A method of generating control data for a manufacture of a three-dimensional object by means of a layer-wise solidification of a building material, wherein said manufactured three-dimensional object is destined to be used in a flow path of a fluid flowing in a designated way around or through said object, said method comprising the following steps: identifying surface data in a three-dimensional computer-based model of said three-dimensional object, said surface data corresponding to at least one surface of the manufactured three-dimensional object, which at least one surface is destined to get into contact with the fluid, determining the flow path adjacent a portion of said at least one surface in said computer-based model modifying said three-dimensional computer-based model thus generating a modified computer-based model such that support structure data are added to the computer-based model, said support structure data specifying a support structure designed to be in contact with said portion of said at least one surface during the manufacture of said three-dimensional object, wherein said support structure data are added to the computer-based model such that at least one contact region between the support structure and said portion of said at least one surface will essentially extend in parallel to the determined flow path adjacent said portion of said at least one surface and/or such that positions of a plurality of contact regions between a plurality of support structures and said portion of said at least one surface will essentially extend in parallel to the determined flow path adjacent said portion of said at least one surface, and deriving control data for the manufacture of the three-dimensional object from the modified computer-based model. identifying surface data in a three-dimensional computer-based model of said three-dimensional object, said surface data corresponding to at least one surface of the manufactured three-dimensional object, which at least one surface is destined to get into contact with the fluid, determining the flow path adjacent a portion of said at least one surface in said computer-based model modifying said three-dimensional computer-based model thus generating a modified computer-based model such that support structure data are added to the computer-based model, said support structure data specifying a support structure designed to be in contact with said portion of said at least one surface during the manufacture of said three-dimensional object, wherein said support structure data are added to the computer-based model such that at least one contact region between the support structure and said portion of said at least one surface will essentially extend in parallel to the determined flow path adjacent said portion of said at least one surface and/or such that positions of a plurality of contact regions between a plurality of support structures and said portion of said at least one surface will essentially extend in parallel to the determined flow path adjacent said portion of said at least one surface, and deriving control data for the manufacture of the three-dimensional object from the modified computer-based model. <EOS>