Let be a real reflexive Banach space with a weakly continuous duality mapping . Let be a nonempty weakly closed star-shaped (with respect to ) subset of . Let = be a uniformly continuous semigroup of asymptotically nonexpansive self-mappings of , which is uniformly continuous at zero. We will show that the implicit iteration scheme: , for all , converges strongly to a common fixed point of the semigroup for some suitably chosen parameters and . Our results extend and improve corresponding ones of Suzuki (2002), Xu (2005), and Zegeye and Shahzad (2009).

We give a brief introduction to some of the recent works on finding geometric structures on triangulated surfaces using variational principles.

This paper presents a skeleton-based method for deforming meshes (the skeleton need not be the medial axis). The significant difference from previous skeleton-based methods is that the latter use the skeleton to control movement of vertices, whereas we use it to control the simplices defining the model. By doing so, errors that occur near joints in other methods can be spread over the whole mesh, via an optimization process, resulting in smooth transitions near joints of the skeleton. By controlling simplices, our method has the additional advantage that no vertex weights need be defined on the bones, which is a tedious requirement in previous skeleton-based methods. Furthermore, by incorporating the translation vector in our optimization, unlike other methods, we do not need to fix an arbitrary vertex, and the deformed mesh moves with the deformed skeleton. Our method can also easily be used to control deformation by moving a few chosen line segments, rather than a skeleton.

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