An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by symbolically reasoning about geometry. This approach, called degrees of freedom analysis, employs a set of specialized routines called plan fragments that specify how to change the configuration of a set of bodies to satisfy a new constraint while preserving existing constraints. A potential drawback, which limits the scalability of this approach, is concerned with the difficulty of writing plan fragments. In this paper we address this limitation by showing how these plan fragments can be automatically synthesized using first principles about geometric bodies, actions, and topology.