Related papers: Bspline solids manipulation with Mathematica
We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control…
R is a language and computing environment that has been developed for data manipulation, statistical computing, and scientific graphing. In the paper, we demonstrate its use analyzing data collected in a few experiments taken from an…
We present an approach for high-quality dynamic Gaussian Splatting from monocular videos. To this end, we in this work go one step further beyond previous methods to explicitly model continuous position and orientation deformation of…
Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of applied mathematics including numerical analysis, approximation…
A method is proposed for constructing a spline curve of the Bezier type, which is continuous along with its first derivative by a piecewise polynomial function. Conditions for its existence and uniqueness are given. The constructed curve…
We introduce a diagrammatic language for compact, orientable 3-dimensional manifolds with boundary. A diagrammatic calculus (both integral and rational version) appropriate for this language is introduced and its completeness is proved in…
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…
Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical…
In this paper we present a brief discussion on the salient points of the computational analysis that are at the basis of the paper \cite{StSc}. The computational and data analysis have been made with the software Mathematica$^\circledR$ and…
The goal of this short note is to prove that every b-spline curve or surface (generated by uniform knots, without multiplicity) may be defined as minimum of positive quadratic operator.
In this paper, we describe a general class of $C^1$ smooth rational splines that enables, in particular, exact descriptions of ellipses and ellipsoids - some of the most important primitives for CAD and CAE. The univariate rational splines…
We describe some new univariate spline quasi-interpolants on uniform partitions of bounded intervals. Then we give some applications to numerical analysis: integration, differentiation and approximation of zeros.
We introduce a smooth B-spline discretization in polar coordinates on the unit disc that corrects the loss of regularity present at the origin caused by the coordinate singularity in standard tensor-product B-spline formulations. The method…
We present BSeries.jl, a Julia package for the computation and manipulation of B-series, which are a versatile theoretical tool for understanding and designing discretizations of differential equations. We give a short introduction to the…
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…
In recent years, the field of statistics has experienced a surge in interest and application, largely due to significant advances in computer technology. This progress has led to remarkable developments in statistics methods and algorithms,…
We examine a variety of numerical methods that arise when considering dynamical systems in the context of physics-based simulations of deformable objects. Such problems arise in various applications, including animation, robotics, control…
Based on spline manifolds we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure, which allows for the definition of function spaces…
This study debuts a new spline dimensional decomposition (SDD) for uncertainty quantification analysis of high-dimensional functions, including those endowed with high nonlinearity and nonsmoothness, if they exist, in a proficient manner.…
Over the past two decades, we have seen an exponentially increased amount of point clouds collected with irregular shapes in various areas. Motivated by the importance of solid modeling for point clouds, we develop a novel and efficient…