Chapter

Artificial Intelligence and Symbolic Computation

Volume 1930 of the series Lecture Notes in Computer Science pp 200-213

Date:

A New Artificial Intelligence Paradigm for Computer-Aided Geometric Design

  • Andres IglesiasAffiliated withDepartment of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de los Castros
  • , Akemi GálvezAffiliated withDepartment of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de los Castros

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Abstract

Functional networks is a powerful and recently introduced Artificial Intelligence paradigm which generalizes the standard neural networks. In this paper functional networks are used to fit a given set of data from a tensor product parametric surface. The performance of this method is illustrated for the case of Bézier surfaces. Firstly, we build the simplest functional network representing such a surface, and then we use it to determine the degree and the coefficients of the bivariate polynomial surface that fits the given data better. To this aim, we calculate the mean and the root mean squared errors for different degrees of the approximating polynomial surface, which are used as our criterion of a good fitting. In addition, functional networks provide a procedure to describe parametric tensor product surfaces in terms of families of chosen basis functions. We remark that this new approach is very general and can be applied not only to B´ezier but also to any other interesting family of tensor product surfaces.