Concept

Non-uniform rational B-spline

Related publications (102)

Mathematical analysis of variational isogeometric methods

Annalisa Buffa, Rafael Vazquez Hernandez

This review paper collects several results that form part of the theoretical foundation of isogeometric methods. We analyse variational techniques for the numerical resolution of PDEs based on splines or NURBS and we provide optimal approximation and error ...

2014

Shape Optimization of an Hydrofoil by Isogeometric Analysis

Matthieu Martin Jean-André Simeoni

We use Isogeometric Analysis as a framework for NURBS-based shape optimization of hydrofoils. We present geometrical representations by NURBS and some of their properties to design an hydrofoil. Then, we consider an irrotational flow around an hydrofoil an ...

2014

Isogeometric Finite Elements With Surface Impedance Boundary Conditions

Annalisa Buffa, Rafael Vazquez Hernandez

First- and second-order surface impedance boundary conditions are introduced in the harmonic 2-D variational formulation based on the magnetic vector potential. The problem is discretized with isogeometric finite elements, a recent method that uses NURBS f ...

2014

Wire Mesh Design

Mark Pauly, Bailin Deng, Akash Garg

We present a computational approach for designing wire meshes, i.e., freeform surfaces composed of woven wires arranged in a regular grid. To facilitate shape exploration, we map material properties of wire meshes to the geometric model of Chebyshev nets. ...

Association for Computing Machinery2014

Isogeometric Analysis for Navier-Stokes equations

Elena Queirolo

In this project, we present some applications of Isogeometric Analysis in stationary fluid dynamics problems. Specially, we focus on the numerical solution of the Stokes and Navier-Stokes equations and the fulfillment of the inf-sup conditions, specificall ...

2014

Atlas-Free Brain Segmentation in 3D Proton-Density-Like MRI Images

Michaël Unser, Daniel Andreas Schmitter, Ricard Delgado Gonzalo

We present a new method for the atlas-free brain segmentation of proton-density-like 3D MRI images. We show how steerable filters can be efficiently combined with parametric spline surfaces to produce a fast and robust 3D brain segmentation algorithm. The ...

IEEE2014

Affine congruences and rational points on a certain cubic surface

Pierre Francis André Le Boudec

We establish estimates for the number of solutions of certain affine congruences. These estimates are then used to prove Manin's conjecture for a cubic surface split over Q whose singularity type is D-4. This improves on a result of Browning and answers a ...

Mathematical Science Publ2014

Analysis-suitable T-splines of arbitrary degree: definition, linear independence and approximation properties

Annalisa Buffa, Rafael Vazquez Hernandez

T-splines are an important tool in IGA since they allow local refinement. In this paper we define analysis-suitable T-splines of arbitrary degree and prove fundamental properties: Linear independence of the blending functions and optimal approximation prop ...

2013

Isogeometric Analysis for the Elastic Wave Equation

Christoph Jäggli

In everyday life of an engineer, CAD (Computer Aided Design) and FE (Finite Element) programs play an important role. The two different structures, CAD and FE programs, use different mathematical functions. In CAD programs, so called NURBS find their appli ...

2013

An Algorithm to Improve Parameterizations of Rational Bézier Surfaces Using Rational Bilinear Reparameterization

Bailin Deng, Wei Zeng

The parameterization of rational Bézier surfaces greatly affects rendering and tessellation results. The uniformity and orthogonality of iso-parametric curves are two key properties of the optimal parameterization. The only rational Bézier surfaces with un ...

2013

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