Geometric constraint solver for interactive design of line drawings

A geometric constraint solver for finding legal configurations for an under-constrained set of geometric components is proposed. While making drawings interactively, the user usually specifies few geometric constraints explicitly because some constraints are not clear to him- or her-self, or it is not practical to specify all constraints at any early design stage. Theoretically, the full geometric constraints are necessary to define a unique layout of every geometric components, but it is naturally not given throughout the process. Therefore, in such an under-constrained situation, the lack of constraints must be supplemented properly to determine the final layout of components remaining undefined. For this purpose, we propose a geometric constraint solver that works in two phases: the former is to satisfy all the explicit constraints imposed by the user, and the latter is to choose appropriate value instances for every geometric component whose layout is not yet determined. We implemented a constraint-based interactive system for designing line drawings which is composed of the solver and the interactive module to let the user input geometric modi.cation commands incrementally, and proved its effectiveness by some experiments.