QOCA: A Constraint Solving Toolkit for Interactive Graphical Applications

We describe an object-oriented constraint solving toolkit, QOCA, designed for interactive graphical applications. It has a simple yet powerful interface based on the metric space model for constraint manipulation. In this model interaction with the constraint solver can occur in three ways: a constraint may be added, a constraint may be deleted, or values for designated “edit” variables may be suggested. Currently, QOCA supports linear arithmetic constraints and two different metrics: the square of the Euclidean distance and Manhattan distance. It provides three solvers, all of which rely on keeping the constraints in solved form and relies on novel algorithms for efficient resolving of constraints during direct manipulation. We provide a thorough evaluation of QOCA, both of the interface design and the speed of constraint solving.