Analytic and discrete fairing of three-dimensional B-spline curves using nonlinear programming

In reverse engineering, curves are constructed by interpolating the data points digitized from existing products. However, the constructed curves could have errors due to the noises in the digitized data points. If the errors remain, designers may get undesirable results. Thus, fairing of the curves is performed during computer modeling process. This paper presents two fairing algorithms for three-dimensional B-spline curves. One is an analytic fairing algorithm, and the other is a discrete fairing algorithm. These algorithms are based on automatic repositioning of the control points or the data points of a B-spline curve using a constrained nonlinear optimization algorithm. We analyzed the tradeoffs of the two fairing algorithms in terms of fairing flexibility and shape preservation.