A Quantum Approach to Geometric Constraint Satisfaction

This paper presents an incremental approach to geometric constraint satisfaction that is suitable for interactive design by categorizing solutions into so called quanta. A quantum is a range of solutions with uniform geometric characteristics. In this way, the constraint management system keeps the intermediate solutions in the geometric domain, so that new geometric constraints can be interpreted on the same high level of abstraction. This approach leads to a number of advantages: the system •can handle (perhaps temporarily) under-constrained specifications, •represents both alternative discrete solutions and continuous ranges of solutions, •performs satisfaction locally and incrementally, •supports constraint inference and geometric reasoning, •preserves the declarative semantics of constraints.