In this paper we present a framework that allows the haptic rendering of interactions between the human hand and a virtual environment consisting of polygonal objects. The proposed solution creates a representation of the human hand through simple geometric primitives (spheres, cylinders etc.) and allows the fast collision detection and calculation of forces of interaction. The forces are calculated with precision and smoothness, especially at the fingertips, where the human haptic perception is more sensitive. The area of each contacted region is taken into account to correctly weigh the importance of each force we calculate. The objective is to give a simulation tool that will allow the use of exoskeletons for the human hand with an improved level of precision, which is necessary for the correct evaluation of these haptic devices and their efficient use.