Displaced signed distance fields for additive manufacturing

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.