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A fast offset surface generation approach is presented in this paper to construct intersection-free offset surfaces, which preserve sharp features, from freeform triangular mesh surfaces. The basic spirit of our algorithm is to sample a narrowband signed distance-field from the input model on a uniform grid and then employ a contouring algorithm to build the resultant offset mesh surface from the signed distance-field. Four filters are conducted to generate the narrowband signed distance-field around the offset surface in a very efficient way by alleviating computation redundancies in the regions far from the offset surfaces. The resultant mesh surfaces are generated by a modified dual contouring algorithm which relies on accurate intersections between the grid edges and the isosurfaces. A hybrid method is developed to prevent the expensive bisection search in the configurations that the analytical solutions exist. Our modified intersection-free dual contouring algorithm is based on convex-concave analysis, which is more robust and efficient. The quality and performance of our approach are demonstrated with a number of experimental tests on various examples.