Computational vademecums for the real-time simulation of haptic collision between nonlinear solids

In this paper a novel strategy is presented for the real-time simulation of contact between non-linear deformable solids at haptic feedback rates. The proposed method is somehow related to the Voxmap Pointshell method for two deformable solids. Its novelty and crucial advantages over existing implementations of this algorithm come from the intensive use of computational vademecums. These are in essence a pre-computed solution of a parametric model in which every possible situation during the on-line phase of the method has been considered through the introduction of the appropriate parameters. Such a high-dimensional parametric model is efficiently solved by using Proper Generalized Decompositions (PGD) and stored in memory as a set of vectors. The paper presents a thorough description of the developed algorithm together with some examples of its performance.