Abstract:

This paper presents modeling research lines in the process of teaching engineering that tackle the creative design process, both to develop new work spaces and to design complex models, which require a strong mathematical background and adequate knowledge of approximation methods.
Nowadays commercial software has been refined to a level of excellence and products cover a wide range of design prototypes. However, working with high specificity models requires understanding of the mathematical base knowledge underlying the programming of these tools.

Our proposal integrates several subjects in engineering such as Informatics, Advanced Computing and Design in an interdisciplinary approach. The students need planning, conducting and publishing design projects of elements, but some of them are not available in the known packages or its availability is limited. The activities take place in workshop classes, in which designing of parts begin with an initial draft developed by themselves, going through several stages until the digital simulation is achieved, using symbolic computational software, applying formal methods, analytical or parametric mathematical models, which are analyzed and investigated in one of the lines of the areas of study mentioned. The conceptual design structure is very significant to know, in order to analyze and understand the requirements of prototyping in commercial 3D design software.

Projects introduced computer-aided design fundamentals, Bezier curves, B-Splines, Nurbs and T-Splines. We applied these tools in the generation of curves and freeform surfaces in order to construct the same models built in by technologies algorithms. The experience had a very positive impact, and students showed great fluency and motivation.

Pursuing the objective of incorporating the basis of 3D design in Engineering studies a new challenge is found when addressing the latest developments of refinement models design through a structure for modeling surfaces such as T-Splines. This topic is explained by a topological analysis of the refinement algorithms to increase the design quality, working as the known software design do.

References:
[1] Tinnirello A., De Federico S., Szekieta P. (2011), Diseño de Formas en un Entorno Multidisciplinar Mediante Herramientas de Simulación, IX WorkShop de Tecnología Informática Aplicada en Educación, XVII CACIC Congreso Argentino de Ciencia de la Computación, Facultad de Informática de la Universidad Nacional de La Plata, Argentina.
[2] Piegl L., Tiller W. (1996), TheNurbs Book, Monograph in Visual Comunication, Springer, Berlin, Germany.
[3] Sederberg T (2011), Computer Aided Geometric Design Course Notes, BYU Brigham Young University, Utah, USA.
[4] Tinnirello A., De Federico S., Szekieta P. (2012),Algoritmos de Modelación Aplicados al Diseño de Elementos de Máquina, III CAIM, Buenos Aires, Argentina.
[5] Tinnirello A., De Federico S., Szekieta P. (2013), Modelos de Refinamiento de Diseño de Geometrías Complejas y su Incorporación a la Enseñanza de la Ingeniería Mecánica, XI CIBIM, La Plata Argentina.

Keywords:

Computational mathematics, parametric models, T-splines, refinement, 3D Design.