An adaptive subdivision method for surface-fitting from sampled data
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Direct least-squares fitting of algebraic surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Self-organization and associative memory: 3rd edition
Self-organization and associative memory: 3rd edition
Introduction to the theory of neural computation
Introduction to the theory of neural computation
On Three-Dimensional Surface Reconstruction Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalized implicit functions for computer graphics
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
The NURBS book
Implicit reconstruction of solids from cloud point sets
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Reconstruction of surfaces from planar contours
Reconstruction of surfaces from planar contours
Some characterizations of families of surfaces using functional equations
ACM Transactions on Graphics (TOG)
Neural Processing Letters
Optimal surface reconstruction from planar contours
Communications of the ACM
Computer Graphics and Geometric Modeling for Engineers
Computer Graphics and Geometric Modeling for Engineers
Simulating Neural Networks with Mathematica
Simulating Neural Networks with Mathematica
IEEE Transactions on Visualization and Computer Graphics
Applying Functional Networks to Fit Data Points from B-Spline Surfaces
CGI '01 Computer Graphics International 2001
Knowledge-Driven Ultrasonic Three-Dimensional Organ Modeling
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Artificial Immune System Approach for B-Spline Surface Approximation Problem
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
Implicit Surface Reconstruction from Scattered Point Data with Noise
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
Symbolic Manipulation of Bspline Basis Functions with Mathematica
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
ICCSA'07 Proceedings of the 2007 international conference on Computational science and Its applications - Volume Part II
Information Sciences: an International Journal
Quasi-interpolants based multilevel b-spline surface reconstruction from scattered data
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
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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Recently, a new extension of the standard neural networks, the so-called functional networks, has been described [E. Castillo, Functional networks, Neural Process. Lett. 7 (1998) 151-159]. This approach has been successfully applied to the reconstruction of a surface from a given set of 3D data points assumed to lie on unknown Bezier [A. Iglesias, A. Galvez, Applying functional networks to CAGD: the tensor-product surface problem, in: D. Plemenos (Ed.), Proceedings of the International Conference on Computer Graphics and Artificial Intelligence, 3IA'2000, 2000, pp. 105-115; A. Iglesias, A. Galvez, A new artificial intelligence paradigm for computer-aided geometric design, in: Artificial Intelligence and Symbolic Computation, J.A. Campbell, E. Roanes-Lozano (Eds.), Lectures Notes in Artificial Intelligence, Berlin, Heidelberg, Springer-Verlag, vol. 1930, 2001, pp. 200-213] and B-spline tensor-product surfaces [A. Iglesias, A. Galvez, Applying functional networks to fit data points from B-spline surfaces, in: H.H.S. Ip, N. Magnenat-Thalmann, R.W.H. Lau, T.S. Chua (Eds.), Proceedings of the Computer Graphics International, CGI'2001, IEEE Computer Society Press, Los Alamitos, CA, 2001, pp. 329-332]. In both cases the sets of data were fitted using Bezier surfaces. However, in general, the Bezier scheme is no longer used for practical applications. In this paper, the use of B-spline surfaces (by far the most common family of surfaces in surface modeling and industry) for the surface reconstruction problem is proposed instead. The performance of this method is discussed by means of several illustrative examples. A careful analysis of the errors makes it possible to determine the number of B-spline surface fitting control points that best fit the data points. This analysis also includes the use of two sets of data (the training and the testing data) to check for overfitting, which does not occur here.