基于谱配点法的过渡曲面构造

Blending Surface Design Based on Spectral-collocation Methods

为进一步提高PDE曲面造型的能力,文章阐述二阶和四阶椭圆型偏微分方程的一类周期边界问题的谱配点法及其在过渡曲面设计中的应用,它不同于传统的PDE方法中的二阶和四阶的偏微分方程,具有更多的形状参数.可以通过改变形状参数的取值,来调整曲面的形状,可以更方便地控制曲面的形状.讨论方程中的形状参数对曲面形状的影响,通过实例说明,如何用谱配点法求解椭圆型偏微分方程边值问题,构造所需的过渡曲面.

In order to further improve the ability of PDE surface modeling,this article discussed the second-order and fourth-order Helmholtz equation of a class of periodic boundary problem and its spectral-collocation methods in the blending surface design,which is different from traditional methods of PDE in the second-order and fourth-order partial differential equations.It has more free items than the traditional the second-order and fourth-order partial differential equations.Therefore,the shape of the surface can be adjusted by changing the value of shape parameters,which can more conveniently control the shape of the surface.The article focused on the equation coefficient’s change effect on the surface shape.Examples are given to illustrate how to use the spectral collocation method to solve the boundary value problem of elliptic partial differential equation and construct the required blending surface.