From 3D Models to 3D Prints: an Overview of the Processing Pipeline <s> Internal supports <s> This paper outlines exact offset procedures for three basic classes of solid primitive: (1) solids of revolution with simple profile curves; (2) solids of linear extrusion with simple profile curves; and (3) convex planar polyhedra. Concepts from differential geometry are used to illustrate the complexity of offsets to general curves and surfaces, and to identify conditions under which offset geometries degenerate. Qualitative descriptions for offset surfaces to simple solids are then presented, in terms of their elementary constituent patches, and the geometrical and topological relationship of these patches to the progenitor primitives. Precise mathematical representations for the required surface elements, as parametric rational polynomial forms, are given in an Appendix. The uses and limitations of offset solids in a solid modeling environment are briefly assessed, and the difficulties of offsets for complex solids are enumerated. <s> BIB001 </s> From 3D Models to 3D Prints: an Overview of the Processing Pipeline <s> Internal supports <s> The real-time shaded display of a solid model being milled by a cutting tool following an NC path is attained by the image-space Boolean subtraction of solid objects. The technique is suitable for implementation in microcode in a raster graphic display processor. Update rates of 10 cutting operations per second are typical. <s> BIB002 </s> From 3D Models to 3D Prints: an Overview of the Processing Pipeline <s> Internal supports <s> This paper presents a simple algorithm for hollowing out a solid CAD model. The algorithm employs voxel elements to do the hollowing. Instead of performing three-dimensional Boolean operations on the solid CAD model, one-dimensional Boolean operations between the ray representations of the model and voxel elements are carried out. The ray representation of the hollowed model in turn, produces the direct slice files as output to the rapid prototyping machine. In order to satisfy strength considerations, square and honeycomb structures are formed in the hollowed object. <s> BIB003 </s> From 3D Models to 3D Prints: an Overview of the Processing Pipeline <s> Internal supports <s> This paper presents a new 3D offset method for modifying CAD model data in the STL format. In this method, vertices, instead of facets, are offset. The magnitude and direction of each vertex offset is calculated using the weighted sum of the normals of the facets that are connected to each vertex. To facilitate the vertex offset calculation, topological information is generated from the collection of unordered triangular facets making up the STL file. A straightforward algorithm is used to calculate the vertex offset using the adjoining facet normals, as identified from the topological information. This newly developed technique can successfully generate inward or outward offsets for STL models. As with any offset methodology, this technique has benefits and drawbacks, which will be discussed in this paper. Finally, conclusions will be made regarding the applicability of the developed methodology. <s> BIB004 </s> From 3D Models to 3D Prints: an Overview of the Processing Pipeline <s> Internal supports <s> Displaying the result of sweeping a solid is usually accomplished by first evaluating the boundaries of the solid being swept out, and a standard shading method is then applied to obtain a realistic image of the solid. This paper present an algorithm for sweeping a 3D object in image space. The result obtained is another solid in image space. Boolean operations can then be performed on this model. By subtracting the swept-out solid from another solid, the proposed method can be used for simulating the material removal process in an NC machining operation. <s> BIB005 </s> From 3D Models to 3D Prints: an Overview of the Processing Pipeline <s> Internal supports <s> We present a new algorithm for the efficient and reliable generation of offset surfaces for polygonal meshes. The algorithm is robust with respect to degenerate configurations and computes (self-)intersection free offsets that do not miss small and thin components. The results are correct within a prescribed e-tolerance. This is achieved by using a volumetric approach where the offset surface is defined as the union of a set of spheres, cylinders, and prisms instead of surface-based approaches that generally construct an offset surface by shifting the input mesh in normal direction. Since we are using the unsigned distance field, we can handle any type of topological inconsistencies including non-manifold configurations and degenerate triangles. A simple but effective mesh operation allows us to detect and include sharp features (shocks) into the output mesh and to preserve them during post-processing (decimation and smoothing). We discretize the distance function by an efficient multi-level scheme on an adaptive octree data structure. The problem of limited voxel resolutions inherent to every volumetric approach is avoided by breaking the bounding volume into smaller tiles and processing them independently. This allows for almost arbitrarily high voxel resolutions on a commodity PC while keeping the output mesh complexity low. The quality and performance of our algorithm is demonstrated for a number of challenging examples. <s> BIB006 </s> From 3D Models to 3D Prints: an Overview of the Processing Pipeline <s> Internal supports <s> The layered depth-normal images (LDNIs) is an implicit representation of solid models that sparsely encodes the shape boundary in three orthogonal directions. We present a LDNI-based geometric modeling method for applications with high accuracy requirements. In our method, we first construct LDNIs models from input polygonal models. The accuracy of the generated LDNIs models can be controlled by setting pixel width during the construction process. Even for very complex geometries and high accuracy requirements, the construction process is fast with the aid of graphics hardware. Based on the LDNIs models, we then perform geometric modeling operations. Two types of operations are presented including regularizing and Boolean operations. The geometric modeling operations are straightforward and easy to be implemented robustly. From the processed LDNIs model, an adaptive sampling method is presented to construct a cell representation that includes both uniform and octree cells. Finally 2-manifold polygonal mesh surfaces are constructed from the cell representation. For high accuracy requirements that are typical in CAD/CAM applications, we present a volume tiling technique and a parallel implementation to accelerate the computation. Our method achieves a good balance between the accuracy and computational resources. We report experimental results on a variety of CAD models. The results demonstrate the effectiveness and efficiency of our approach especially for modeling complex geometries.© 2008 ASME <s> BIB007 </s> From 3D Models to 3D Prints: an Overview of the Processing Pipeline <s> Internal supports <s> We present a novel technique for the efficient boundary evaluation of sweep operations applied to objects in polygonal boundary representation. These sweep operations include Minkowski addition, offsetting, and sweeping along a discrete rigid motion trajectory. Many previous methods focus on the construction of a polygonal superset (containing self-intersections and spurious internal geometry) of the boundary of the volumes which are swept. Only few are able to determine a clean representation of the actual boundary, most of them in a discrete volumetric setting. We unify such superset constructions into a succinct common formulation and present a technique for the robust extraction of a polygonal mesh representing the outer boundary, i.e. it makes no general position assumptions and always yields a manifold, watertight mesh. It is exact for Minkowski sums and approximates swept volumes polygonally. By using plane-based geometry in conjunction with hierarchical arrangement computations we avoid the necessity of arbitrary precision arithmetics and extensive special case handling. By restricting operations to regions containing pieces of the boundary, we significantly enhance the performance of the algorithm. <s> BIB008 </s> From 3D Models to 3D Prints: an Overview of the Processing Pipeline <s> Internal supports <s> A fast offset surface generation approach is presented in this paper to construct intersection-free offset surfaces, which preserve sharp features, from freeform triangular mesh surfaces. The basic spirit of our algorithm is to sample a narrowband signed distance-field from the input model on a uniform grid and then employ a contouring algorithm to build the resultant offset mesh surface from the signed distance-field. Four filters are conducted to generate the narrowband signed distance-field around the offset surface in a very efficient way by alleviating computation redundancies in the regions far from the offset surfaces. The resultant mesh surfaces are generated by a modified dual contouring algorithm which relies on accurate intersections between the grid edges and the isosurfaces. A hybrid method is developed to prevent the expensive bisection search in the configurations that the analytical solutions exist. Our modified intersection-free dual contouring algorithm is based on convex-concave analysis, which is more robust and efficient. The quality and performance of our approach are demonstrated with a number of experimental tests on various examples. <s> BIB009
The interior of an object is a key factor regarding the material use, print time and mechanical properties of the final result. The impact on material use and print time is easily explained by the fact that the inner volume grows to the cube of the scaling factor (i.e. doubling the size of an object multiplies its volume by eight). Therefore, most of the time and material is spent on the inside of the object. Carving the inside can lead to large savings. However, care must be taken to ensure that the object can still be fabricated (e.g. avoiding the introductions of overhangs or islands, not forming pockets) and that the end result will remain rigid enough. In addition, modifying the structure of the inside of an object gives the opportunity to change its global mechanical behaviour, for instance making it flexible or rigid in different places, or changing its balance. We organize this section as follows. We first consider in Section 3.3.2.1 techniques that focus on creating large empty pockets within objects. Next, we discuss in Section 3.3.2.2 and in Section 3.3.2.3 approaches that focus on how to infill the object interior, from dense to sparse infill patterns. These techniques have an emphasis on material/time savings and exploit specificities of the processes. We focus in Section 3.3.2.4 on frame structures, which are typically beam or cellular structures optimized to create a strong structure within the object interior. We discuss in Section 3.3.2.5 techniques that focus on changing the mechanical behaviour of the object by filling its inside with micro-structures. Since this is a very large topic, we keep the focus on techniques that tightly integrate with the process planning pipeline. 3.3.2.1. Hollowing. Most of the techniques we discuss here treat the general geometric problem of computing an inner cavity at a fixed distance from the object surface. The surface of the inner cavity is called the offset surface of the model BIB001  . These approaches can be used to compute inner cavities that are either left empty or filled with the approaches described in Section 3.3.2.3. Early approaches obtain a superset of geometric primitives of the offset surface that are trimmed and filtered to form the final offset boundary  . Qu and Stucker BIB004 presented a vertex convolution method for STL files without explicit treatment of self-intersections. Campen and Kobbelt BIB008 introduced an exact convolution approach. Hollowing can also be performed by first computing the distance field of the model, and extracting the offset surface from it. Frisken et al. [FPRJ00] presented and adaptively sampled distance field. Varadhan and Manocha  approximate the offset surface with a distance field isosurface extraction, guaranteeing a Hausdorff distance bound on the approximation. Pavić and Kobbelt BIB006 traverse an octree distance field and split each cell which is potentially intersected by the offset surface. Liu and Wang BIB009 extract the isosurface of a narrow band distance field. Another class of hollowing methods consider ray representations of solids such as the dexel structure BIB002 or the layered depth normal images (LDNI) BIB007 . For a single direction and a uni- form grid of rays parallel to that direction, a ray-representation stores the intervals of the rays lying inside the solid. Hui BIB005 computes the sweeping of a solid along a trajectory by considering the union of a finite set of ray representations of the solid. Chiu and Tan BIB003 Figure 7) .