Virtual environments for surgical training, planning and rehearsal have the potential to significantly enhance patient treatment and diagnosis. Haptic feedback devices provide forces to the physician through a manipulator, simulating palpation, scalpel cuts, or retraction of tissue. While haptics have been studied in other fields, medical applications of haptics remain in their infancy. We propose a method of haptically rendering isosurfaces (representing hard structures) directly from anatomical datasets rather than through traditional intermediate graphical representations such as polygons. Our algorithm determines an implicit surface representation of a volumetric isosurface on the fly, and renders the structure using standard haptic algorithms to calculate the forces felt by the user. This approach has the advantage of providing easy access to the rich volume dataset containing the actual anatomy. By relating Hounsfield units to density, haptic rendering has the ability to provide different resistances based on the tissue type being rendered. We developed and tested our algorithm using a quadric implicit surface, a common primitive in computer graphics, and have applied it to a variety of anatomical image datasets. Our paper describes the algorithm in sufficient detail to facilitate reproduction by others.