Perceptualization Of Geometry Using Intelligent Haptic And Visual Sensing

We present a set of paradigms for investigating geometric structures using haptic and visual sensing. Our principal test cases include smoothly embedded geometry shapes such as knotted curves embedded in 3D and knotted surfaces in 4D, that contain massive intersections when projected to one lower dimension. One can exploit a touch-responsive 3D interactive probe to haptically override this conflicting evidence in the rendered images, by forcing continuity in the haptic representation to emphasize the true topology. In our work, we exploited a predictive haptic guidance, a "computer-simulated hand" with supplementary force suggestion, to support intelligent exploration of geometry shapes that will smooth and maximize the probability of recognition. The cognitive load can be reduced further when enabling an attention-driven visual sensing during the haptic exploration. Our methods combine to reveal the full richness of the haptic exploration of geometric structures, and to overcome the limitations of traditional 4D visualization.