The recurrence algorithm is given for the calculation of NUAH B-splines in the space Sn+1 = span{sinh t, cosh t, t , · · · , t, t, 1} (n ≥ 3). The case of NUAH B-spline bases of low order with multiple knot sequences is studied. The limiting cases of UAH Bsplines are recovered when shape parameters α′s → 0and + ∞. Then the corresponding NUAH B-spline curve is defined and its main properties suc...

In this paper, we discuss the problem of instability in the dimension of a spline space over a T-mesh. For bivariate spline spaces S (5, 5, 3, 3) and S (4, 4, 2, 2), the instability in the dimension is shown over certain types of T-meshes. This result could be considered as an attempt to answer the question of how large the polynomial degree (m,m) should be relative to the smoothness (r, r) to ...

This article presents an inexpensive approach to provide (s,t) texture coordinates of a spline surface that mitigates texture compression and stretching artifacts. It employs a chordlength approximation based on the original spline surface parameterization.

To generate analysis-suitable T-splines for arbitrary topologies, in this paper we introduce a new method to deal with extraordinary nodes in the T-mesh. Knot interval duplication method is used to extract knot vectors for the extraordinary nodes and spoke nodes. From defined bicubic weighted T-spline basis functions, the extracted Bézier coefficients are modified to obtain a gap-free T-spline ...

In this thesis, we propose to analyze panel count data using a spline-based sieve generalized estimating equation method with a semiparametric proportional mean model E(N(t)|Z) = Λ0 (t) e T 0 Z . The natural log of the baseline mean function, logΛ0 (t), is approximated by a monotone cubic B-spline function. The estimates of regression parameters and spline coefficients are the roots of the spli...

We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allows to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions ...

We propose a construction of trivariate C 1 spline functions over a special tetrahedron partition and compare our construction with other known constructions of C 1 spline functions which are summarized in this paper. We improve the Alfeld construction of C 1 quintic spline spaces. For those polygonal domains in R 3 which admit the special tetrahedron partition, our construction provides a more...

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 ...