Physically Interacting with Four Dimensions

We exploit the combination of a virtual world containing physicallyinteracting 4D objects with a multimodal haptics-driven user-interface model; the goal is to facilitate the development of accurate cognitive models enabling the visualization of 4D space. Our primary test domain supports tactile interaction with physically colliding and deformable curves and surfaces embedded in 4D, an important and challenging subject area of classical topology. We implement intricate interactions involving 4D curves and surfaces by haptically manipulating 3D projections of these objects.