Publications related to B-spline

Isogeometric approximation of cardiac electrophysiology models on surfaces: An accuracy study with application to the human left atrium

Alfio Quarteroni, Toni Mikael Lassila, Andrea Bartezzaghi, Alessandro Samuele Patelli

We consider Isogeometric Analysis in the framework of the Galerkin method for the spatial approximation of cardiac electrophysiology models defined on NURBS surfaces; specifically, we perform a numerical comparison between basis functions of degree p >= 1 ...

Elsevier2017

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

Michaël Unser, Daniel Andreas Schmitter, Ricard Delgado Gonzalo

Interpolatory basis functions are helpful to specify parametric curves or surfaces that can be modified by simple user-interaction. Their main advantage is a characterization of the object by a set of control points that lie on the shape itself (i.e., curv ...

2016

A parametric augmented Lagrangian algorithm for real-time economic NMPC

Colin Neil Jones, Jean-Hubert Hours, Harsh Ambarishkumar Shukla

In this paper, a novel optimality-tracking algorithm for solving Economic Nonlinear Model Predictive Control (ENMPC) problems in real-time is presented. Developing online schemes for ENMPC is challenging, since it is unclear how convexity of the Quadratic ...

IEEE2016

Similarity-Based Shape Priors for 2D Spline Snakes

Michaël Unser, Daniel Andreas Schmitter

We present a new formulation of a shape space containing all continuously defined 2D spline curves up to a similarity transform of a reference shape. We are able to measure a distance between an arbitrary curve and the shape space itself. Our contribution ...

IEEE2015

Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation

Alfio Quarteroni, Luca Dede', Christoph Jäggli

In this paper, we carry out a numerical dispersion analysis for the linear two-dimensional elastodynamics equations approximated by means of NURBS-based Isogeometric Analysis in the framework of the Galerkin method; specifically, we consider the analysis o ...

Elsevier2015

MATHICSE Technical Report : Isogeometric approximation of cardiac electrophysiology models on surfaces: an accuracy study with application to the human left atrium

Alfio Quarteroni, Luca Dede', Toni Mikael Lassila, Andrea Bartezzaghi, Alessandro Samuele Patelli

We consider Isogeometric Analysis in the framework of the Galerkin method for the spatial approximation of cardiac electrophysiology models defined on NURBS surfaces; specifically, we perform a numerical comparison between basis functions of degree p≥1and ...

MATHICSE2015

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

Iterative FBP For Improved Reconstruction Of X-Ray Differential Phase-Contrast Tomograms

Michaël Unser, Cédric René Jean Vonesch, Peter Modregger, Masih Nilchian, Marco Stampanoni

X-ray differential phase-contrast tomography is a recently-developed modality for the imaging of low-contrast biological samples. Its mathematical model is based on the first derivative of the Radon transform and the images, in practice, are reconstructed ...

IEEE2013

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

Exponential splines and minimal-support bases for curve representation

Michaël Unser, Philippe Thévenaz, Ricard Delgado Gonzalo

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the ...

Elsevier2012

B-spline

Isogeometric approximation of cardiac electrophysiology models on surfaces: An accuracy study with application to the human left atrium

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

A parametric augmented Lagrangian algorithm for real-time economic NMPC

Similarity-Based Shape Priors for 2D Spline Snakes

Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation

MATHICSE Technical Report : Isogeometric approximation of cardiac electrophysiology models on surfaces: an accuracy study with application to the human left atrium

Isogeometric Analysis for Navier-Stokes equations

Iterative FBP For Improved Reconstruction Of X-Ray Differential Phase-Contrast Tomograms

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

Exponential splines and minimal-support bases for curve representation

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Isogeometric approximation of cardiac electrophysiology models on surfaces: An accuracy study with application to the human left atrium

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

Exponential splines and minimal-support bases for curve representation

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

Isogeometric Analysis for Navier-Stokes equations

MATHICSE Technical Report : Isogeometric approximation of cardiac electrophysiology models on surfaces: an accuracy study with application to the human left atrium

Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation

Similarity-Based Shape Priors for 2D Spline Snakes

A parametric augmented Lagrangian algorithm for real-time economic NMPC

Iterative FBP For Improved Reconstruction Of X-Ray Differential Phase-Contrast Tomograms