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现有自由曲面的重建和还原制造是整个逆向工程中最关键的技术。当某些表面被部分损坏或者曲面模型不甚完整时，这些技术就显得非常有用。为了能在现有自由曲面基础上建立模型，首先用坐标测量机或激光扫描仪获取数字值，随后，将这些数据用于转换成模型。本文叙述以神经网络逼近方法用计算机重建模型再现已有自由曲面及制造加工这些曲面。在这里，我们设计了三个四层神经网络并使用误差反向传播法（ＢＰ）来训练网络。
Existing freeform surface reconstruction and reduction manufacturing is the most crucial technology in reverse engineering. These techniques are useful when some surfaces are partially damaged or when the surface model is not complete. In order to be able to build a model based on existing freeform surfaces, first a digital value is taken with a CMM or laser scanner, and then the data is used to convert it into a model. This paper describes the use of neural network approximation method using computer reconstruction model to reproduce the existing free-form surface and manufacture and processing of these surfaces. Here, we have designed three four-layer neural networks and trained the network using error back propagation (BP).