N-Sided Hole Filling Algorithm Based on GNURBS

N-sided hole filling is a fundamental problem in the field of computer-aided design (CAD), which is widely used in engineer design and surface modeling. A n-sided hole filling algorithm based on generalized non-uniform rational B-splines (GNURBS) that can construct a globally G¹ continuous filling surface for any given surface boundaries was proposed. The algorithm first divides the n-sided hole into a quadrilateral mesh, which can be used to define corresponding GNURBS basis functions, and then the position and weight of control points in GNURBS are computed according to the boundary continuity constraints and the energy optimization methods. The new algorithm is fully compatible with non-uniform rational B-splines (NURBS), can be transfer between CAD software without loss. This paper presents a comparison between the GNURBS-based filling surfaces and the filling surfaces generated by the commercial CAD software CATIA. Several filling examples demonstrate that the GNURBS-based filling surfaces exhibit superior boundary continuity and surface quality.