Reverse engineering of a NURBS surface from digitized points subject to boundary conditions

Reverse engineering is an approach for constructing a CAD model from a physical part through dimensional measurement and surface modeling. In most applications, the creation of a NURBS surface usually is not a stand-alone project. The surface that fits the data points must also satisfy boundary conditions, such as positional, normal and other practical boundary conditions. In order to obtain surfaces subject to boundary conditions, a method based on a new algorithm for fitting NURBS surfaces to data points is presented in this paper. The proposed method uses chosen data points as control points to construct initial NURBS surfaces and then modifies them using minimization of deviation under boundary condition constraints (positional, normal and other practical boundary condition constraints), solved by the method of Lagrange multipliers. (C) 2003 Elsevier Ltd. All rights reserved.