隐式曲线与曲面是当前计算机图形学研究的热点之一。通过把BP神经网络与隐式曲线构造原理相结合，提出了一种构造隐式曲线的新方法，即首先由约束点构造神经网络的输入与输出，把描述物体边界曲线的隐式函数转化为显式函数；然后用BP神经网络对此显式函数进行逼近；最后由仿真曲面得到物体边界的拟合曲线。该新方法不同于传统的对显式函数的逼近方法，因为传统方法无法描述封闭的曲线；也不同于基于优化的拟合隐式曲线方法，因为它无须考虑函数的形式或多项式的次数。实验表明，该新方法有很强的物体边界描述能力和缺损修复能力，因而在物体边界重建、缺损图像复原等领域有一定的应用前景。

The implicit polynomial curves have a lot of merits, such as the capability to describe irregularly shaped objects, object recognition and insensitivity to noise, and are used widely in CAGD and computer graphics. A new method for closed curve construction is introduced which is based on the combination of BP neural network and principle of implicit curve construction. The algorithm, first constructs the input and output of the BP neural network from the constraint points and changes the implicit function that represents object boundary into explicit function, then uses BP neural network to fit the curve of the explicit function, and finally obtains the fitting curves that represent the object boundary from the simulation surface. The algorithm has more advancements than the method of fitting the curves of explicit functions by BP network, which can not fit the closed curves. It has good numerical stability and robustness in dealing with noisy or missing data. The Experimental results are given to verify the effectiveness of recovering incomplete images and object boundary reconstruction.