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Fitting B-splines to discrete data is especially challenging when the given data contain noise, jumps, or corners. Here, we describe how periodic data sets with these features can be efficiently and robustly approximated with B-splines by…
In this paper, we introduce the hierarchical B-spline complex of discrete differential forms for arbitrary spatial dimension. This complex may be applied to the adaptive isogeometric solution of problems arising in electromagnetics and…
We present a Hermite interpolation problem via splines of odd-degree which, to the best knowledge of the authors, has not been considered in the literature on interpolation via odd-degree splines. In this new interpolation problem, we…
Interpolation by various types of splines is the standard procedure in many applications. In this paper we shall discuss harmonic spline "interpolation" (on the lines of a grid) as an alternative to polynomial spline interpolation (at…
We present Hybrid-CSR, a geometric deep-learning model that combines explicit and implicit shape representations for cortical surface reconstruction. Specifically, Hybrid-CSR begins with explicit deformations of template meshes to obtain…
In this technical report, we document our attempt to visualize adaptive heightfields with smooth interpolation using ray casting in real time. The performance of ray casting depends strongly on the used interpolant and its efficient…
The task of reconstructing smooth signals from streamed data in the form of signal samples arises in various applications. This work addresses such a task subject to a zero-delay response; that is, the smooth signal must be reconstructed…
In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are…
Spline quasi-interpolation (QI) is a general and powerful approach for the construction of low cost and accurate approximations of a given function. In order to provide an efficient adaptive approximation scheme in the bivariate setting, we…
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface…
Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two…
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…
It is well-known that univariate cubic spline interpolation, if carried out on point sets with fill distance $h$, converges only like ${\cal O}(h^2)$ in $L_2[a,b]$ for functions in $W_2^2[a,b]$ if no additional assumptions are made. But…
In this work we present a new WENO b-spline based quasi-interpolation algorithm. The novelty of this construction resides in the application of the WENO weights to the b-spline functions, that are a partition of unity, instead to the…
This paper proposes a level set-based method for optimizing shell structures with large design changes in shape and topology. Conventional shell optimization methods, whether parametric or nonparametric, often only allow limited design…
We propose an approach to the problem of global reconstruction of an orientation field. The method is based on a geometric model called "bisector line fields", which maps a pair of vector fields to an orientation field, effectively…
Multi-fidelity simulation is a widely used strategy to reduce the computational cost of many-query numerical simulation tasks such as uncertainty quantification, design space exploration, and design optimization. The reduced basis approach…
Best $L_1$ approximation of the Heaviside function and best $\ell_1$ approximation of multiscale univariate datasets by cubic splines have a Gibbs phenomenon. Numerical experiments show that it can be reduced by using $L_1$ spline fits…
We present a local interpolation method in four dimensions utilising cubic splines. An extension of the three-dimensional tricubic method, the interpolated function has C$^1$ continuity and its partial derivatives are analytically…
Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing…