As set forth herein, computer-implemented methods and systems facilitate halftoning using boundaries and centers of a polygonal tiling with a parameterized spot function that operates within the tiles. Defining the halftone structure includes defining the polygonal tiling with a specification of the polygon boundaries and center, and setting and applying parameters of the spot function, which utilizes center-to-boundary distances. The tiling can be defined explicitly, by defining a tile structure, or providing centers, one per polygon, and vertices for the polygons. The vertices and centers are used to generate the polygon boundaries. The polygonal tiling can be regular (e.g., repetitive) or irregular, and can also be varied in a manner adapted to the image content or to data that is being embedded.