Making constraint solvers more usable: overconstraint problem

The richness and expressive power of geometric constraints causes unintended ambiguities and inconsistencies during their solution or realization. For example, geometric constraint problems may turn out to be overconstrained requiring the user to delete one or more of the input constraints, and the solutions must then be dynamically updated. Without proper guidance by the constraint solver, the user must have profound insight into the mathematical nature of constraint systems and understand the internals of the solver algorithm. But a general user is most likely unfamiliar with those problems, so that the required interaction with the constraint solver may well be beyond the user's ability. In this paper, we present strategies and techniques to empower the user to deal effectively with the overconstraint problem while not requiring him or her to become an expert in the mathematics of constraint solving.We formulate this problem as a series of formal requirements that gel with other essentials of constraint solvers. We then give algorithmic solutions that are both general and efficient (running time typically linear in the number of relevant constraints).