A computer application for teaching and learning approximation and interpolation algorithms of curves

A computer teaching and learning application to help to understand the approximation and interpolation algorithms most used in engineering design has been developed. It is aimed at providing students with a visual, practical and easy-to-manage tool for learning and applying the principles of modelling and depicting the results of different curve generation algorithms. This application permits the user to carry out any operation related to the handling of curves depending on the characteristics and parameters of each of the algorithms included within an interactive interface. © 2009 Wiley Periodicals, Inc.Peer reviewe

The geometric characterization of mouldboard plough surfaces by using splines

For historic reasons, mouldboard ploughs have a wide variety of surfaces. The concentration of manufacturers has reduced the number of different types but there are still few complete geometric descriptions of the surfaces of a mouldboard plough. With the aim of describing and characterizing the three-dimensional shape of the plough, permitting the obtaining of a tool for an adequate preparation of the soil for cultivation, as well as reducing labour costs, in this work different approximation methods of three-dimensional surfaces have been explored. The results obtained allow us to conclude that the application of non uniform rational B-splines, combined with an optimization algorithm based on assigning different weights to the control points of the surface analyzed, is a method which succeeds in improving the quality of the fit with respect to other algorithms proposed by several authors in different previous works also based on the use of splines. The root mean square error of the fit of these algorithms to a mouldboard plough was the lowest 1.9. mm in the observed, and increases up to 14.4. mm using a simple Bézier bicubic parametric surface. Using the efficiency index of Nash and Sutclife (1970), the highest value, 0.995, corresponded to the non uniform rational B-splines method. © 2010 Elsevier B.V.The support from the Spanish Ministry of Science and Innovation ERDF Project AGL2009-12936-C03-02 is acknowledged.Peer Reviewe

Description of the seasonal pattern in ozone concentration time series by using the strange attractor multifractal formalism

Ozone is a secondary pollutant that, at high concentrations in urban environment, affects human health. Thus, suitable knowledge of ozone dynamics is essential for avoiding undesirable effects on the population. Ten-minute ozone concentration time series recorded at Córdoba (southern Spain) in 2007, for January, April, July and October, have been analysed by using the strange attractor multifractal formalism with the aim of describing the seasonal pattern of this pollutant. The multifractal nature of ozone concentration was detected in a study of the mass exponent functions for autumn-winter and spring-summer seasons. Multifractal spectra showed a greater heterogeneity in the low values of the time series. The presence of rare values in ozone data sets was also investigated, showing that the multifractal approach provided considerable detailed information on the time series structure that completes the statistical descriptive analysis. © 2008 Springer Science+Business Media B.V.The authors gratefully acknowledge the support of the Consejería de Innovación, Ciencia y Em- presa (Junta de Andalucía) Project P08-RNM-3989.Peer Reviewe