基于Helmholtz方程的过渡曲面设计

Blend Surface Design Based on Helmholtz Equations

阐述了二阶和四阶Helmholtz方程的一类周期边界问题的差分解法及其在过渡曲面设计中的应用。这类方法不同于传统的PDE方法中的二阶和四阶的偏微分方程,比传统的二阶和四阶偏微分方程有了更多的自由项,因此,在曲面设计的时候,就有更多的形状控制参数可进行调整,文中重点讨论了方程中的系数对曲面形状的影响,并研究了边界切矢条件对曲面形状的影响及其在曲面形状设计中的应用。设计者只需给出边界曲线和边界切矢,并通过对它们的控制就可构造和修改曲面形状。

The problem discussed in this paper is about the second-order and fourth-order of Helmholtz equation of a class of periodic boundary problem and its difference solution in the transition surface design, which is different from traditional method of PDE in the second-order and fourth-order partial differential equations. It has more free items than the traditional method, so more shape control parameters can be adjusted in the surface design. The focused attention is to discuss the changing effects of equati...