Navigation through 3D spaces is required in many i n teractive 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 b e t ween the goal of such a n a vigation activity, the control device, and the skills of the average user. We propose a uni ed 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 demonstrate the approach w i t h a v aried spectrum of examples including terrain models, interior architectural spaces, and complex molecules.

Figure 1: Assisted collaborative exploration scenario with the leader's guide avatar being a dog, and two groups of following collaborators. Observe that the guide avatar points to objects of interest even if they are not aligned with the direction of locomotion or the observer's ground plane, and that the local leader serves as the guide avatar for all attached followers. AbstractWe approach the problem of exploring a virtual space by exploiting positional and camera-model constraints on navigation to provide extra assistance that focuses the user's explorational wanderings on the task objectives. Our specific design incorporates not only task-based constraints on the viewer's location, gaze, and viewing parameters, but also a personal "guide" that serves two important functions: keeping the user oriented in the navigation space, and "pointing" to interesting subject areas as they are approached. The guide's cues may be ignored by continuing in motion, but if the user stops, the gaze shifts automatically toward whatever the guide was interested in. This design has the serendipitous feature that it automatically incorporates a nested collaborative paradigm simply by allowing any given viewer to be seen as the "guide" of one or more viewers following behind; the leading automated guide (we tend to select a guide dog for this avatar) can remind the leading live human guide of interesting sites to point out, while each real human collaborator down the chain has some choices about whether to follow the local leader's hints. We have chosen VRML as our initial development medium primarily because of its portability, and we have implemented a variety of natural modes for leading and colEmail: fewernert, hansong@cs.indiana.edu laborating, including ways for collaborators to attach to and detach from a particular leader.

We attack the problem of image-based rendering with occlusions and general camera motions by using distorted multiperspective images; such images provide multiple-viewpoint photometry similar to the paintings of cubist artists. We take scene geometry, in contrast, to be embodied in mappings of viewing rays from their original 3D intercepts into the warped multiperspective image space. This approach allows us to render approximations of scenes with occlusions using time-dense and spatially sparse sequences of camera rays, which is a significant improvement over the storage requirements of an equivalent animation sequence. Additional data compression can be achieved using sparse time keyframes as well. Interpolating the paths of sparse time key-rays correctly in image space requires singular interpolation functions with spatial discontinuities. While there are many technical questions yet to be resolved, the employment of these singular interpolation functions in the multiperspective image space appears to be of potential interest for generating general-viewpoint scene renderings with minimal data storage.