Recent work has demonstrated that the interior material layout of a 3D model can be designed to make a fabricated replica satisfy application-specific demands on its physical properties such as resistance to external loads. A widely used practice to fabricate such models is by layer-based additive manufacturing (AM) or 3D printing, which however suffers from the problem of adding and removing interior supporting structures. In this paper, we present a novel method for generating support-free elliptic hollowing for 3D shapes which can entirely avoid additional supporting structures. To achieve this, we perform the ellipse hollowing in the polygons on parallel section planes and protrude the ellipses of one plane to its neighboring planes. To pack the ellipses in a polygon, we construct the Voronoi diagram of ellipses to efficiently reason the free-space around the ellipses and other geometric features by taking advantage of the available algorithm for the efficient and robust construction of the Voronoi diagram of circles. We demonstrate the effectiveness and feasibility of our proposed method by generating interior designs for and printing various 3D shapes.
Significant work has been done in generating interior structure of a model to meet various geometric and or physical properties. @cite_59 hollows a 3D-printed object while maintaining its structural strength by adding some internal struts. The interior is optimized by a reduced-order parameterization of offset surfaces in @cite_81 . Various internal structures, such as the skin-frame structure @cite_24 , the honeycomb-like structure @cite_20 , and the medial axis tree structure @cite_10 , were developed for cost-effective purposes while preserving the structural strength of printed objects. Both static balance and dynamic balance have been studied by designing the interior infills as well as changing the model shapes @cite_28 @cite_78 @cite_52 . Instead of designing hollowing structure explicitly, a lot of efforts have been put on topology optimization to obtain distributions of material according to certain performance criteria during the last three decades @cite_25 @cite_72 . However, these works have not handled the problem of avoiding large overhangs. We study this problem by developing a carving operator via support-free elliptic voids.
@cite_78 @cite_28 @cite_52 @cite_24 @cite_81 @cite_72 @cite_59 @cite_10 @cite_25 @cite_20
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Abstract Recent work has demonstrated that the interior material layout of a 3D model can be designed to make a fabricated replica satisfy application-specific demands on its physical properties, such as resistance to external loads. A widely used practice to fabricate such models is by layer-based additive manufacturing (AM), which however suffers from the problem of adding and removing interior supporting structures. In this paper, we present a novel method for generating application-specific infill structures on rhombic cells so that the resultant structures can automatically satisfy manufacturing requirements on overhang-angle and wall-thickness. Additional supporting structures can be avoided entirely in our framework. To achieve this, we introduce the usage of an adaptive rhombic grid, which is built from an input surface model. Starting from the initial sparse set of rhombic cells, via numerical optimization techniques an objective function can be improved by adaptively subdividing the rhombic grid and thus adding more walls in cells. We demonstrate the effectiveness of our method for generating interior designs in the applications of improving mechanical stiffness and static stability. The emergence of low-cost 3D printers steers the investigation of new geometric problems that control the quality of the fabricated object. In this paper, we present a method to reduce the material cost and weight of a given object while providing a durable printed model that is resistant to impact and external forces. We introduce a hollowing optimization algorithm based on the concept of honeycomb-cells structure. Honeycombs structures are known to be of minimal material cost while providing strength in tension. We utilize the Voronoi diagram to compute irregular honeycomb-like volume tessellations which define the inner structure. We formulate our problem as a strength--to--weight optimization and cast it as mutually finding an optimal interior tessellation and its maximal hollowing subject to relieve the interior stress. Thus, our system allows to build-to-last 3D printed objects with large control over their strength-to-weight ratio and easily model various interior structures. We demonstrate our method on a collection of 3D objects from different categories. Furthermore, we evaluate our method by printing our hollowed models and measure their stress and weights. In this paper, we present a two-level generative model for representing the images and surface depth maps of drapery and clothes. The upper level consists of a number of folds which will generate the high contrast (ridge) areas with a dictionary of shading primitives (for 2D images) and fold primitives (for 3D depth maps). These primitives are represented in parametric forms and are learned in a supervised learning phase using 3D surfaces of clothes acquired through photometric stereo. The lower level consists of the remaining flat areas which fill between the folds with a smoothness prior (Markov random field). We show that the classical ill-posed problem-shape from shading (SFS) can be much improved by this two-level model for its reduced dimensionality and incorporation of middle-level visual knowledge, i.e., the dictionary of primitives. Given an input image, we first infer the folds and compute a sketch graph using a sketch pursuit algorithm as in the primal sketch (, 2003). The 3D folds are estimated by parameter fitting using the fold dictionary and they form the "skeleton" of the drapery cloth surfaces. Then, the lower level is computed by conventional SFS method using the fold areas as boundary conditions. The two levels interact at the final stage by optimizing a joint Bayesian posterior probability on the depth map. We show a number of experiments which demonstrate more robust results in comparison with state-of-the-art work. In a broader scope, our representation can be viewed as a two-level inhomogeneous MRF model which is applicable to general shape-from-X problems. Our study is an attempt to revisit Marr's idea (Marr and Freeman, 1982) of computing the 2frac12D sketch from primal sketch. In a companion paper (Barbu and Zhu, 2005), we study shape from stereo based on a similar two-level generative sketch representation. Abstract Frequently, terrestrial LiDAR and image data are used to extract high resolution building geometry like windows, doors and protrusions for three-dimensional (3D) facade reconstruction. However, such a purely data driven bottom-up modelling of facade structures is only feasible if the available observations meet considerable requirements on data quality. Errors in measurement, varying point densities, reduced accuracies, as well as incomplete coverage affect the achievable correctness and reliability of the reconstruction result. While dependence on data quality is a general disadvantage with data driven bottom-up approaches, model based top-down reconstructions are much more robust. Algorithms introduce knowledge about the appearance and arrangement of objects. Thus, they cope with data uncertainty and allow for a procedural modelling of building structures in a predefined architectural style, which is inherent in grammar or model descriptions. We aim at a quality sensitive facade reconstruction which is on the one hand robust against erroneous and incomplete data, but on the other hand not subject to prespecified rules or models. For this purpose, we combine bottom-up and top-down strategies by integrating automatically inferred rules into a data driven reconstruction process. Facade models reconstructed during a bottom-up method serve as a knowledge base for further processing. Dominant or repetitive features and regularities as well as their hierarchical relationship are detected from the modelled facade elements and automatically translated into rules. These rules together with the 3D representations of the modelled facade elements constitute a formal grammar. It holds all the information which is necessary to reconstruct facades in the style of the given building. The paper demonstrates that the proposed algorithm is very flexible towards different data quality and incomplete sensor data. The inferred grammar is used for the verification of the facade model produced during the data driven reconstruction process and the generation of synthetic facades for which only partial or no sensor data is available. Moreover, knowledge propagation is not restricted to facades of one single building. Based on a small set of formal grammars derived from just a few observed buildings, facade reconstruction is also possible for whole districts featuring uniform architectural styles.