Currently, virtually all objects in haptic force-feedback systems are represented by surfaces consisting of large numbers of flat triangular patches. Such surfaces have the advantage of fitting within current computer hardware constraints. However, they are computationally very expensive because the flat triangular patches must be small and numerous for the model to be accurate. In this project, a new approach is to be adopted. The plan is to replace the flat triangular patches by L1 splines, a new class of geometric models that achieve compression and accuracy much greater than that of flat triangular patches and other alternatives. Use of L1 splines will permit accurate modeling with far fewer elements, thus reducing the computational load. This project will develop trivariate parametric L1 splines on tetrahedral irregular networks as geometric models and mechanical models on the same tetrahedral networks, and then integrate the geometric and mechanical models via a two-level optimization procedure. The integrated geometric/mechanical model will be implemented in software for an operational 6-degree-of-freedom haptic system.
Success in this project will lead to high-performance haptic force-feedback devices with both speed and accuracy. More generally, this project will provide the scientific community and the national economy with a new class of computationally efficient L1 splines for modeling the geometry and mechanics of many kinds of irregularly shaped objects and processes, including but not limited to human beings, clothes, biological objects, mechanical objects, natural and urban terrain, geophysical features, geographical data, images such as those in computer games, economic processes and social processes. This research will be incorporated into graduate and undergraduate education to enrich regular courses and to attract a diverse group of undergraduate students, as the haptic research is applicable to such a wide set of disciplinary and societal applications.
