Haptics is a field of robotics that involves many aspects of engineering, requiring the collaboration of different disciplines like mechanics, electronics, control theory and computer science. Although multi-disciplinarity is an element in common with other robotic application, haptic system has the additional requirement of high performance because of the human perception requirement of 1KHz feedback rate. Such high computing requirement impacts the design of the whole haptic system but it is has particular effects in the design and implementation of haptic rendering algorithms. In the chain of software and hardware components that describe a haptic system the haptic rendering is the element that has the objective of computing the force feedback given the interaction of the user with the device.A variety of haptic rendering algorithms have been proposed in the past for the simulation of three degree of freedom (3DoF) interactions in which a single point touches a complex object as well as 6DoF interactions in which two complex objects interact in multiple points. The use of 3DoF or 6DoF algorithms depends mostly from the type of application and consequently the type of device. For example applications like virtual prototype require 6DoF interaction while many simulation applications have less stringent requirements. Apart the number of degree of freedom haptic rendering algorithms are characterized by the geometrical representation of the objects, by the use of rigid or deformable objects and by the introduction of physical properties of the object surface like friction and texture properties. Given this variety of possibilities and the presence of the human factor in the computation of haptic feedback it is hard to compare different algorithms to asses whether one specific solution performs better than any other previously proposed.The goal of the proposed work is two-fold. First this thesis proposes a framework allowing for more objective comparison of haptic rendering algorithms. Such comparison take into account the perceptual aspect of haptic interaction but tries to remove it from the comparison with the aim of obtaining an objective comparison between algorithms. Second, this thesis proposes a new haptic rendering algorithm for 3DoF interaction and one for 6DoF interaction. The first algorithm for 3DoF interaction provides interaction with rotational friction based on a simulation of the soft finger contact model. The new 6DoF interaction algorithm allows the computation of the haptic feedback of interaction between voxel models.