相关论文: Construction of $C^2$ cubic splines on arbitrary t…
The question of adaptive mesh generation for approximation by splines has been studied for a number of years by various authors. The results have numerous applications in computational and discrete geometry, computer aided geometric design,…
In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral…
Invariant-based models for incompressible isotropic hyperelasticity are typically formulated as functions of the first and second invariants, $W = W(\bar{I}_1, \bar{I}_2)$. A widely used class of models employs separable representations of…
Multi-degree Tchebycheffian splines are splines with pieces drawn from extended (complete) Tchebycheff spaces, which may differ from interval to interval, and possibly of different dimensions. These are a natural extension of multi-degree…
In the paper, we give methods of construction of dual bases for the B-spline basis and truncated power basis. Explicit formulas for the dual B-spline basis are obtained using the Legendre-like orthogonal basis of the polynomial spline space…
This paper presents a general framework for calculating the dimension of spline spaces over arbitrary rectilinear partitions using the smoothing cofactor method. The approach extends existing dimension theory for polynomial splines over…
A notion of effective gauge fields which does not involve a background metric is introduced. The role of scale is played by cellular decompositions of the base manifold. Once a cellular decomposition is chosen, the corresponding space of…
A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…
Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging…
Spline functions have long been used in numerically solving differential equations. Recently it revives as isogeometric analysis, which uses NURBS for both parametrization and element functions. In this paper, we introduce some multivariate…
The construction of B-spline wavelet bases on nonequispaced knots is extended to wavelets that are piecewise segments from any combination of smooth functions. The extended wavelet family thus provides multiresolution basis functions with…
We study structurable algebras of skew-dimension one. We present two different equivalent constructions for such algebras: one in terms of non-linear isotopies of cubic norm structures, and one in terms of hermitian cubic norm structures.…
We construct a quantisation of the Teichmueller spaces of super Riemann surfaces using coordinates associated to ideal triangulations of super Riemann surfaces. A new feature is the non-trivial dependence on the choice of a spin structure…
This paper develops a new way to create smooth piecewise polynomial free-form spline surfaces from quad- meshes that include T-junctions, where surface strips start or terminate. All mesh nodes can be interpreted as control points of…
Constructing $C^r$ conforming finite element spaces in any dimension is a long-standing problem. For general triangulations, this problem was recently addressed by Hu-Lin-Wu (2024), under certain conditions on supersmoothness and polynomial…
Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve a seamless integration between the design and the analysis of thin-walled structures in industrial settings. In this work, we generalize AST-splines to allow…
We introduce trimmed NURBS surfaces with accurate boundary control, briefly called ABC-surfaces, as a solution to the notorious problem of constructing watertight or smooth ($G^1$ and $G^2)$ multi-patch surfaces within the function range of…
We consider a class of non-polynomial spline spaces over T-meshes, that is, of spaces locally spanned both by polynomial and by suitably-chosen non-polynomial functions, which we will refer to as generalized splines over T-meshes. For such…
This paper derives strong relations that boundary curves of a smooth complex of patches have to obey when the patches are computed by local averaging. These relations restrict the choice of reparameterizations for geometric continuity. In…
In this thesis, a new approach for constructing subdivision algorithms for generalized quadratic and cubic B-spline subdivision for subdivision surfaces and volumes is presented. First, a catalog of quality criteria for these subdivision…