基于几何约束求解的完备方法

针对参数化CAD在约束求解中的应用,提出了基于智能连杆的算法,该算法在扩充几何作图范围、改善算法复杂度方面都有明显的优势.将其同LIMO算法、几何变换方法、C-Tree算法、数值求解方法等方法相互融合,能够组成一套非常完备的几何约束求解框架,来完成对平面和空间几何约束问题的自动求解与图像生成.将该算法应用于智能动态几何软件的设计中,实验显示可以取得令人满意的结果.     

自适应微调扰动和声搜索算法几何约束求解研究*

几何约束求解的方法关系到特征造型系统的性能,为提高几何约束求解的速度,将和声搜索算法应用于几何约束求解中。通过优先选择较小的和声库,利用最好解的评价值确定微调扰动的幅度,并将其嵌入到拉斯维加斯算法中,提高了和声搜索算法的性能。实验结果表明,改进的和声算法具有自适应性,能有效克服局部收敛问题,提高了求解速度。     

Geometric constraint solving with conics and linkages

Most geometric construction methods of geometric constraint solving systems use line and circle (rule and compass) as basic drawing tools. In this paper, by introducing conics and linkages, we provide a set of complete drawing tools for the construction approach of geometric constraint solving. Using these tools, we may enlarge the drawing scope of the construction approach and still keep the elegant style of geometric solutions to geometric constraint solving. As applications, we obtain pure geometric solutions to three sets of well-known constraint problems: the 10 Apollonian drawing problems, the 13 cases of a smallest tri-connected constraint graph, and constraint problems with distance constraints only.     

Extensions of the witness method to characterize under-, over- and well-constrained geometric constraint systems

This paper describes new ways to tackle several important problems encountered in geometric constraint solving, in the context of CAD, and which are linked to the handling of under- and over-constrained systems. It presents a powerful decomposition algorithm of such systems.Our methods are based on the witness principle whose theoretical background is recalled in a first step. A method to generate a witness is then explained. We show that having a witness can be used to incrementally detect over-constrainedness and thus to compute a well-constrained boundary system. An algorithm is introduced to check if anchoring a given subset of the coordinates brings the number of solutions to a finite number.An algorithm to efficiently identify all maximal well-constrained parts of a geometric constraint system is described. This allows us to design a powerful algorithm of decomposition, called W-decomposition, which is able to identify all well-constrained subsystems: it manages to decompose systems which were not decomposable by classic combinatorial methods.     

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。     

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。     

基于改进鱼群算法的几何约束求解

几何约束求解是CAD建模中的关键技术。针对求解质量不高和求解速度慢的问题,进行了研究。提出了一种鱼群算法和混沌算法相结合的几何约束求解方法。首先,将CAD模型中的几何约束关系表示为一组代数方程组;然后,利用代数方程组来构造目标函数。将几何约束求解问题转换为目标函数的优化问题。最后,使用混沌算法来改进鱼群算法以寻找目标函数的最优解。实验结果表明：该方法可以有效地解决几何约束问题。     

交互更新模式的量子遗传算法的几何约束求解

目的针对传统量子遗传算法无法充分利用种群中未成熟个体信息的不足,提出了基于交互更新模式的量子遗传算法(IUMQGA)并应用于几何约束求解中。方法几何约束问题的约束方程组可转化为优化模型,因此约束求解问题可以转化为优化问题。采用将遗传算法与量子理论相结合的量子遗传算法,使用双串量子染色体结构,使用交互更新策略将遗传算法中的交叉操作利用量子门变换来实现,根据不同情况采用不同的交互更新策略。这里的交互,指的是两个个体进行信息交换的过程,该过程用以产生新的个体。这不仅增加了个体间信息的交换而且充分利用了种群中未成熟个体的信息,提高了算法的收敛速度。结果通过非线性方程实例和几何约束实例测试并与其他方法比较表明,基于交互更新模式的量子遗传算法求解几何约束问题具有更好的求解精度和求解速率。双圆外公切线问题实例中,IUMQGA算法比QGA算法稳定;单圆填充问题和双圆外公切线问题实例中,通过实验求得各变量的最优值与其相应的精确值的误差在1E-2以下。结论采用交互更新模式的量子遗传算法可以很好地求解几何约束问题。     

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.     

用于三维几何约束求解的分组重写方法

提出一种基于分组重写的解决三维几何约束的方法,原有的算法在解决大型系统几何约束求解时效率较低,系统开销较大,并且由于算法规则的局限性,使得很多复杂系统无法解决,包括三维几何约束问题。该方法提出了两种新的分组表示类型,拓展子集和放射子集,使得分组更加直观,准确,并有效地提高了求解效率,减小了开销,方法在三维领域更能发挥其作用,能够满足计算机辅助造型中集合造型的需求。     

动态种群划分量子遗传算法求解几何约束

几何约束问题的约束方程组可转化为优化模型,因此约束求解问题可以转化为优化问题。针对传统量子遗传算法个体间信息交换不足,易使算法陷入局部最优的缺点,提出了动态种群划分量子遗传算法（dynamic population divided quantum genetic algorithm,DPDQGA）,并将其应用于几何约束求解中。该算法种群中的个体按照一定规则自发地进行信息交换。在每一代进化的开始阶段,分别对两个初始种群中的个体计算个体适应度。将两个种群合并,使用联赛选择的方法为种群中的个体打分,并按照得分对种群进行排序。最后将合并的种群重新划分为两个子种群。实验表明,基于动态种群划分的量子遗传算法求解几何约束问题具有更好的求解精度和求解速率。     

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     

Incremental constraint modelling in a feature modelling system

The techniques of constraint propagation have recently been successfully applied to feature-based design. Because of their speed, constraint propagation methods allow incremental design and rapid local modifcations of the part. However, cyclic constraints cause serious problems to current constraint propagation algorithms. Variational geometric design systems can, in principle, manage these cases. Unfortunately, this typically requires complete re-evaluation of the underlying set of constraint equations, making the method unsuitable for interactive use. The proposed system aims to localize the problem of constraint solving and maintenance. The constraint graph of the part or assembly is divided into several independent partial graphs, subsystems. Afterwards, each subsystem is handled separately using a selected constraint solving technique for the subsystem.     

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.     

基于雁群启示的粒子群优化算法的几何约束求解

几何约束是约束求解技术中最关键的问题之一.求解一个几何约束问题的最终目的是确定几何图形中每一个几何体的具体坐标位置.几何约束问题可以等价为求解非线性方程组问题.约束问题转化为一个优化问题.本文采用基于雁群启示的粒子群优化算法来求解该问题.该算法受雁群飞行特征启发,一方面将粒子排序,每个粒子跟随其前面那个较优粒子飞行,保持了多样性;另一方面使每个粒子利用更多其他粒子的有用信息,粒子之间的竞争被增强.两个方面的结合将平衡速度和精度之间的矛盾.实验表明,该方法可以提高几何约束求解的效率和收敛性.     

Fast iterative refinement of articulated solid dynamics

A new dynamics algorithm for articulated solid animation is presented. It provides enhancements of computational efficiency and accuracy control with respect to previous solutions. Iterative refinement allows us to perform interactive animations which could be only computed off-line using previous methods. The efficiency results from managing two sets of constraints associated with the kinematic graph, and proceeding in two steps. First, the acyclic constraints are solved in linear time. An iterative process then reduces the closed-loop errors while maintaining the acyclic constraints. This allows the user to efficiently trade off accuracy for computation time. We analyze the complexity and investigate practical efficiency compared with other approaches. In contrast with previous research, we present a single method which is computationally efficient for acyclic bodies as well as for mesh-like bodies. The accuracy control is provided by the iterative improvement performed by the algorithm and also from the existence of two constraint priority levels induced by the method. Used in conjunction with a robust integration scheme, this new algorithm allows the interactive animation of scenes containing a few thousand geometric constraints, including closed loops. It has been successfully applied to real-time simulations     

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.     

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...     

A Repeated-Update Problem in the DeltaBlue Algorithm

We observe a repeated-update problem in the process of updating walkabout strengths of the DeltaBlue algorithm, which is known as a fast constraint solving method based on local propagation. According to the basic references on the DeltaBlue algorithm, the time complexity of the planning phase is described as O(MN) for a constraint problem such that the number of constraints is N and the maximum number of methods a constraint has is M . We, however, point out that the time complexity is not O(MN) using a very simple example. In this example, the time complexity is exponential order for N . Then we present a corrected DeltaBlue algorithm whose time complexity is O(EN ²) for a constraint problem such that the number of constraints is N and the maximum number of variables a constraint has is E . Finally we measure the performance of the corrected DeltaBlue algorithm using two benchmarks.