In this paper, we introduce a new type of splines—polynomial splines over hierarchical T-meshes (called PHT-splines) to model geometric objects. PHT-splines are a generalization of B-splines over hierarchical T-meshes. We present the detailed construction process of spline basis functions over T-meshes which have the same important properties as B-splines do, such as nonnegativity, local suppor...

In this paper we present a new technique for sample-based sound synthesis. The approach comprises the analysis of sounds of an instruments sound database, a parameter estimation for an instrument model and a sound synthesis using this model together with the analyzed sounds. The analysis of the sounds is carried out by the segregation of each sound into a sinusoidal and noise component and extr...

in this paper, we propose to extend the hierarchical bivariatehermite interpolant to the spherical case. let $t$ be an arbitraryspherical triangle of the unit sphere $s$ and  let $u$ be a functiondefined over the triangle $t$. for $kin mathbb{n}$, we consider ahermite spherical interpolant problem $h_k$ defined by some datascheme $mathcal{d}_k(u)$ and which admits a unique solution $p_k$in the ...

Analysis on two dimensional surfaces and in particular on the sphere S found many applications in computerized tomography, statistics, signal analysis, seismology, weather prediction, and computer vision. During last years many problems of classical harmonic analysis were developed for functions on manifolds and especially for functions on spheres: splines, interpolation, approximation, differe...

Analysis-suitable T -splines (AS T -splines) are a mildly topological restricted subset of T -splines which are linear independent regardless of knot values [1–3]. The present paper provides some more iso-geometric analysis (IGA) oriented properties for AS T splines and generalizes them to arbitrary topology AS T -splines. First, we prove that the blending functions for analysis-suitable T -spl...

An exposition on the use of O’Sullivan penalized splines in contemporary semiparametric regression, including mixed model and Bayesian formulations, is presented. O’Sullivan penalized splines are similar to P-splines, but have the advantage of being a direct generalization of smoothing splines. Exact expressions for the O’Sullivan penalty matrix are obtained. Comparisons between the two types o...

This paper discusses the convergence of the collocation method using splines of any order k for rst kind integral equations with logarithmic kernels on closed polygonal boundaries in R 2. Before discretization the equation is transformed to an equivalent equation over ?; ] using a nonlinear parametrization of the polygon which varies more slowly than arc{length near each corner. This has the ee...

A variety of techniques to facilitate fast graphical display of curves and surfaces for interactive CAGD purposes have been developed, in the past years. Many of these are commonly referred to as subdivision algorithms PI. In this paper we propose a method for subdividing simplex splines, i.e., splines that can be defined over non-regular grid partitions. There is a relatively exhaustive theory...

the harmonic index h(g) , of a graph g is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in e(g), where deg (u) denotes the degree of a vertex u in v(g). in this paper we define the harmonic polynomial of g. we present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in caterpill...