Shape dithering for 3D printing

We present an efficient, purely geometric, algorithmic, and parameter free approach to improve surface quality and accuracy in voxel-controlled 3D printing by counteracting quantization artifacts. Such artifacts arise due to the discrete voxel sampling of the continuous shape used to control the 3D printer, and are characterized by low-frequency geometric patterns on surfaces of any orientation. They are visually disturbing, particularly on small prints or smooth surfaces, and adversely affect the fatigue behavior of printed parts. We use implicit shape dithering, displacing the part's signed distance field with a high-frequent signal whose amplitude is adapted to the (anisotropic) print resolution. We expand the reverse generalized Fourier slice theorem by shear transforms, which we leverage to optimize a 3D blue-noise mask to generate the anisotropic dither signal. As a point process it is efficient and does not adversely affect 3D halftoning. We evaluate our approach for efficiency, geometric accuracy and show its advantages over the state of the art.