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 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.

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.

Advances in multimaterial 3D printing have the potential to reproduce various visual appearance attributes of an object in addition to its shape. Since many existing 3D file formats encode color and translucency by RGBA textures mapped to 3D shapes, RGBA information is particularly important for practical applications. In contrast to color (encoded by RGB), which is specified by the object’s reflectance, selected viewing conditions, and a standard observer, translucency (encoded by A ) is neither linked to any measurable physical nor perceptual quantity. Thus, reproducing translucency encoded by A is open for interpretation. In this article, we propose a rigorous definition for A suitable for use in graphical 3D printing, which is independent of the 3D printing hardware and software, and which links both optical material properties and perceptual uniformity for human observers. By deriving our definition from the absorption and scattering coefficients of virtual homogenous reference materials with an isotropic phase function, we achieve two important properties. First, a simple adjustment of A is possible, which preserves the translucency appearance if an object is rescaled for printing. Second, determining the value of A for a real (potentially non-homogenous) material, can be achieved by minimizing a distance function between light transport measurements of this material and simulated measurements of the reference materials. Such measurements can be conducted by commercial spectrophotometers used in graphic arts. Finally, we conduct visual experiments employing the method of constant stimuli, and we derive from them an embedding of A into a nearly perceptually uniform scale of translucency for the reference materials.

We present an efficient and scalable pipeline for fabricating full-colored objects with spatially-varying translucency from practical and accessible input data via multi-material 3D printing. Observing that the costs associated with BSSRDF measurement and processing are high, the range of 3D printable BSSRDFs are severely limited, and that the human visual system relies only on simple high-level cues to perceive translucency, we propose a method based on reproducing perceptual translucency cues. The input to our pipeline is an RGBA signal defined on the surface of an object, making our approach accessible and practical for designers. We propose a framework for extending standard color management and profiling to combined color and translucency management using a gamut correspondence strategy we callopaque relative processing.We present an efficient streaming method to compute voxel-level material arrangements, achieving both realistic reproduction of measured translucent materials and artistic effects involving multiple fully or partially transparent geometries.

Accurate color reproduction is important in many applications of 3D printing, from design prototypes to 3D color copies or portraits. Although full color is available via other technologies, multi-jet printers have greater potential for graphical 3D printing, in terms of reproducing complex appearance properties. However, to date these printers cannot produce full color, and doing so poses substantial technical challenges, from the shear amount of data to the translucency of the available color materials. In this paper, we propose an error diffusion halftoning approach to achieve full color with multi-jet printers, which operates on multiple isosurfaces or layers within the object. We propose a novel traversal algorithm for voxel surfaces, which allows the transfer of existing error diffusion algorithms from 2D printing. The resulting prints faithfully reproduce colors, color gradients and fine-scale details.

We propose a novel approach to automatically fill holes in triangulated models. Each hole is filled using a minimum energy surface that is obtained in three steps. First, we unfold the hole boundary onto a plane using energy minimization. Second, we triangulate the unfolded hole using a constrained Delaunay triangulation. Third, we embed the triangular mesh as a minimum energy surface in Ropf3. The running time of the method depends primarily on the size of the hole boundary and not on the size of the model, thereby making the method applicable to large models. Our experiments demonstrate the applicability of the algorithm to the problem of filling holes bounded by highly curved boundaries in large models.