Smooth-surface approximation and reverse engineering

Abstract The paper identifies the steps involved in the reverse-engineering process. The procedure begins with the division of the whole array of measurement data points into regions, according to shape-change detection. In each region, points are parameterized, and knots are selected. Smooth parametric surface approximation is obtained by the least-square fitting of B-splines. Nonlinear least-square minimization is applied for parameter optimization with simple bounds on the parameter values. The objective function minimized is the explicit error expression for the sum of the squares of error values at the data points.