Abstract: A method is disclosed for additively manufacturing a layer of a structure. The method may include determining a surface representing the layer of the structure, and determining a seed tool path lying on the surface. The method may further include, at each of a plurality of seed points along a length of the seed tool path, determining an offset direction that is transverse to an axis of the seed tool path at each of the plurality of seed points and parallel with the surface. The method may additionally include generating a plurality of offset points, each of which is offset in the offset direction from a corresponding one of the plurality of seed points. The method may also include determining an offset tool path based on the plurality of offset points, and causing a machine to discharge material along the offset tool path.