Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1997. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 24)

HOFFMANN, M. and VÁRADY, L., Free-form curve design by neural networks

Free-form curve design by neural networks Results and further possibilities 103 The following figures show the ordering of the input vectors and the approximating B-spline curve. There are 20 input vectors and 80 output nodes. initial state Output vectors| the map after 1000 iterations the approximating B-spline Figure 2. We plan to generalize the method to three dimensional input points using the Kohonen net. In this case the output map is two dimensional and the input vectors and the weights are three dimensional. When the net converges, the grid approximates the input points and an interpolating or approximating surface can be fitted to the input points. References [1] W. BOEHM, G. FARÍN and J. KAHMANN, A survey of curve and surface methods in CAGD, CAGD 1 (1984), 1-60. [2] T. KOHONEN, Self-organization and associative memory, Springer Verlag, 1984. [3] M. ALDER, R. TOGNERI, ,E. LAI and Y. ATTIKIOUZEL, Kohonen's algorithm for the numerical parametrisation of manifolds, Pattern Recognition Letters 11 (1990), 313-319. [4] L. D. FAUX and M. J. PRATT, Computational Geometry for Design and Manufacture, Wiley & Sons, NY, 1979.