Abstract:

The study of the geometrical properties of surfaces in space is of great interest in many fields of civil and industrial engineering, architecture, physics, engineering in geodesy, cartography and surveying, among others, and have many important applications. The visualization of these properties enables students to enhance their knowledge on the subject.

In recent years, the teaching/ learning process using new technologies has become increasingly more important. The acquisition of competencies and skills by students is improved by this fact. In particular, the contribution of virtual laboratories to the study of many fields of mathematics, physics, and engineering, is highlighting. Using virtual labs the student can play a more active role in the transmission of knowledge.

In this work we present a graphical user interface (GUI) of Matlab that allows the visualization of the geometric properties of surfaces such as the Gaussian curvature, the mean curvature, the principal curvatures, the tangent plane and the normal line at a point, the concepts of elliptical, hyperbolic, parabolic and flat point, and some especially important curves contained in a surface as are the asymptotic curves and the lines of curvature. Additionally, the application provides a list of the expressions for the different curvatures depending on the parameters that define the surface. With the developed tool we try to consolidate the theoretical knowledge acquired by students about the theory of surfaces, paying special attention to the visualization, study, knowledge and appreciation of the different types of curvatures defined from a surface, the classification of your points, the study of the asymptotic curves and lines of curvature and some of the most famous surfaces.

The designed GUI can be used both in the computer rooms and individual computers, even though is not available Matlab package, because it was generated an executable version of the program. In all cases the student will be provided by a detailed guide of the virtual laboratory with a description of the parameters of the application and accompanied by illustrative examples.

Keywords:

Active methodologies, virtual laboratory, gaussian curvature, mean curvature, principal curvatures, curvature lines.