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A linear polarization field on a surface is expressed in terms of scalar functions, providing an invariant separation into two components; one of these is the B mode, important as a signature of primordial gravitational waves, which would…

General Relativity and Quantum Cosmology · Physics 2019-12-02 Jack Kwok , King Lau , Edward Young , Kenneth Young

Inspired by shape constrained estimation under general nonnegative derivative constraints, this paper considers the B-spline approximation of constrained functions and studies the asymptotic performance of the constrained B-spline…

Classical Analysis and ODEs · Mathematics 2015-10-20 Teresa M. Lebair , Jinglai Shen

We study nonlinear approximation in $\operatorname{BMO}$ from splines generated by a hierarchy of B-splines over regular multilevel nested partitions of $\mathbb R$. Companion Jackson and Bernstein estimates are established that allow to…

Classical Analysis and ODEs · Mathematics 2020-01-30 Kamen G. Ivanov , Pencho Petrushev

A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current…

Combinatorics · Mathematics 2015-06-18 Peter Sin

Continuous formulations of trajectory planning problems have two main benefits. First, constraints are guaranteed to be satisfied at all times. Secondly, dynamic obstacles can be naturally considered with time. This paper introduces a novel…

Robotics · Computer Science 2022-12-21 Changhao Wang , Ting Xu , Masayoshi Tomizuka

This survey paper describes the role of splines in geometry and topology, emphasizing both similarities and differences from the classical treatment of splines. The exposition is non-technical and contains many examples, with references to…

Numerical Analysis · Mathematics 2015-11-25 Julianna Tymoczko

An expository description of smooth cubic curves in the real or complex projective plane.

Algebraic Geometry · Mathematics 2021-02-23 Araceli Bonifant , John Milnor

One of the possible variants of the classification of trigonometric interpolation splines is considered, depending on the chosen convergence factors, the distribution of signs of the basis functions and the interpolation factors. The…

Numerical Analysis · Mathematics 2019-10-03 V. P. Denysiuk

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…

Numerical Analysis · Mathematics 2023-02-16 Hiba Nassar , Krzysztof Podgórski

B\'ezier curves provide the basic building blocks of graphic design in 2D. In this paper, we port B\'ezier curves to manifolds. We support the interactive drawing and editing of B\'ezier splines on manifold meshes with millions of…

Graphics · Computer Science 2021-08-24 Claudio Mancinelli , Giacomo Nazzaro , Fabio Pellacini , Enrico Puppo

In this paper, we propose a novel gradient-based method to optimize curvilinear masks in optical lithography. The mask pattern is represented by periodic B-spline curves. We apply Delaunay triangulation to discretize the domains circled by…

Optimization and Control · Mathematics 2025-04-17 Xiaoru Yi , Junqing Chen

This document provides and in-depth introduction to the mlr framework for machine learning experiments in R.

B-splines of order $k$ can be viewed as a mapping $N$ taking a $(k+1)$-tuple of increasing real numbers $a_0 < \cdots < a_k$ and giving as a result a certain piecewise polynomial function. Looking at this mapping $N$ as a whole, basic…

Classical Analysis and ODEs · Mathematics 2021-12-08 Anna Kamont , Markus Passenbrunner

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…

Image and Video Processing · Electrical Eng. & Systems 2022-06-28 Icíar Lloréns Jover , Thomas Debarre , Shayan Aziznejad , Michael Unser

Lighting has a strong influence on visual appearance, yet understanding and representing lighting in images remains notoriously difficult. Various lighting representations exist, such as environment maps, irradiance, spherical harmonics, or…

Computer Vision and Pattern Recognition · Computer Science 2026-03-05 Zitian Zhang , Iliyan Georgiev , Michael Fischer , Yannick Hold-Geoffroy , Jean-François Lalonde , Valentin Deschaintre

A class of trigonometric interpolation splines depending on parameter vectors, selected convergence factors and interpolation factors is considered. The concept of crosslink grids and interpolation grids is introduced; these grids can match…

Numerical Analysis · Mathematics 2020-11-13 Vldimir Denysiuk

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…

Numerical Analysis · Mathematics 2019-06-27 Guohui Zhao

In this article, we consider some generalizations of polynomial and exponential B-splines. Firstly, the extension from integral to complex orders is reviewed and presented. The second generalization involves the construction of uncountable…

Metric Geometry · Mathematics 2019-02-18 Peter Massopust

We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. Our approach has several advantages over existing methods. We discuss these differences and…

Functional Analysis · Mathematics 2010-03-16 Stephan Ramon Garcia , Daniel E. Poore , Madeline K. Wyse

A visualisation tool is presented to facilitate the study on large-scale communications networks. This tool provides a simple and effective way to summarise the topology of a complex network at a coarse level.

Networking and Internet Architecture · Computer Science 2009-09-29 Yuchun Guo , Changjia Chen , Shi Zhou