Mathematical elements for computer graphics (2nd ed.)
Mathematical elements for computer graphics (2nd ed.)
Computational geometry: curve and surface modeling
Computational geometry: curve and surface modeling
Introduction to the theory of neural computation
Introduction to the theory of neural computation
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Some characterizations of families of surfaces using functional equations
ACM Transactions on Graphics (TOG)
Neural Processing Letters
Simulating Neural Networks with Mathematica
Simulating Neural Networks with Mathematica
Extending Neural Networks for B-Spline Surface Reconstruction
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
An Artificial Immune System Approach for B-Spline Surface Approximation Problem
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
Symbolic Computation of Petri Nets
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
Particle Swarm Optimization for Bézier Surface Reconstruction
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
Information Sciences: an International Journal
Information Sciences: an International Journal
The calculation of parametric NURBS surface interval values using neural networks
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
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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 BÉzier but also to any other interesting family of tensor product surfaces.