In this paper we suggest two extensions to our previous work in data-driven haptic rendering. First, we propose a two-staged process to handle inhomogeneous material behavior. In an initial broad phase, representative locations of similar force responses are identified, based on a pattern clustering algorithm. Thereafter, separate detail-rich radial basis function approximations are generated for each detected region. These are employed in the rendering to provide varying feedback depending on the contact location. Secondly, we suggest a new computational formulation for obtaining the radial basis function reconstructions of the reaction force signal. Inspired by Compressive Sensing, we employ an ℓ¹-minimization with a random selection strategy. The improved performance of both extensions is illustrated on different test cases.