基于周期B 样条曲面的环状<italic>N</italic> 边洞<italic>G<sup>n</sup></italic> 连续性过渡

Abstract

The orbicular <italic>N</italic>-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 <italic>N</italic>-sided hole to ensure the compatibility of neighboring cross-boundary derivatives on the connecting points, preserving their <italic>Gⁿ</italic> continuity. Then we compute the control points of the periodic B-spline surface using the sufficient <italic>Gⁿ</italic> continuity condition on the pole and the algorithm of extending parametric surfaces. This method generates single blending surface, which can be converted into standard B-spline surface by adding knots without introducing errors. It only elevates the degree of the boundary by <italic>n</italic>. The construction method is simple and efficient, without iteration nor large-scale matrix solving. It achieves <italic>Gⁿ</italic> continuity under compatible conditions. The blending examples underline its feasibility and practicability.