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A non-rigid cluster rewriting approach to solve systems of 3D geometric constraints

机译：解决3D几何约束系统的非刚性簇重写方法

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摘要

We present a new constructive solving approach for systems of 3D geometric constraints. The solver is based on the cluster rewriting approach, which can efficiently solve large systems of constraints on points, and incrementally handle changes to a system, but can so far solve only a limited class of problems. The new solving approach extends the class of problems that can be solved, while retaining the advantages of the cluster rewriting approach. Whereas previous cluster rewriting solvers only determined rigid clusters, we also determine two types of non-rigid clusters, i.e. clusters with particular degrees of freedom. This allows us to solve many additional problems that cannot be decomposed into rigid clusters, without resorting to expensive algebraic solving methods. In addition to the basic ideas of the approach, an incremental solving algorithm, two methods for solution selection, and a method for mapping constraints on 3D primitives to constraints on points are presented.
机译：我们为3D几何约束系统提出了一种新的构造性求解方法。该求解程序基于集群重写方法，可以有效地解决大型系统对点的约束，并逐步处理系统的更改，但到目前为止只能解决有限的问题。新的解决方法扩展了可以解决的问题类别，同时保留了集群重写方法的优点。以前的集群重写求解器仅确定刚性集群，而我们还确定了两种非刚性集群，即具有特定自由度的集群。这使我们能够解决许多无法分解为刚性簇的附加问题，而无需诉诸昂贵的代数求解方法。除了该方法的基本思想外，还提出了一种增量求解算法，两种用于求解的方法，以及一种将3D图元上的约束映射到点上约束的方法。

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