An Improved N-Sided Filling Algorithm Based on GNURBS Surface

This paper proposes an N-side hole filling algorithm based on generalized non-uniform rational B-splines (GNURBS) to address the limitations of existing methods in handling the topological complexity and smoothness of filling surfaces, and the trade-off between surface quality and the number of control points. First, cubic uniform B-splines are employed to fit the given boundary curves along with their corresponding C¹ and C² curves, determining the required number of control points to satisfy error tolerances. Next, a quadrilateral topology for the N-side hole is constructed based on the control point counts of each boundary, facilitating the generation of a compatible GNURBS control grid and basis functions. Finally, an optimization objective incorporating shape energy and boundary constraint energy is established, and the positions of the control points are optimized by iteratively solving a system of linear equations to generate a high-quality filling surface. Comparative experiments with the commercial software XNURBS demonstrate that, under identical conditions of error, constraints, and surface quality, the proposed algorithm reduces the number of control points by approximately 70%.