Neural networks are an attempt to build computer networks called artificial neurons, which imitate the activities of the human brain. Its origin dates back to 1943 when neurophysiologist Warren Me Cello and logician Walter Pits produced the first artificial neuron. Since then there has been tremendous development of neural networks and their applications to pattern and optical character recognition, speech processing, time series prediction, image processing and scattered data approximation. Since it has been shown that neural nets can approximate all but pathological functions, Neil Cotter considered neural network architecture based on Stone-Weierstrass Theorem. Using exponential functions, polynomials, rational functions and Boolean functions one can follow the method given by Cotter to obtain neural networks, which can approximate bounded measurable functions. Another problem of current research in computer graphics is to construct curves and surfaces from scattered spatial points by using B-Splines and NURBS or Bezier surfaces. Hoffman and Varady used Kohonen neural networks to construct appropriate grids. This thesis is concerned with two types of neural networks viz. those which satisfy the conditions of the Stone-Weierstrass theorem and Kohonen neural networks. We have used self-organizing maps for scattered data approximation. Neural network Tool Box from MATLAB is used to develop the required grids for approximating scattered data in one and two dimensions.