NOMENCLATURE R = offset distance P = original vertex O = offset vertex e = length of original edge d = distance from offset vertex to original edge θ = internal angle between two original edges An offset edge algorithm is a common method of creating contour-parallel paths that has been widely studied. The method includes approaches such as pair-wise intersection and Voronoi diagrams. The method proposed in this paper is unlike these approaches in that it determines an offset algorithm via the offset vertex. In addition, the proposed method differs from common approaches because: (1) the offset vertices are computed based on bisectors, (2) the validity of combining the direction and position checking for each offset edge is the main point of the proposed method; (3) an efficient algorithm is constructed to connect all offset edges simultaneously to generate raw offset lines without local invalid loops, and (4) an offset-distance check is performed to remove the global invalid loops from the raw offset lines as well as the interference loops in joining boundaries and multiple islands. The proposed method was verified with various slice contour shapes, with or without islands, and good results were obtained with significant reductions in the calculation time.