The edge effect is a problem that has to be tackled when performing haptic interaction with discontinuous primitives. In this paper, an innovated algorithm is designed to render a smooth haptic feedback force with a locally constructed C1 continuous Gregory patch. The continuous Gregory patch is generated from n-sided polygon, which is determined by a real-time contact region prediction method. The contact region prediction algorithm, derived from the dynamic model of the haptic device, is able to deal with the inconsistency of the local nearest point and global nearest point when obtaining the potential contact region. The parametric patch can be achieved in three steps employing boundary generation, height model interpolation, and Gregory patch construction. For a better shape preserving character, the height model of the contact region is respected by the parametric Gregory patch construction algorithm. The generated patch is continuous on boundaries and can render continuous feedback force as the proxy point transits between different patches. Since the presented scheme needs fewer primitives than conventional method, it consumes less memory and runs more efficiently in computation. The experimental results have shown that the smooth haptic force can be achieved with the proposed method. Meanwhile, the motion predictor also presents a good performance in the validating experiment.

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