  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.
