Computer haptics, an emerging field of research that is analogous to computer graphics, is concerned with the generation and rendering of haptic virtual objects. In this paper, we propose an efficient haptic rendering method for displaying the feel of 3-D polyhedral objects in virtual environments (VEs). Using this method and a haptic interface device, the users can manually explore and feel the shape and surface details of virtual objects. The main component of our rendering method is the “neighborhood watch” algorithm that takes advantage of precomputed connectivity information for detecting collisions between the end effector of a force-reflecting robot and polyhedral objects in VEs. We use a hierarchical database, multithreading techniques, and efficient search procedures to reduce the computational time such that the haptic servo rate after the first contact is essentially independent of the number of polygons that represent the object. We also propose efficient methods for displaying surface properties of objects such as haptic texture and friction. Our haptic-texturing techniques and friction model can add surface details onto convex or concave 3-D polygonal surfaces. These haptic-rendering techniques can be extended to display dynamics of rigid and deformable objects.