Intelligent systems and simulated environments require intuitive interfaces for man-machine interaction. These may include visual, auditory, and haptic interfaces. Compared to the presentation of visual and auditory information, methods for haptic display are not as well developed. To exploit the possibility of haptic interaction for performing assembly or dis-assembly tasks in an electronic prototyping environment, it is imperative to develop the necessary real-time algorithms and software systems, in addition to the force/torque-feedback devices. The PI proposes to design robot algorithms for haptic interaction. Specifically, these include interactive contact determination for non-linear models and deformable bodies, and fast penetration depth computation between general three-dimensional geometric models. The PI will develop prototype software systems and integrate them with force-feedback devices for haptic interaction in virtual prototyping environments. Besides force display, the resulting algorithms and systems will also be useful for robot motion planning and dynamic simulation. The research efforts will be complemented by developing a teaching curriculum in geometric computing for robotics and virtual prototyping, in order to enable better human resource development. In addition to the intellectual pursuit of our research goals, the PI will also interact with potential users of the proposed research to facilitate technology transition.