Level-set-based partitioning and packing optimization of a printable model

As the 3D printing technology starts to revolutionize our daily life and the manufacturing industries, a critical problem is about to e-merge: how can we find an automatic way to divide a 3D model into multiple printable pieces, so as to save the space, to reduce the printing time, or to make a large model printable by small printers. In this paper, we present a systematic study on the partitioning and packing of 3D models under the multi-phase level set framework. We first construct analysis tools to evaluate the qualities of a partitioning using six metrics: stress load, surface details, interface area, packed size, printability, and assembling. Based on this analysis, we then formulate level set methods to improve the qualities of the partitioning according to the metrics. These methods are integrated into an automatic system, which repetitively and locally optimizes the partitioning. Given the optimized partitioning result, we further provide a container structure modeling algorithm to facilitate the packing process of the printed pieces. Our experiment shows that the system can generate quality partitioning of various 3D models for space saving and fast production purposes.

[1]  Olga Sorkine-Hornung,et al.  Assembling self-supporting structures , 2014, ACM Trans. Graph..

[2]  N. Carr,et al.  PackMerger: A 3D Print Volume Optimizer , 2014, Comput. Graph. Forum.

[3]  Radomír Mech,et al.  Stress relief , 2012, ACM Trans. Graph..

[4]  Thomas A. Funkhouser,et al.  A benchmark for 3D mesh segmentation , 2009, ACM Trans. Graph..

[5]  Yong-Liang Yang,et al.  TrayGen: Arranging Objects for Exhibition and Packaging , 2013, Comput. Graph. Forum.

[6]  Markus H. Gross,et al.  Meshless deformations based on shape matching , 2005, ACM Trans. Graph..

[7]  Chi-Wing Fu,et al.  Making burr puzzles from 3D models , 2011, ACM Trans. Graph..

[8]  J. Sethian,et al.  The Voronoi Implicit Interface Method for computing multiphase physics , 2011, Proceedings of the National Academy of Sciences.

[9]  Jens Egeblad,et al.  Translational packing of arbitrary polytopes , 2009, Comput. Geom..

[10]  Daniel Cohen-Or,et al.  Stackabilization , 2012, ACM Trans. Graph..

[11]  Peng Song,et al.  Recursive interlocking puzzles , 2012, ACM Trans. Graph..

[12]  José Fernando Oliveira,et al.  Solving Irregular Strip Packing problems by hybridising simulated annealing and linear programming , 2006, Eur. J. Oper. Res..

[13]  Ronald Fedkiw,et al.  Nonconvex rigid bodies with stacking , 2003, ACM Trans. Graph..

[14]  Ian M. Mitchell,et al.  A hybrid particle level set method for improved interface capturing , 2002 .

[15]  Daniel Cohen-Or,et al.  Build-to-last , 2014, ACM Trans. Graph..

[16]  Alexandru Telea,et al.  Voxel-Based Assessment of Printability of 3D Shapes , 2011, ISMM.

[17]  Wojciech Matusik,et al.  Chopper: partitioning models into 3D-printable parts , 2012, ACM Trans. Graph..

[18]  Olga Sorkine-Hornung,et al.  Spin-it , 2014, ACM Trans. Graph..

[19]  Hiroshi Nagamochi,et al.  A Multi-sphere Scheme for 2D and 3D Packing Problems , 2007, SLS.

[20]  Jan Kautz,et al.  3D-printing of non-assembly, articulated models , 2012, ACM Trans. Graph..

[21]  Sylvain Lefebvre,et al.  Bridging the gap , 2014, ACM Trans. Graph..

[22]  Ligang Liu,et al.  Cost-effective printing of 3D objects with skin-frame structures , 2013, ACM Trans. Graph..

[23]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[24]  J. Sethian,et al.  FRONTS PROPAGATING WITH CURVATURE DEPENDENT SPEED: ALGORITHMS BASED ON HAMILTON-JACOB1 FORMULATIONS , 2003 .

[25]  Ronald Fedkiw,et al.  Multiple interacting liquids , 2006, ACM Trans. Graph..

[26]  Marcin Novotni,et al.  Gomputing geodesic distances on triangular meshes , 2002 .

[27]  Doug L. James,et al.  Fabricating articulated characters from skinned meshes , 2012, ACM Trans. Graph..

[28]  Frédo Durand,et al.  Structural optimization of 3D masonry buildings , 2012, ACM Trans. Graph..

[29]  John Hart,et al.  ACM Transactions on Graphics , 2004, SIGGRAPH 2004.

[30]  Daniel Cohen-Or,et al.  Approximate pyramidal shape decomposition , 2014, ACM Trans. Graph..

[31]  Greg Turk,et al.  Simplification and Repair of Polygonal Models Using Volumetric Techniques , 2003, IEEE Trans. Vis. Comput. Graph..

[32]  Russell E. King,et al.  Multi-objective Optimization of 3D Packing Problem in Additive Manufacturing , 2014 .

[33]  Ariel Shamir,et al.  A survey on Mesh Segmentation Techniques , 2008, Comput. Graph. Forum.

[34]  George K. Knopf,et al.  Serial packing of arbitrary 3D objects for optimizing layered manufacturing , 1998, Other Conferences.

[35]  Plácido Rogério Pinheiro,et al.  Tackling the Irregular Strip Packing problem by hybridizing genetic algorithm and bottom-left heuristic , 2013, 2013 IEEE Congress on Evolutionary Computation.

[36]  T. Chan,et al.  A Variational Level Set Approach to Multiphase Motion , 1996 .

[37]  D. Chopp,et al.  A projection method for motion of triple junctions by level sets , 2002 .

[38]  Steven J. Ruuth A Diffusion-Generated Approach to Multiphase Motion , 1998 .

[39]  Kun Zhou,et al.  An asymptotic numerical method for inverse elastic shape design , 2014, ACM Trans. Graph..

[40]  Hiroshi Nagamochi,et al.  An iterated local search algorithm based on nonlinear programming for the irregular strip packing problem , 2009, Discret. Optim..

[41]  Olga Sorkine-Hornung,et al.  Designing unreinforced masonry models , 2013, ACM Trans. Graph..

[42]  F. Gibou A fast hybrid k-means level set algorithm for segmentation , 2005 .

[43]  Tony F. Chan,et al.  A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model , 2002, International Journal of Computer Vision.

[44]  Denis Zorin,et al.  Worst-case structural analysis , 2013, ACM Trans. Graph..

[45]  Byungmoon Kim,et al.  Multi-phase fluid simulations using regional level sets , 2010, ACM Trans. Graph..

[46]  Takeo Igarashi,et al.  Converting 3D furniture models to fabricatable parts and connectors , 2011, ACM Trans. Graph..