基于偏微分方程的隐式曲面光顺方法

提出隐式曲面的光顺问题．针对该问题，给出刻画隐式曲面光顺程度的能量模型，并将能量解释为关于隐函数的泛函．基于变分原理，构造出隐函数关于时间的偏微分方程。通过求解该方程得到隐函数序列，使得光顺能量逐渐变小，从而达到光顺隐式曲面的目的．另外．针对光顺问题提出的其它约束条件，如尽可能保持面积不变，保持原有的形状特征等，对模型进行修正．最后，给出方程的实用解法及实验结果。并作简单讨论．实验结果表明该方法通用、灵活、有效，而且程序易于实现．

Fairing of Implicit Surface Via Partial Differential Equations

This paper put forward the fairing issue of implicit surfaces. We introduce several energy models which characterize the smoothness of implicit surfaces, and treat the energy as the functional of implicit surfaces. Based on variational theory, we derive a partial differential equation (PDE) of the implicit function for each energy model. By solving the PDE, we get a series of implicit functions whose faring energy diminish accordingly, and thus achieve the goal of fairing the implicit surface. Furthermore, in order to satisfy other constrains in surface fairing process, such as preserving surface areas and features, we present some techniques to modify the corresponding energy models. Finally, we present some practical numerical methods to solve the partial differential equations and illustrate some examples to demonstrate the computational results. The experimental results show that our methods are in general flexible, effective and simple to implement.