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Papers by Christophe Rabut

HAL (Le Centre pour la Communication Scientifique Directe), Feb 1, 2017

We present here research for deriving a collaborative learning situation which is not base don a ... more We present here research for deriving a collaborative learning situation which is not base don a Project or problem. The method mainly consists in working in small teams (4 or 5 students) in order to debate on a lesson which has been previously studied individually (as homework) by each student. Coupled with a classical exercises usually solved within the team, this method appears to be very efficient, motivating for the students and well adapted to any subject, including those often considered as difficult to be studied in active PBL, such as mathematics.

The construction of a smooth surface from an irregular mesh in space is considered. The mesh vert... more The construction of a smooth surface from an irregular mesh in space is considered. The mesh vertices can either be interpolated or approximated as a control net. A collection of triangular Bezier patches results from a local, ane invariant and visually smooth interpolation scheme that can represent surfaces of arbitrary topological type. It is based on a domain 4-split. Beside the surface construction scheme, the optimal employment of the numerous degrees of freedom is crucial for an overall pleasing shape. Dierent local minimum norm criteria are tested to see if they produce satisfactory shapes.

Transportation Research Part C: Emerging Technologies, 2014

This paper considers the problem of short to mid-term aircraft trajectory prediction, that is, th... more This paper considers the problem of short to mid-term aircraft trajectory prediction, that is, the estimation of where an aircraft will be located over a 10 to 30 minutes time horizon. Such a problem is central in decision support tools, especially in conflict detection and resolution algorithms. It also appears when an air traffic controller observes traffic on the radar screen and tries to identify convergent aircraft, which may be in conflict in the near future. An innovative approach for aircraft trajectory prediction is presented in this paper. This approach is based on local linear functional regression that considers data preprocessing, localizing and solving linear regression using wavelet decomposition. This algorithm takes into account only past radar tracks, and does not use any physical or aeronautical parameters. This approach has been successfully applied to aircraft trajectories between several airports on the data set that is one year air traffic over France. The method is intrinsic and independent from airspace structure.

This paper is a reflexion on the main properties we demand to a quasi-interpolant. We give and co... more This paper is a reflexion on the main properties we demand to a quasi-interpolant. We give and compare the interest of the most used criteria, and explain the importance of the transfer function and of the "interpolating power of φ" to evaluate how far from the data (a, y_a)a∈A the function P a2A y a B a is. A definition of a "quasi-interpolant" is then proposed, and six criteria to evaluate the quality of a quasi-interpolant are listed in the order of importance. Examples, as well in one and in many dimensions, are given.

Refereed and edited papers on the most current developments in the theory and applications of cur... more Refereed and edited papers on the most current developments in the theory and applications of curves and surfaces.

—Le probleme de la prediction de la trajectoire d'unavion partir des informations de position... more —Le probleme de la prediction de la trajectoire d'unavion partir des informations de positions passees est fondamen-tal dans le domaine de la gestion du trac aerien. Nous presentonsune approche nouvelle en utilisant une technique de regressionlineaire locale en espace de Sobolev. Une decomposition enondelettes des trajectoires avion permet une implementationefcace. Un exemple de prediction de trajectoires sur une based'apprentissage est donne.Abstract —In this paper we consider the problem of short tomidd-term aircraft trajectory prediction. That problem aims toavoid the collisions between aircraft in airspace. Our innovativeapproach is based on local functional regression, i.e. there arethree steps towards solving prediction problem: Data manage-ment, localizing and solving the regression. Results we obtainedbased on aircraft trajectories between Toulouse and Paris isgiven. Keywords : Analyse des donnees - data mining, OndelettesI. I NTRODUCTION A. What is Functional Data A...

Dans le cadre de l'amelioration du trafic aerien, des projets ont ete inities afin de contrai... more Dans le cadre de l'amelioration du trafic aerien, des projets ont ete inities afin de contraindre l'avion en position et en temps (trajectoire 4D). On s'interesse ici a la planification des vols en tenant compte du vent, des zones de survol interdites et de la congestion du trafic aerien. Nous proposons une methodologie qui genere, a l'aide d'un algorithme Fast Marching adapte, une trajectoire optimale, par rapport au temps de parcours, d'un vol en croisiere. Pour ce faire, nous imposons le niveau de vol et la vitesse de l'avion. La trajectoire ainsi obtenue tient compte du vent, des zones interdites et de la congestion du trafic global.

This paper compares two different ways of building B-spline curves and surfaces for even degree p... more This paper compares two different ways of building B-spline curves and surfaces for even degree polynomial splines. Viewing these problems as digital filters, we find that one way gives better results than the other one. This paper is intended to be a reflection and a continuation of the paper “B-spline Curves and Surfaces Viewed as Digital Filters,” by A. Goshtasby, F. Cheng, and B. Barsky (Comput. Vision Graphics Image Process. 52, 1990, 264 275). 0 19% Academic Press, he.

2015 IEEE/AIAA 34th Digital Avionics Systems Conference (DASC), 2015

Numerical Algorithms, 1992

For any integer values of n and k (usually n>k) and any real function f, we give explicit form... more For any integer values of n and k (usually n>k) and any real function f, we give explicit formulae to derive a discrete approximation of f (k) (b) as a linear combination of pointwise values of the function. This approximation is ℙ k+n -exact in the sense that if f is any polynomial of degree at most n, the obtained approximation is exactly f (k) (b). This approximation is a generalization of the usual divided difference. We then use this approximation in order to derive some generalization of polynomial B-splines and we use these functions in order to improve the linear system obtained in interpolation in quite usual cases.

... edited by Albert Cohen, Christophe Rabut, and Larry. L. Schumaker ... 145 MIPS: An Efficient ... more ... edited by Albert Cohen, Christophe Rabut, and Larry. L. Schumaker ... 145 MIPS: An Efficient Global Parametrization Method Kai Hormann and Günther Greiner . . . . . ... 287 Convergence of Approximations for Arrangements of Curves Manuela Neagu and Bernard Lacolle . . . . ...

In this paper, we build a multidimensional wavelet decomposition based on polyharmonic B-splines.... more In this paper, we build a multidimensional wavelet decomposition based on polyharmonic B-splines. The pre-wavelets are polyharmonic splines and so not tensor products of univariate wavelets. Explicit construction of the filters specified by the classical dyadic scaling relations is given and the decay of the functions and the filters is shown. We then design the decomposition/recomposition algorithm by means of downsampling/upsampling and convolution products.

La methode « Peer instruction » (Mazur 1997) consiste a poser des questions a l’auditoire, qui re... more La methode « Peer instruction » (Mazur 1997) consiste a poser des questions a l’auditoire, qui repond a l’aide d’un dispositif de vote. En fonction du taux de bonnes reponses, l’enseignant invite les etudiants a argumenter leur reponse avec leurs voisins, puis a voter a nouveau avant de commenter les resultats. Le projet ACTIFS vise a developper cette methode sur l’ensemble des 15 formations d’ingenieurs de Midi-Pyrenees, et a touche environ 120 enseignants, 7000 etudiants. La diversite de cet environnement est donc consequente et a ete largement prise en compte dans ce projet. Nous examinons dans cette etude le type et l’impact des alterites impliquees par ce projet et nous presentons un premier bilan en termes de ressenti par les etudiants et les enseignants.

HAL (Le Centre pour la Communication Scientifique Directe), Feb 1, 2017

We present here research for deriving a collaborative learning situation which is not base don a ... more We present here research for deriving a collaborative learning situation which is not base don a Project or problem. The method mainly consists in working in small teams (4 or 5 students) in order to debate on a lesson which has been previously studied individually (as homework) by each student. Coupled with a classical exercises usually solved within the team, this method appears to be very efficient, motivating for the students and well adapted to any subject, including those often considered as difficult to be studied in active PBL, such as mathematics.

The construction of a smooth surface from an irregular mesh in space is considered. The mesh vert... more The construction of a smooth surface from an irregular mesh in space is considered. The mesh vertices can either be interpolated or approximated as a control net. A collection of triangular Bezier patches results from a local, ane invariant and visually smooth interpolation scheme that can represent surfaces of arbitrary topological type. It is based on a domain 4-split. Beside the surface construction scheme, the optimal employment of the numerous degrees of freedom is crucial for an overall pleasing shape. Dierent local minimum norm criteria are tested to see if they produce satisfactory shapes.

Transportation Research Part C: Emerging Technologies, 2014

This paper considers the problem of short to mid-term aircraft trajectory prediction, that is, th... more This paper considers the problem of short to mid-term aircraft trajectory prediction, that is, the estimation of where an aircraft will be located over a 10 to 30 minutes time horizon. Such a problem is central in decision support tools, especially in conflict detection and resolution algorithms. It also appears when an air traffic controller observes traffic on the radar screen and tries to identify convergent aircraft, which may be in conflict in the near future. An innovative approach for aircraft trajectory prediction is presented in this paper. This approach is based on local linear functional regression that considers data preprocessing, localizing and solving linear regression using wavelet decomposition. This algorithm takes into account only past radar tracks, and does not use any physical or aeronautical parameters. This approach has been successfully applied to aircraft trajectories between several airports on the data set that is one year air traffic over France. The method is intrinsic and independent from airspace structure.

This paper is a reflexion on the main properties we demand to a quasi-interpolant. We give and co... more This paper is a reflexion on the main properties we demand to a quasi-interpolant. We give and compare the interest of the most used criteria, and explain the importance of the transfer function and of the "interpolating power of φ" to evaluate how far from the data (a, y_a)a∈A the function P a2A y a B a is. A definition of a "quasi-interpolant" is then proposed, and six criteria to evaluate the quality of a quasi-interpolant are listed in the order of importance. Examples, as well in one and in many dimensions, are given.

Refereed and edited papers on the most current developments in the theory and applications of cur... more Refereed and edited papers on the most current developments in the theory and applications of curves and surfaces.

—Le probleme de la prediction de la trajectoire d'unavion partir des informations de position... more —Le probleme de la prediction de la trajectoire d'unavion partir des informations de positions passees est fondamen-tal dans le domaine de la gestion du trac aerien. Nous presentonsune approche nouvelle en utilisant une technique de regressionlineaire locale en espace de Sobolev. Une decomposition enondelettes des trajectoires avion permet une implementationefcace. Un exemple de prediction de trajectoires sur une based'apprentissage est donne.Abstract —In this paper we consider the problem of short tomidd-term aircraft trajectory prediction. That problem aims toavoid the collisions between aircraft in airspace. Our innovativeapproach is based on local functional regression, i.e. there arethree steps towards solving prediction problem: Data manage-ment, localizing and solving the regression. Results we obtainedbased on aircraft trajectories between Toulouse and Paris isgiven. Keywords : Analyse des donnees - data mining, OndelettesI. I NTRODUCTION A. What is Functional Data A...

Dans le cadre de l'amelioration du trafic aerien, des projets ont ete inities afin de contrai... more Dans le cadre de l'amelioration du trafic aerien, des projets ont ete inities afin de contraindre l'avion en position et en temps (trajectoire 4D). On s'interesse ici a la planification des vols en tenant compte du vent, des zones de survol interdites et de la congestion du trafic aerien. Nous proposons une methodologie qui genere, a l'aide d'un algorithme Fast Marching adapte, une trajectoire optimale, par rapport au temps de parcours, d'un vol en croisiere. Pour ce faire, nous imposons le niveau de vol et la vitesse de l'avion. La trajectoire ainsi obtenue tient compte du vent, des zones interdites et de la congestion du trafic global.

This paper compares two different ways of building B-spline curves and surfaces for even degree p... more This paper compares two different ways of building B-spline curves and surfaces for even degree polynomial splines. Viewing these problems as digital filters, we find that one way gives better results than the other one. This paper is intended to be a reflection and a continuation of the paper “B-spline Curves and Surfaces Viewed as Digital Filters,” by A. Goshtasby, F. Cheng, and B. Barsky (Comput. Vision Graphics Image Process. 52, 1990, 264 275). 0 19% Academic Press, he.

2015 IEEE/AIAA 34th Digital Avionics Systems Conference (DASC), 2015

Numerical Algorithms, 1992

For any integer values of n and k (usually n>k) and any real function f, we give explicit form... more For any integer values of n and k (usually n>k) and any real function f, we give explicit formulae to derive a discrete approximation of f (k) (b) as a linear combination of pointwise values of the function. This approximation is ℙ k+n -exact in the sense that if f is any polynomial of degree at most n, the obtained approximation is exactly f (k) (b). This approximation is a generalization of the usual divided difference. We then use this approximation in order to derive some generalization of polynomial B-splines and we use these functions in order to improve the linear system obtained in interpolation in quite usual cases.

... edited by Albert Cohen, Christophe Rabut, and Larry. L. Schumaker ... 145 MIPS: An Efficient ... more ... edited by Albert Cohen, Christophe Rabut, and Larry. L. Schumaker ... 145 MIPS: An Efficient Global Parametrization Method Kai Hormann and Günther Greiner . . . . . ... 287 Convergence of Approximations for Arrangements of Curves Manuela Neagu and Bernard Lacolle . . . . ...

In this paper, we build a multidimensional wavelet decomposition based on polyharmonic B-splines.... more In this paper, we build a multidimensional wavelet decomposition based on polyharmonic B-splines. The pre-wavelets are polyharmonic splines and so not tensor products of univariate wavelets. Explicit construction of the filters specified by the classical dyadic scaling relations is given and the decay of the functions and the filters is shown. We then design the decomposition/recomposition algorithm by means of downsampling/upsampling and convolution products.

La methode « Peer instruction » (Mazur 1997) consiste a poser des questions a l’auditoire, qui re... more La methode « Peer instruction » (Mazur 1997) consiste a poser des questions a l’auditoire, qui repond a l’aide d’un dispositif de vote. En fonction du taux de bonnes reponses, l’enseignant invite les etudiants a argumenter leur reponse avec leurs voisins, puis a voter a nouveau avant de commenter les resultats. Le projet ACTIFS vise a developper cette methode sur l’ensemble des 15 formations d’ingenieurs de Midi-Pyrenees, et a touche environ 120 enseignants, 7000 etudiants. La diversite de cet environnement est donc consequente et a ete largement prise en compte dans ce projet. Nous examinons dans cette etude le type et l’impact des alterites impliquees par ce projet et nous presentons un premier bilan en termes de ressenti par les etudiants et les enseignants.