Reconstructing NURBS surface from randomly digitized points

A method based on cubic non uniform rational B-spline (NURBS) representation is proposed for generating optimal NURBS curve and surface models from randomly digitized points. A LSF plane-based parametrization is constructed to calculate the initial parameters of unorganized points. An explicit formula to calculate the error between the resultant shape and the measured points is derived and the constraints are defined. An optimization process based on NURBS model is developed in order to determine the quality of the approximation. The modified Levenberg-Marquardt algorithm is used to solve the non-linear constrained optimization problem. The advantage of the proposed method is that analytic and free form curves and surfaces can be represented in a unified manner and the precision of the approximation is improved by usng added weights in a reasonable time range. All the algorithms are implemented in a reverse engineering computer software. Preliminary results from the considered examples, related to a turbine blade, gear teeth surfaces or mouse surface demonstrate the efficiency of the proposed approach.