Constrained 3D navigation with 2D controllers

Navigation through 3D spaces is required in many interactive graphics and virtual reality applications. We consider the subclass of situations in which a 2D device such as a mouse controls smooth movements among viewpoints for a "through the screen" display of a 3D world. Frequently, there is a poor match between the goal of such a navigation activity, the control device, and the skills of the average user. We propose a unified mathematical framework for incorporating context-dependent constraints into the generalized viewpoint generation problem. These designer-supplied constraint modes provide a middle ground between the triviality of a single camera animation path and the confusing excess freedom of common unconstrained control paradigms. We illustrate the approach with a variety of examples, including terrain models, interior architectural spaces, and complex molecules.