The project concerns high-performance haptic (sense of touch) interaction with three-dimensional (3D) computed (virtual) and real environments. The principal research objective is to quantitatively determine how much reality is achievable in 3D haptic/visual virtual and remote real environments. The approach is based on six-degree-of-freedom (6-DOF) haptic interaction technology using Lorentz magnetic levitation. Both proprioceptive (kinesthetic) senses of the fingers, hand, and wrist as well as the tactile senses in the skin are involved in the interaction. Lorentz levitation provides higher bandwidths and motion resolutions than are available with traditional technologies. The project includes i) adding direct force-torque sensing, combining favorable aspects of both impedance- and admittance-type devices; ii) the creation of a highly realistic 3D peg-in-hole virtual environment; iii) development of an elastic deformation environment with buckling phenomena; iv) comparison of subjects' interaction with virtual, real, and remote-real environments, and v) performance of a suite of psychophysical experiments to quantitatively measure the degree of reality provided. The quantitative characterization of haptic interaction transparency afforded by this approach contrasts markedly with pure engineering measurements or purely subjective evaluations. The research results provide knowledge for the engineering science of haptic interface design while helping to elucidate the nature of the human haptic interaction process. This could lead to the future widespread use of haptic technology for computer augmented design, medical training, telemanipulation and telepresence systems, vehicle piloting simulation, and the exploration of complex multi-dimensional data sets. The project has an important educational impact which includes the study of haptics in undergraduate and graduate course work.