基于解析解的四阶PDE曲面裁剪方法

Analytical Solution Based on the Fourth-order PDE Surface Trimming Method

该文提出了一种可以广泛应用于四阶PDE曲面的裁剪方法。利用PDE的参数域内的曲线在曲面上投影,得到所求裁剪曲面的边界曲线,然后通过边界曲线的导矢与曲面在边界曲线处的法向量得到边界曲线处的跨界导矢,最后以求得的裁剪曲面的边界曲线以及裁剪曲面在边界曲线处的跨界导矢为PDE曲面的边界条件,用四阶的PDE曲面方程求得PDE裁剪曲面。

This paper proposes a fourth-order PDE can be widely used method of cutting surface. The we use the PDE within the parameters of the curve on the surface projection,get the required cutting surface boundary curves,then the derivative vector boundary curves and surfaces in the normal vector at the boundary curves obtained at the cross-boundary curve derivative vector,and finally to the cut surfaces obtained and trimmed surface boundary curves at the boundary curves cross derivative vector of PDE surface boundary conditions, with the fourth-order PDE surface equation obtained by cutting surfaces.