整体下降到局部 ,使大部分求解过程能够采用几何求解实现 ,提高了求解和后续修改的效率 ,通过实验数据测试证明 ,该方法对于大型约束求解问题可以达到实时处理的效果 ,具有较强的实用性     

二维几何约束求解器

开发了一个二维几何约束求解器.该求解器是新一代智能CAD系统的核心,它采用了基于图和规则的几何推理方法,高效、稳定、实用.论文提出了几何约束模型及其约束图表示,深入介绍了基于点刚体归约的几何推理算法,描述了求解器的体系结构.     

Singularity Analysis of Geometric Constraint Systems

Singularity analysis in an important subject of the geometric constraint satisfaction problem.In this paper,three kinds of singularities are described and corresponding identifcation methods are presented for both under0constrained systems and over-constrained systems,Another special but common singularity for under-constrained geometric systems,pseudo-singularity,is analyzed.Pseudo-singularity is caused by a variety of constraint mathching of under-constrained systems and can be removed by improving constraint distribution.To avoid pseudo-singularity and decide redundant constraints adaptively,a differentiaiton algorithm is proposed in the paper.Its corrctness and effciency have been validated through its practical applications in a 2D/3D geometric constraint solver CBA.     

A Constructive Approach to Solving Geometric Constraint Systems

This paper proposes a constructive approach to solving geometric constraint systems.The approach incorporates graph-based and rule-based approaches, and achieves interactive speed.The paper presents a graph representation of geometric conStraint syStems, and discusses in detailthe algorithm of geometric reasoning based on poinl-cluster reduction. An example is made forillustration.     

混合式几何约束满足的研究

几何约束系统可以分为陈述式和构造式两类。为了使基于约束的设计更加符合使用要求,参数化CAD系统需要综合满足两类约束。文中研究了三维情况下和构造统一的约束满足策略,通过引入形状自由度的概念,将形状变化和集团变化统一处理。约束系统采用约束图来表示,各个子系统之间的层次结构利用约束层次树来表示。采用剪枝和凝聚相结合的策略实现了欠约束和完备约束系统的分解,使用解析法和数值法对约束进行求解。该策略已经在参数化CAD系统GEMS5．0的二维和三维上实现。     

全参数化设计实现机理及约束可视管理

为了提高设计效率,提出一种全参数化设计方法,系统阐述其实现机理,给出自动施加约束、约束实时显示及约束可视管理算法。并运用AutoCAD二次开发技术,将几何约束求解器CBA和CAD绘图平台有机结合,实现全参数化绘图。     

Computing parameter ranges in constructive geometric constraint solving: Implementation and correctness proof

In parametric design, changing values of parameters to get different solution instances to the problem at hand is a paramount operation. One of the main issues when generating the solution instance for the actual set of parameters is that the user does not know in general which is the set of parameter values for which the parametric solution is feasible. Similarly, in constraint-based dynamic geometry, knowing the set of critical points where construction feasibility changes would allow to avoid unexpected and unwanted behaviors.We consider parametric models in the Euclidean space with one internal degree of freedom. In this scenario, in general, the set of values of the variant parameter for which the parametric model is realizable and defines a valid shape is a set of intervals on the real line.In this work we report on our experiments implementing the van der Meiden Approach to compute the set of parameter values that bound intervals for which the parametric object is realizable. The implementation is developed on top of a constructive, ruler-and-compass geometric constraint solver. We formalize the underlying concepts and prove that our implementation is correct, that is, the approach exactly computes all the feasible interval bounds.     

几何约束求解的简化迭代算法

针对几何约束系统图分解中复合顶点的求解问题,提出复合顶点的图分解算法和等价自由变量的简化迭代求解算法.通过去除复合顶点部分边界约束对复合顶点进行图分解,对求解序列中的欠约束顶点添加等价自由变量、以等价自由变量的部分迭代求解、替代系统的整体数值求解,以提高求解效率和稳定性.该算法具有很强的通用性,并在实际应用中得到验证.     

一种设计分解的正确性证明

二维变量化设计系统可以用含有n个未知数、m个方程的非线性方程组表示．通过设计分解可以提高几何约束求解的效率和数值稳定性．给出了一种基于图论的设计分解方法及其正确性证明．该方法可以（1）处理结构欠约束系统的分解;（2）检测出冗余约束．分解算法在有限步内终止,其结果是结构相容的     

h-graphs: A new representation for tree decompositions of graphs

In geometric constraint solving, 2D well constrained geometric problems can be abstracted as Laman graphs. If the graph is tree decomposable, the constraint-based geometric problem can be solved by a Decomposition–Recombination planner based solver. In general decomposition and recombination steps can be completed only when steps on which they are dependent have already been completed. This fact naturally defines a hierarchy in the decomposition–recombination steps that traditional tree decomposition representations do not capture explicitly.In this work we introduce h-graphs, a new representation for decompositions of tree decomposable Laman graphs, which captures dependence relations between different tree decomposition steps. We show how h-graphs help in efficiently computing parameter ranges for which solution instances to well constrained, tree decomposable geometric constraint problems with one degree of freedom can actually be constructed.     

面向集成变量化设计的三维几何约束求解方法

针对集成变量化设计中三维几何约束和装配几何约束的混合建模与求解问题,提出改进的有向图方法.该方法采用几何约束的基本约束表达和几何实体的抽象对偶实体表达,引入定向弧表达实体之间的内在依赖关系建立混合几何约束有向图模型;结合约束有向图的优化处理,实现了几何约束系统的细粒度分解和高效并行求解.最后用实例验证了文中方法的正确性和有效性.     

动态识别三维几何约束冲突的方法研究

基于装配几何特征的广义几何约束图,避免了传统几何约束图的超图性质和模糊性,为几何约束满足问题提供了一个清晰的分析模型。文中以此模型来分析产生约束冲突的原因。空间分析法定义和推导了约束满足空间约束满足条件,提出了自由空间和自由度的计算方法,并据此在动态满足三维几何约束的过程中识别约束冲突,明确指出产生约束冲突的原因。     

A neural network approach to CSG-based 3-D object recognition

Describes the recognition subsystem of a computer vision system based on constructive solid geometry (CSG) representation scheme. Instead of using the conventional CSG trees to represent objects, the proposed system uses an equivalent representation scheme-precedence graphs-for object representation. Each node in the graph represents a primitive volume and each are between two nodes represents the relation between them. Object recognition is achieved by matching the scene precedence graph to the model precedence graph. A constraint satisfaction network is proposed to implement the matching process. The energy function associated with the network is used to enforce the matching constraints including match validity, primitive similarity, precedence graph preservation, and geometric structure preservation. The energy level is at its minimum only when the optimal match is reached. Experimental results on several range images are presented to demonstrate the proposed approach     

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.     

二维几何约束多解问题的研究

对采用自由度分析方法求解几何约束问题进行了研究.对几何约束问题的图用自由度分析的方法进行分解可以使约束系统得到充分分解,并可以对高耦合的几何约束问题进行分离.通过转换把几何元素的求解问题,转换为点的定位问题,从而使几何约束的多解问题得到简化,几何约束的多解问题被归结为初始设计图形中点和直线间的相对关系.对未知半径和圆心的圆的求解问题进行了讨论,提供了几种比较通用的算法,可以简化程序的设计.     

几何约束有向图的规划分解研究

在基于有向图表达的几何约束系统中,几何约束的匹配方向、分布状态以及有向图中强连通分量的规模直接影响到整个约束系统的求解;如何对几何约束系统进行合理规划,得到正确有效的求解序列,是目前约束分解研究的重要内容。该文提出了一个规划分解算法,它针对欠约束几何系统的特点,能够优化约束的初始匹配方向,对于约束匹配过程中生成的强连通子图,通过调整约束匹配方向,自适应地改善约束分布,从而减小强连通子图的规模,以求得到几何约束系统正确而高效的求解序列。同时,基于规划分解算法,完成了约束的奇异性分析,提供了面向分解的奇异性分析算法。