Sparsity And Low-Rank Representations Of Geometry Feature And Their Application In 3D Printing

Geometry features, such as vertex positions, normal vectors, curvatures, are used to de-scribe the geometric properties of a specific object. Geometry features combined with sparsity and low-rank techniques can be used to deal with many problems in digital geometric process-ing, such as 3D model upright,3D model classification, mesh matching and registration, and so on. Furthermore, geometry features can be used to handle complex problems in 3D print-ing, such as printing material reduction, printing efficiency and quality improvement. The main works are listed as follows:(1) We present a multi-objective optimization to reduce the printing material. The interior of the model is divided with density skin-frame structure firstly. A multi-objective optimization model is constructed to optimize the volume of the 3D model. Meanwhile, the mechanical properties (structural analysis), e.g. stiffness and bulking, serf-balance, stiffness, geometrical approximation, and printability are guaranteed. The redundant struts are removed by topology optimization and the radii of the remaining struts and node positions are optimized by geometry optimization. In addition, the external supporting structures are designed based on the frame-structure. The proposed algorithm can largely reduce the consumption of the printing material and supporting material, and the printed object has sufficient strength and can stably stand on the ground.(2) To reduce printing time, an adaptive slicing algorithm is proposed based on the geo-metric properties of the mesh. At first, the saliency of the model is calculated. Then, the slicing thickness is optimized according to the visual saliency to reduce the printing time. During the optimization, the high salient regions are sliced with high resolution, while the low salient re-gions are sliced with low resolution. In this way, the printing time can be largely reduced, while preserving the printing quality of the high salient regions. In order to further reduce the printing time, a saliency based segmentation algorithm is proposed and all patches are printed together to reduce the visual artifacts. Compared with the groundtruth, the object generated by our method has competitive visual quality, while the printing time is dramatically reduced.(3) To improve the printing quality, a printing direction based decomposition method is proposed. First of all, the input model is segmented into several patches so that each patch can be printed with high quality. Then, the cutting planes between adjacent patches are constructed. Voronoi cells are generated according to the cutting planes. Finally, the printable parts can be obtained by intersecting Voronoi cells with the input model. In addition, the assembly order and directions are optimized and connectors between neighbouring parts are designed. Compared with the previous methods, the proposed method can largely reduce the printing error and time.(4) To match and retrieve 3D models, a sparsity optimization algorithm based on subspace clustering is proposed. First of all, the poses of the input 3D models are normalized through scaling, translation, and rotation; then, several existing geometry features are calculated, and multi-features sparsity subspace clustering algorithm is used to optimize the representation co-efficients between geometry features; finally, spectral clustering algorithm is applied on an affin-ity matrix, constructed with representation coefficients, to obtain the classification results. Our algorithm has been tested with a large number of 3D models. The experimental results show that the proposed method has very high classification accuracy.(5) To upright the 3D model, an algorithm is proposed to minimize the rank of the three-order tensor. At first, vertex positions and the bounding box of the 3D model are used to con-struct a three-order tensor matrix; then, the proposed algorithm is used to align the model with axis; finally, the geometric properties are used to obtain the upright orientation. Since three-order tensor matrix can capture the global symmetry information of the model, the proposed method can obtain a global solution. Our method has been tested on several 3D model databas-es. The experimental results demonstrate the effectiveness and applicability of our method on several kinds of 3D objects (point cloud, non-manifold, and incomplete models).