Space walking [topological manifold visualization]

Proposes an interactive method for exploring topological spaces based on the natural local geometry of the space. Examples of spaces appropriate for this visualization approach occur in abundance in mathematical visualization, surface and volume visualization problems, and scientific applications such as general relativity. Our approach is based on using a controller to choose a direction in which to “walk” a manifold along a local geodesic path. The method automatically generates orientation changes that produce a maximal viewable region with each step of the walk. The proposed interaction framework has many natural properties to help the user develop a useful cognitive map of a space and is well-suited to haptic interfaces that may be incorporated into desktop virtual reality systems