When a subdivision scheme is factorised into lifting steps, it admits an in-place and invertible implementation, and it can be the predictor of many multiresolution biorthogonal wavelet transforms. In the regular setting where the underlying lattice hierarchy is defined by Z s and a dilation matrix M , such a factorisation should deal with every vertex of each subset in Z s /M Z s in the same way. We define a subdivision scheme which admits such a factorisation as being uniformly elementary factorable. We prove a necessary and sufficient condition on the directions of the Box spline and the arity of the subdivision for the scheme to admit such a factorisation, and recall some known keys to construct it in practice.
Abstract:In this paper we propose a simple framework to compute flexible skinning weights, which allows the creation from quasi-rigid to soft deformations. We decompose the input mesh into a set of overlapping regions, in a way similar to the constructive manifold approach. Regions are associated to skeleton bones, and overlaps contain vertices influenced by several bones. A smooth transition function is then defined on overlaps, and is used to compute skinning weights. The size of overlaps can be tuned by the user, enabling an easy control of the desired type of deformations.
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