Just as we can work with two-dimensional floor plans to communicate 3D architectural design, we can exploit reduced-dimension shadows to manipulate the higher-dimensional objects generating the shadows. In particular, by taking advantage of physically reactive 3D shadow-space controllers, we can transform the task of interacting with 4D objects to a new level of physical reality. We begin with a teaching tool that uses 2D knot diagrams to manipulate the geometry of 3D mathematical knots via their projections; our unique 2D haptic interface allows the user to become familiar with sketching, editing, exploration, and manipulation of 3D knots rendered as projected images on a 2D shadow space. By combining graphics and collision-sensing haptics, we can enhance the 2D shadow-driven editing protocol to successfully leverage 2D penand-paper or blackboard skills. Building on the reduced-dimension 2D editing tool for manipulating 3D shapes, we develop the natural analogy to produce a reduced-d...
Hui Zhang, Andrew J. Hanson