Constraint objects - integrating constraint definition and interaction

This paper describes the implementation of a new constraint-based technique for direct manipulation in interactive CAD. We introduce so called Constraint Objects and Parameter Objects which constitute an object-oriented view on constraints. A graph algorithm is employed to analyze the relative degrees of freedom and dependencies between objects for which a geometric relation (distance, angle, parallel, congruence, etc.) has been defined. The dependency graph is used to evaluate the changes during interactive manipulations. Also, a 2-D profile editor has been realized for interactively constructing lines and circles in various ways. Each construction operation, implicitly defines constraints (derived from post conditions) to capture the intent of the operation. This way, imperative definition (by a sequence of construction operations) and declarative definition (by constraints) of geometric shapes can be combined naturally. This greatly increases the flexibility of design systems, simplifying the design process, especially in the early stages.