As 3D printing becomes more prevalent, more attention is being paid to its ability to adequately reproduce the appearance of surfaces. Research into methods to accurately represent grayscale images through halftoning is well-developed in 2D printing, but work in the halftoning of
surfaces in 3D printing is less developed. The halftoning method of tone-dependent fast error diffusion has been shown in 2D printing to be an effective means of achieving both high image quality and computational efficiency, making it an ideal algorithm to run in printing units where computational
power is restricted. This work seeks to adapt tone-dependent fast error diffusion to halftone the surfaces of three-dimensional objects.
Here, the ideal tone-dependent error diffusion parameters will be calculated for an image. Then, a surface traversal mechanism will be implemented
to navigate the surface of a threedimensional object while error diffusion is applied to halftone it. The expected result is an algorithm that can halftone the surface of an object with quality approaching that of iterative methods, with a fraction of the processing that they require. Iterative
methods currently produce the highest halftoning quality for 3D surfaces, but their use is limited due to the amount of computation they entail. The development of a tone-dependent fast error diffusion algorithm allows 3D halftoning to represent a continuoustone surface with comparably high
quality, but the computation it requires is more appropriate for standard printers; thus, it improves on the quality of surface halftoning that most printing units can produce.