While conventional engineering transforms engineering concepts into real parts, in reverse engineering real parts are transformed into engineering models. The construction of a surface from three-dimensional (3D) measuring data points is an important problem in reverse engineering. This paper presents a reconstruction method for the sculptured surfaces from the 3D measuring data points. The surface reconstruction scheme is presented based on a neural network. The reconstruction of the existing surfaces is realized by training the network. A series of measuring points from existing sculptured surfaces is used as a training set. Once the neural network has been trained, it serves as a geometric model to generate all the points that are needed. However, the learning rate for the neural network is relatively slow, and the learning accuracy is often unacceptably low. In this paper, to improve the performance of the neural network, a pre-processor is proposed before the input layer. The pre-processor maps the input into the larger space by generating a set of linearly independent values. The effect of the pre-processor is to increase modelling accuracy, and reduce learning time. Based on this method, experimental results are given to show that the reconstructed surfaces are faithful to the original data points. The proposed scheme is useful for regular or irregular digitized data.