基于周期B样条曲面的环状N边洞G^n连续性过渡

G^n filling orbicular N-sided holes using periodic B-spline surfaces

环状N边洞经常产生于零件端部的大半径过渡或光滑填充操作中,现有的基于四边形分割或约束求解的方法对此难以得到法向或更高阶连续的过渡曲面.本文首先对环状N边洞的边界进行保持Gn连续的重新参数化,以确保相邻边界跨越切矢曲线在连接处的相容性.然后根据极点处的Gn连续充分条件和通过参数连续曲面延伸,分别得到周期B样条曲面的内外两侧控制顶点.该方法仅生成单个填充曲面,控制顶点少,可直接通过插节点转化为标准B样条曲面,次数仅相对原边界曲线升n次.其构造方法简单快速,不涉及大方程求解和迭代,在几何相容条件下曲面连续性可达到Gn.本文提供了过渡实例来说明其有效性和实用性.

The orbicular N-sided hole filling problem is usually introduced by filleting an end-point of a part with large radius.The existing methods based on quadrilateral partition or constrained-optimization can rarely generate high-order continuous blending surfaces under these circumstances.This paper first reparameterizes the boundary of the specified orbicular N-sided hole to ensure the compatibility of neighboring cross-boundary derivatives on the connecting points,preserving their Gn continuity.Then we compute the control points of the periodic B-spline surface using the suffcient Gn continuity condition on the pole and the algorithm of extending parametric surfaces.This method generates single blending surface,which can be converted into standard Bspline surface by adding knots without introducing errors.It only elevates the degree of the boundary by n.The construction method is simple and effcient,without iteration nor large-scale matrix solving.It achieves Gn continuity under compatible conditions.The blending examples underline its feasibility and practicability.