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

机译：使用相关性分析求解3-D几何约束系统的一种建设性方法

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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.
机译：解决3D几何约束系统比2D中的几何约束系统复杂得多，这是因为变量的数量更大，并且2D中有效的某些结果无法扩展到3D。在本文中，我们提出了一种新的基于DOF的图构造方法来求解几何约束系统，该方法可以基于相关性分析有效地处理良好，过度和欠约束的系统。基本思想是，由于几何元素之间的约束，某些几何元素的解依赖于其他几何元素。如果某些几何元素相互依赖，则必须将它们一起求解。在我们的方法中，我们首先确定所有结构上冗余的约束，然后添加一些约束以很好地约束系统。并且我们证明了在处理约束不足的情况后约束系统的顺序不超过原始系统乘以5的顺序。之后，我们应用了递归搜索过程来识别所有聚类，这证明是有能力的。获得良好约束的系统的最小降阶结果的方法。我们还简要描述了约束评估阶段，并展示了该方法的实施结果。

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