中文摘要：

为了实现交互式的偏微分方程曲面造型，针对传统静态偏微分方程构造过渡面存在的不足，提出了基于动态偏微分方程构造C^1连续的过渡面，并引入迭代有限差分法求解偏微分方程的数值解，在此基础上构造了光滑过渡曲面。讨论了形状控制因子、密度、阻尼系数等物理参数的变化对曲面形状的影响，其中形状控制因子对生成曲面的形状影响最为明显。造型实例表明，利用动态偏微分方程构造过渡面具有更高的灵活性，大大提高了工业几何设计的交互性，在CAD/CAM中具有重要的应用价值。

英文摘要：

To implement interacitve surface modeling and for the problem ofgernarting blending surfaces based on previous tradional PDE＇ s drawbacks, a dynamic PDE to generate blending surfaces is proposed. It uses iterative finite difference algorithm to solve dynamic PDE, and investigates how different user handles affect dynamic deformations of surfaces, such as parametric variables, density and damping coefficient on. Among these, the influence of the change of parametric variables is most obvious. The modeling esarnples illustrate that the new dynamic PDE method brings more and better flexibility. It is very valuable for aided geometric design.