Abstract: This paper presents a new constructive solving approach for systems of geometric constraints.The solver is based on the cluster rewriting approach.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 determine rigid clusters，two types of non-rigid clusters are determined，i.e.clusters with particular degrees of freedom.Many additional problems that cannot be decomposed into rigid clusters are solved，without resorting to expensive algebraic solving methods.

Key words: geometric constraint solving, cluster rewriting, rigid clusters, scalable clusters, radial clusters

摘要： 提出一种新的解决几何约束系统的构造求解方法。这是一种基于簇改写的求解器，新的解决方法扩展了可被解决的问题的种类，保持了簇改写方法的优点。相比先前的簇改写求解器只确定了刚性簇以及两种非刚性簇，也就是有着特定的自由度的簇。许多不能被分解为刚性簇的问题得以解决，而不用求助于那些复杂的代数解决方法。

关键词: 几何约束求解, 簇改写, 刚性簇, 可扩展簇, 放射性簇