A Developmental Study of the Free-formed Surface System Using the Neural Networks

本研究的第一个目的是确定布朗表面的参数，该参数可以使用张力和偏置控制程序处理表面特征。采用神经网络的一种反向传播方法来确定控制值。表面的特征有其相关的控制值。这些值由神经网络学习，学习后应用于表面控制。实现了五层反向传播方法。实验表面设计表明，这种尝试为表面设计带来了良好的效果。在研究反向传播方法的性质时，注意到反向传播方法本身具有插值函数。这意味着5层的反向传播方法可以直接用于曲面的插值和设计。为了确定这些特性，尝试通过数值实验来收集它们在利用自由曲面插值时的行为。它给出了一个很好的曲线拟合结果。在不久的将来，计划将这一结果应用于自由曲面的设计。

The first purpose of this research is to determine parameters of Brown surface, which can handle the surface features with the use of tension and bias control procedures. The back propagation method, one of the neural networks, is employed for determining the control values. The feature of surface have their related control values. These values are learned by the neural networks, and they are applied to surface control after leaning. The five layers back propagation method is implemented. Experimental surface designs show that this attempt introduces good results into surface designing.In investigating properties of the back propagation method, it is noticed that the back propagation method itself has the interpolation functions. This means that the back propagation method with 5 layers is able to be directly used for interpolating and designing the surfaces. In order to make sure of these properties, numerical experiments are attempted to collect their behaviors for making use of free-formed curves interpolation. It give us a good result as a curve fitting. In near future, it is planed to apply this result to design free-formed surface.