Incremental Constraint Satisfaction for Variational Design Systems 1

Variational Design is a general and powerful technique for supporting the preliminary stages of a design. It allows the coupling of engineering constraints and geometric constraints by converting them into a system of equations. Such a facility provides the user with appropriate tools to explore design alternatives during the early design stages. However, algorithms employed by the current variational modellers iteratively evaluate the entire set of equations whenever a new constraint is inserted. This hinders the interactive design performance when dealing with large constraint equation sets. The paper presents an algorithm to speed up the constraint equation solving process of a Variational Design system. Based on an incremental approach, the algorithm maintains an evolving solution by locally accommodating an inserted constraint into the previously solved equation set. Constraint cycles as well as underand over-constrained situations, which constantly emerge during the design process, are also incrementally handled by the algorithm.