Fairing B-spline Surfaces Using Optimization Technique

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The needs for smooth curves and surfaces are increasing in modeling cars, ships, airplanes, and other consumer products either for aesthetic or functional purpose. However, the curves and surfaces generated by conventional modeling methods usually exhibit an unwanted behavior due to digitizing errors or inadequate generation method, and thus much time and extra effort is spent afterwards to get the faired results. The objective of this work is to develop a fairing scheme by which well refined shape of a surface can be acquired with detecting and removing the shape imperfections of the given surface represented by NURBS. The fairing scheme is based on an optimization process in which the control points of the given surface are repositioned to minimize the integration of the jumps(perturbations) of the unit normal vectors at all surface points.