We present an approach for handling geometric constraint problems
with under-constrained configurations.
The approach works by completing the given set of constraints with
constraints that can be defined either automatically or drawn from an
independently given set of constraints placed on the geometries of
the problem. In both cases, the resulting completed set of constraints
is not over-constrained. If every well-constrained subproblem in the
given under-constrained configuration is solvable, the completed
constraint problem is also solvable.
Keywords: Constraint solving, geometric constraints, rule-based
and graph-based constraint solvers, over- and underconstrained systems.