Function-based visualization and haptic rendering in shared virtual spaces

We seek to further expand the collaborative potential of shared virtual spaces by using haptic force-feedback. We propose how to define tangible physical properties of the objects, together with their geometry and appearance, by using mathematical functions. We illustrate this concept by developing software which allows us to touch and feel surfaces of VRML and X3D objects, convert them to solid objects, as well as create any other solid objects using the function-based extension of VRML and X3D. We define geometry, appearance and tangible physical properties of the solid objects by implicit, explicit and parametric functions straight in the VRML/X3D code or in loadable libraries. Since the function-defined models are small in size, it is possible to perform their collaborative interactive modifications with concurrent synchronous visualization at each client computer with any required level of detail. We illustrate the proposed models with several application examples.