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This article presents a general sweeping technique for nonuniform rational B-splines. This operator allows sweeps with several cross sections along a 3D path. One can scale the cross sections along the path according to the shape of a profile curve. The definition of the resulting surface is inherited from the initial curves, and you compute its control mesh from the control polygon of these curves. We shall consider several special cases, like straight lines and rational curves; characteristics of circles and straight lines are preserved.