Please note that this is strictly an unfinished working draft and the entire project is definitely a work very much in progress. The reader will find whole sections unfinished with lists of relevant literature only and as such is implored to please accept the author's apologies for the unfinished nature of this initial draft. (As such do not quote without permission). grant which made the resea...

This paper develops the manifold T-splines, which naturally extend the concept and the currently available algorithms/techniques of the popular planar tensor-product NURBS and T-splines to arbitrary manifold domain of any topological type. The key idea is the global conformal parameterization that intuitively induces a tensor-product structure with a finite number of zero points, and hence offe...

Recently, Niels Ferguson submitted comments to NIST detailing an attack on GCM message authentication when authentication tags are truncated [3]. This work underscores the risks of using GCM with very short tags, and highlights the need for guidance on tag length. However, it does not violate the claims of GCM’s security analysis [4], nor does it present any weakness that was not described in t...

The present authors have introduced polynomial splines over T-meshes (PHT-splines) and provided the theories and applications for PHT-splines over hierarchical T-meshes. This paper generalizes PHT-splines to arbitrary topology over general T-meshes with any structures. The general PHT-spline surfaces can be constructed through an unified scheme to interpolate the local geometric information at ...

A refinable spline is a compactly supported refinable function that is piecewise polynomial. Refinable splines, such as the well known B-splines, play a key role in computer aided geometric designs. Refinable splines have been studied in several papers, most noticably in [7] for integer dilations and [3] for real dilations. There are general characterizations in these papers, but these characte...

This paper is concerned with a study of some new formulations of smoothness conditions and conformality conditions for multivariate splines in terms of B-net representation. In the bivariate setting, a group of new parameters of bivariate quartic and quintic polynomials over a planar simplex is introduced, new formulations of smoothness conditions of bivariate quartic C1 splines and quintic C2 ...