M. L. Rodríguez

On Chebyshev-type integral quasi-interpolation operators

Spline quasi-interpolants on the real line are approximating splines to given functions with optimal approximation orders. They are called integral quasi-interpolants if the coefficients in the spline series are linear combinations of weighted mean values of the function to be approximated. This paper is devoted to the construction of new integral quasi-interpolants with compactly supported piecewise polynomial weights. The basic idea consists of minimizing an expression appearing in an estimate for the quasi-interpolation error. It depends on how well the quasi-interpolation operator approximates the first non-reproduced monomial. Explicit solutions as well as some numerical tests in the B-spline case are given.

Construction of ODE curves

This paper deals with a construction problem of free-form curves from data constituted by some approximation points and a boundary value problem for an ordinary differential equation (ODE). The solution of this problem is called an ODE curve. We discretize the problem in a space of B-spline functions. Finally, we analyze a graphical example in order to illustrate the validity and effectiveness of our method.

Optimization of parameters for curve interpolation by cubic splines

In this paper, we present an interpolation method for curves from a data set by means of the optimization of the parameters of a quadratic functional in a space of parametric cubic spline functions. The existence and the uniqueness of this problem are shown. Moreover, a convergence result of the method is established in order to justify the method presented. The aforementioned functional involves some real non-negative parameters; the optimal parametric curve is obtained by the suitable optimization of these parameters. Finally, we analyze some numerical and graphical examples in order to show the efficiency of our method.

A hole filling method for surfaces by using C1-Powell-Sabin splines. Estimation of the smoothing parameters

Abstract: Let D@?R^2 be a polygonal domain, H be a subdomain of D and f@?C^1(D@?-H@?). In this paper we propose a method to reconstruct f over the whole D@? using a technique based on the minimization of an energy functional J. More precisely, we construct a new C^1-Powell-Sabin spline function f^* over D@? that approximates f outside H, and fills the hole of f inside H. The resulting filling patch strongly depends on the values of two smoothing parameters involved in the functional J. We give a criteria to select optimum values of the parameters and we present some graphical and numerical examples.

An approximation method with data selection process

In this paper we present a method curve approximation from a given Lagrangian data set. An approximating problem of curves is obtained by minimizing a quadratic functional in a suitable space. This method is justified by a convergence result and an analysis of a numerical and graphical example.

Construction of blending surfaces by parametric discrete interpolation PDE splines

In this paper the problem of blending parametric surfaces is discussed. We present a constructing method of blending surfaces by parametric discrete interpolation PDE splines. These functions are obtained from some boundary conditions and a given interpolation data point set, by minimizing a functional associated with a partial differential equation (PDE) in a parametric finite element space. We formulate the corresponding problem and we establish a variational characterization of the solution and some convergence results. Finally, we show a graphical example.

Original article: A hole filling method for explicit and parametric surfaces by using C1-Powell Sabin splines

In this work we develop a method to fill a hole in a surface, either explicit or in parametric form, or just in a set of three dimensional scattered data. We will construct a new surface which is very close to the original one where it is known and that fills the hole in a homogeneous way, in such a way that the final reconstruction is of class C^1. We give results which prove the existence and uniqueness of solution of the proposed method, and we present several graphical examples which show the efficiency of the theory developed.

An Innovation Teaching Experience Following Guidelines of European Space of Higher Education in the Interactive Learning

The Area of Environmental Technology in Department of Civil Engineering has developed an innovation education project, entitled Application of new Information and Communication Technologies in Area of Environmental Technology teaching, to create a Web site that benefits both parties concerned in teaching-learning process, teachers and students. Here teachers conduct a supervised teaching and students have necessary resources to guide their learning process according to their capacities and possibilities. The project has also included a pilot experience to introduce European Space of Higher Education (ESHE) new teaching concept based on student’s work, in one subject of Environmental Science degree, considering interactive learning complementary to presence teaching. The experience has showed strength and weakness of the method and it is the beginning in a gradual process to guide e-learning education in future.

An Innovative Educational Project at the University of Granada: A New Teaching-Learning Model for Adapting the Organization of Curricula to Interactive Learning

The European Space of Higher Education (ESHE) is a new conceptual formulation of the organization of teaching at the university, largely involving the development of new training models based on the individual student’s work. In this context, the University of Granada has approved two plans of Educational Excellence to promote a culture of quality and stimulate excellence in teaching. The Area of Environmental Technology in the Department of Civil Engineering has developed an innovative project entitled Application of new Information and Communication Technologies (ICT) to the Area of Environmental Technology teaching to create a new communication channel consisting of a Web site that benefits teacher and student (“Environmental Studies Centre†: http://cem.ugr.es). Through this interactive page, teachers can conduct supervised teaching, and students will have the tools necessary for guiding their learning process, according to their capacities and possibilities. However, the material is designed to serve as a complement to the traditional method of attended teaching.