基于解析伪谱法的四边PDE曲面生成方法

为解决高效、快速、精确地生成曲面等问题,将偏微分方程（PDE）应用到曲面生成中（PDE方法优越性在于可以通过相对较少的参数生成一张光滑的曲面）。研究了用解析伪谱法快速生成一张解析近似的四边PDE曲面片,与分离变量法不同的是,该方法生成曲面的近似解由3部分组成：一个特征函数;一个多项式的解,两者皆可精确地满足偏微分方程;附加一个剩余函数,以确保精确的满足边界条件;进行了相同边界条件下分离变量法与解析伪谱法生成曲面的试验。实验结果表明,解析伪谱法生成的PDE曲面较分离变量法精确度高,且更为光滑。

Four sides PDE surfaces generation method based on Pseudo-spectral method

In order to solve the problems of generate the surface quickly, efficiently and accurately,the partial differential equation（PDE） was applied to the surface generation. The power of the PDE method lies in its ability to represent smooth surfaces in terms of a relatively small set of design parameters. Based on PDE analytical method, a four sided PDE surface patch based on pseudo-spectral method for rapidly calculating an analytic approximation was investigated. Different from separation of variables, the generated approximate solution was consisted of three parts ： an eigenfunction solution and a polynomial solution, both of which satisfied the generating partial differential equation exactly, and a remainder function ensured the boundary conditions were satisfied exactly. The method of separation of variables and analytic pseudo-spectral to generate surface were tested in the same boundary conditions. The experimental results show that the method based on pseudo-spectral has high accurate and more smooth compared with the separation of variables.