• East Asian mathematical journal
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• v.28 no.3
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• pp.265-280
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• 2012

In this paper, we introduce an iterative sequence by using a hybrid generalized $f$-projection algorithm for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping an the set of solutions of a generalized variational inequality in a Banach space. Our results extend and improve the recent ones announced by Y. Liu [Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings, J. Glob. Optim. 46 (2010), 319-329], J. Fan, X. Liu and J. Li [Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces, Nonlinear Analysis 70 (2009), 3997-4007], and many others.

• The Journal of Korea Robotics Society
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• v.8 no.3
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• pp.173-178
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• 2013

We present six-degree-of-freedom (6DoF) haptic rendering algorithms using translational ($PD_t$) and generalized penetration depth ($PD_g$). Our rendering algorithm can handle any type of object/object haptic interaction using penalty-based response and makes no assumption about the underlying geometry and topology. Moreover, our rendering algorithm can effectively deal with multiple contacts. Our penetration depth algorithms for $PD_t$ and $PD_g$ are based on a contact-space projection technique combined with iterative, local optimization on the contact-space. We circumvent the local minima problem, imposed by the local optimization, using motion coherence present in the haptic simulation. Our experimental results show that our methods can produce high-fidelity force feedback for general polygonal models consisting of tens of thousands of triangles at near-haptic rates, and are successfully integrated into an off-the-shelf 6DoF haptic device. We also discuss the benefits of using different formulations of penetration depth in the context of 6DoF haptics.