Interactive physically-based manipulation of discrete/continuous models

Physically-based modeling has been used in the past to support a variety of interactive modeling tasks including free-form surface design, mechanism design, constrained drawing, and interactive camera control. In these systems, the user interacts with the model by exerting virtual forces, to which the system responds subject to the active constraints. In the past, this kind of interaction has been applicable only to models that are governed by continuous parameters. In this paper we present an extension to mixed continuous/discrete models, emphasizing constrained layout problems that arise in architecture and other domains. When the object being dragged is blocked from further motion by geometric constraints, a local discrete search is triggered, during which transformations such as swapping of adjacent objects may be performed. The result of the search is a "nearby" state in which the target object has been moved in the indicated direction and in which all constraints are satisfied. The transition to this state is portrayed using simple but effective animated visual effects. Following the transition, continuous dragging is resumed. The resulting seamless transitions between discrete and continuous manipulation allow the user to easily explore the mixed design space just by dragging objects. We demonstrate the method in application to architectural floor plan design, circuit board layout, art analysis, and page layout.