Related papers: A Refinement Algorithm for Generalized B-splines
B-spline modeling is fundamental to CAD systems, and its evaluation and manipulation algorithms currently in use were developed decades ago, specifically for CPU architectures. While remaining effective for many applications, these…
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…
We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on…
This paper addresses asymptotic properties of general penalized spline estimators with an arbitrary B-spline degree and an arbitrary order difference penalty. The estimator is approximated by a solution of a linear differential equation…
A systematic construction of higher order splines using two hierarchies of polynomials is presented. Explicit instructions on how to implement one of these hierarchies are given. The results are limited to interpolations on regular,…
We used a collocation method in refinable spline space to solve a linear dynamical system having fractional derivative in time. The method takes advantage of an explicit derivation rule for the B-spline basis that allows us to efficiently…
In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform…
We formulate as an inverse problem the construction of sparse parametric continuous curve models that fit a sequence of contour points. Our prior is incorporated as a regularization term that encourages rotation invariance and sparsity. We…
This paper introduces a novel adaptive refinement strategy for Isogeometric Analysis (IGA) using Truncated Hierarchical B-splines (THB-splines). The proposed strategy enhances locally-refined meshes for specific applications, simplifying…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
The exponential B-spline basis function set is used to develop a collocation method for some initial boundary value problems (IBVPs) to the Gardner equation. The Gardner equation has two nonlinear terms, namely quadratic and cubic ones. The…
We present a procedure to approximate a plane contour by piecewise polynomial functions, depending on various parameters, such as degree, number of local patches, selection of knots. This procedure aims to be adopted to study how…
We present a novel approach enabling interactive visualization of volumetric Locally Refined B-splines (LR-splines). To this end we propose a highly efficient algorithm for direct visualization of scalar and vector fields given by an…
We explain four variants of an adaptive finite element method with cubic splines and compare their performance in simple elliptic model problems. The methods in comparison are Truncated Hierarchical B-splines with two different refinement…
Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
We present SplineNets, a practical and novel approach for using conditioning in convolutional neural networks (CNNs). SplineNets are continuous generalizations of neural decision graphs, and they can dramatically reduce runtime complexity…
Periodic splines are a special kind of splines that are defined over a set of knots over a circle and are adequate for solving interpolation problems related to closed curves. This paper presents a method of implementing the objects…
Optimizing k-space sampling trajectories is a promising yet challenging topic for fast magnetic resonance imaging (MRI). This work proposes to optimize a reconstruction method and sampling trajectories jointly concerning image…
Existing methods for constructing splines and Bezier curves on a Lie group G involve repeated products of exponentials deduced from local geodesics, w.r.t. a Riemannian metric, or rely on general polynomials. Moreover, each of these local…