Systems, devices, and methods for printing on surfaces of three-dimensional objects are provided. The systems, devices, and methods allow for images, and three-dimensional structures, to be printed onto a surface of a three-dimensional object. The surface of the three-dimensional object can have many different shapes, including an arbitrary or non-uniform shape having multiple curves. In one exemplary embodiment, the method includes associating a pattern of polygons with a surface of a three-dimensional object and then scaling a pattern of polygons associated with an image to be printed onto the surface with the pattern of polygons associated with the surface. One or more polygons of the scaled pattern of polygons are then progressively projected onto the surface, and a photosensitive material associated with the surface is cured to set projected image portion on the surface. Systems, devices, and other methods for printing onto surfaces of three-dimensional objects are also provided.