AbstractA hole patching algorithm for discrete geometry using a parametric approach based on Non‐Uniform Rational B‐Spline (NURBS) curves and surfaces is being presented in this paper. This algorithm is focused on recovering the missing geometric information based on the neighboring points surrounding the topologically simple but geometrically complex holes. The neighboring points are utilized to reconstruct a set of three‐dimensional (3D) NURBS surface patches covering the hole region which in turn are used to produce a smooth surface patch covering the hole. This algorithm can automatically identify the hole, obtain surrounding points, create the NURBS surfaces, and perform the projection of points onto the surface to complete the process. The algorithm also provides a way for the user to control the size and density of triangulation in the patches matching that of the surroundings. This paper describes the algorithm step by step in detail with a test case for description purposes. The validation of the algorithm is performed on several analytical geometries to assess the accuracy of the algorithm. Several complex geometries are used to demonstrate the success and robustness of the algorithm. Finally, a conclusion provides the overall assessment of this research and identifies its weaknesses for future improvements. Copyright © 2011 John Wiley & Sons, Ltd.