Goniochromatic materials and objects appear to have different colors depending on viewing direction. This occurs in nature, such as in wood or minerals, and in human-made objects such as metal and effect pigments. In this paper, we propose algorithms to control multi-material 3D printers to produce goniochromatic effects on arbitrary surfaces by procedurally augmenting the input surface with meso-facets, which allow distinct colors to be assigned to different viewing directions of the input surface while introducing minimal changes to that surface. Previous works apply only to 2D or 2.5D surfaces, require multiple fabrication technologies, or make considerable changes to the input surface and require special post-processing, whereas our approach requires a single fabrication technology and no special post-processing. Our framework is general, allowing different generating functions for both the shape and color of the facets. Working with implicit representations allows us to generate geometric features at the limit of device resolution without tessellation. We evaluate our approach for performance, showing negligible overhead compared to baseline color 3D print processing, and for goniochromatic quality.

We propose displaced signed distance fields, an implicit shape representation to accurately, efficiently and robustly 3D-print finely detailed and smoothly curved surfaces at native device resolution. As the resolution and accuracy of 3D printers increase, accurate reproduction of such surfaces becomes increasingly realizable from a hardware perspective. However, representing such surfaces with polygonal meshes requires high polygon counts, resulting in excessive storage, transmission and processing costs. These costs increase with print size, and can become exorbitant for large prints. Our implicit formulation simultaneously allows the augmentation of low-polygon meshes with compact meso-scale topographic information, such as displacement maps, and the realization of curved polygons, while leveraging efficient, streaming-compatible, discrete voxel-wise algorithms. Critical for this is careful treatment of the input primitives, their voxel approximation and the displacement to the true surface. We further propose a robust sign estimation to allow for incomplete, non-manifold input, whether human-made for onscreen rendering or directly out of a scanning pipeline. Our framework is efficient both in terms of time and space. The running time is independent of the number of input polygons, the amount of displacement, and is constant per voxel. The storage costs grow sub-linearly with the number of voxels, making our approach suitable for large prints. We evaluate our approach for efficiency and robustness, and show its advantages over standard techniques.