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A progressive algorithm for block decomposition of solid models

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Abstract

At present, the dual structure-based block decomposition methods can generally obtain relatively ideal results. However, current dual structure-based block decomposition algorithms suffer from reliability and efficiency issues. To this end, to enable them to effectively deal with complex models, this paper proposes a progressive block decomposition algorithm. The algorithm first simplifies the input model by suppressing features and decomposes the simplified model into a block structure. Then, to recover the suppressed features in the simplified model’s block structure, for each suppressed feature, the algorithm generates a local model to cover the feature. After decomposing the local model into a block structure with constraints, the algorithm replaces the corresponding block set in the block structure with the local model’s block structure. In this step, the block structures are refined to obtain a consistency-ensured block structure. Finally, to achieve a balance between the total number of blocks and the blocks’ quality in the block structure, the algorithm optimizes the consistency-ensured block structure by simplifying the structure. Experimental results show the effectiveness of the proposed method.

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References

  1. Calderan S, Hutzler G, Ledoux F (2020) Dual-based user-guided hexahedral block generation using frame fields. https://doi.org/10.5281/zenodo.3653430

  2. Campen M, Bommes D, Kobbelt L (2012) Dual loops meshing: quality quad layouts on manifolds. ACM Trans Graph (TOG) 31(4):1–11

    Article  Google Scholar 

  3. Carey GF (2002) Hexing the tet. Commun Numer Methods Eng 18(3):223–227

    Article  MATH  Google Scholar 

  4. Dey TK, Fan F, Wang Y (2013) An efficient computation of handle and tunnel loops via reeb graphs. ACM Trans Graph (TOG) 32(4):1–10

    Article  MATH  Google Scholar 

  5. Diamanti O, Vaxman A, Panozzo D, Sorkine-Hornung O (2014) Designing n-polyvector fields with complex polynomials. In: Computer graphics forum, vol 33. Wiley Online Library, pp 1–11

  6. Fang X, Xu W, Bao H, Huang J (2016) All-hex meshing using closed-form induced polycube. ACM Trans Graph (TOG) 35(4):124

    Article  Google Scholar 

  7. Fu XM, Bai CY, Liu, Y (2016) Efficient volumetric polycube-map construction. In: Computer graphics forum, vol. 35. Wiley Online Library, pp 97–106

  8. Gao X, Deng Z, Chen G (2015) Hexahedral mesh re-parameterization from aligned base-complex. ACM Trans Graph (TOG) 34(4):1–10

    Article  MATH  Google Scholar 

  9. Gao X, Martin T, Deng S, Cohen E, Deng Z, Chen G (2015) Structured volume decomposition via generalized sweeping. IEEE Trans Vis Comput Graph 22(7):1899–1911

    Article  Google Scholar 

  10. Gao X, Panozzo D, Wang W, Deng Z, Chen G (2017) Robust structure simplification for hex re-meshing. ACM Trans Graph (TOG) 36(6):1–13

    Google Scholar 

  11. Goldstein H, Poole C, Safko J (2002) Classical mechanics

  12. Gregson J, Sheffer A, Zhang E (2011) All-hex mesh generation via volumetric polycube deformation. In: Computer graphics forum, vol 30. Wiley Online Library, pp 1407–1416

  13. Hu K, Zhang YJ (2016) Centroidal voronoi tessellation based polycube construction for adaptive all-hexahedral mesh generation. Comput Methods Appl Mech Eng 305:405–421

    Article  MathSciNet  MATH  Google Scholar 

  14. Hu K, Zhang YJ, Liao T (2017) Surface segmentation for polycube construction based on generalized centroidal voronoi tessellation. Comput Methods Appl Mech Eng 316:280–296

    Article  MathSciNet  MATH  Google Scholar 

  15. Huang J, Jiang T, Shi Z, Tong Y, Bao H, Desbrun M (2014) l1-based construction of polycube maps from complex shapes. ACM Trans Graph (TOG) 33(3):25

    Article  MATH  Google Scholar 

  16. Kowalski N, Ledoux F, Frey P (2016) Smoothness driven frame field generation for hexahedral meshing. Comput Aided Des 72:65–77

    Article  Google Scholar 

  17. Kowalski N, Ledoux F, Staten ML, Owen SJ (2012) Fun sheet matching: towards automatic block decomposition for hexahedral meshes. Eng Comput 28(3):241–253

    Article  Google Scholar 

  18. Kremer M, Bommes D, Kobbelt L (2013) Openvolumemesh—a versatile index-based data structure for 3d polytopal complexes. In: Proceedings of the 21st international meshing roundtable. Springer, pp 531–548

  19. Lai Y, Liu L, Zhang YJ, Chen J, Fang E, Lua J (2016) Rhino 3d to abaqus: a t-spline based isogeometric analysis software framework. In: Advances in computational fluid-structure interaction and flow simulation. Springer, pp 271–281

  20. Lai Y, Zhang YJ, Liu L, Wei X, Fang E, Lua J (2017) Integrating cad with abaqus: a practical isogeometric analysis software platform for industrial applications. Comput Math Appl 74(7):1648–1660

    Article  MathSciNet  MATH  Google Scholar 

  21. Ledoux F, Shepherd J (2010) Topological and geometrical properties of hexahedral meshes. Eng Comput 26(4):419–432

    Article  Google Scholar 

  22. Ledoux F, Shepherd J (2010) Topological modifications of hexahedral meshes via sheet operations: a theoretical study. Eng Comput 26(4):433–447

    Article  Google Scholar 

  23. Li L, Zhang P, Smirnov D, Abulnaga SM, Solomon J (2021) Interactive all-hex meshing via cuboid decomposition. arXiv preprint arXiv:2109.06279

  24. Li T, McKeag R, Armstrong C (1995) Hexahedral meshing using midpoint subdivision and integer programming. Comput Methods Appl Mech Eng 124(1–2):171–193

    Article  Google Scholar 

  25. Li Y, Liu Y, Xu W, Wang W, Guo B (2012) All-hex meshing using singularity-restricted field. ACM Trans Graph (TOG) 31(6):1–11

    Article  Google Scholar 

  26. Liu L, Zhang Y, Hughes TJ, Scott MA, Sederberg TW (2014) Volumetric t-spline construction using Boolean operations. Eng Comput 30(4):425–439

    Article  Google Scholar 

  27. Liu L, Zhang Y, Liu Y, Wang W (2015) Feature-preserving t-mesh construction using skeleton-based polycubes. Comput Aided Des 58:162–172

    Article  Google Scholar 

  28. Livesu M, Muntoni A, Puppo E, Scateni R (2016) Skeleton-driven adaptive hexahedral meshing of tubular shapes. In: Computer graphics forum, vol 35. Wiley Online Library, pp 237–246

  29. Livesu M, Pietroni N, Puppo E, Sheffer A, Cignoni P (2019) Loopy cuts: surface-field aware block decomposition for hex-meshing. arXiv preprint arXiv:1903.10754

  30. Livesu M, Pietroni N, Puppo E, Sheffer A, Cignoni P (2020) Loopycuts: practical feature-preserving block decomposition for strongly hex-dominant meshing. ACM Trans Graph (TOG) 39(4):121–1

    Article  Google Scholar 

  31. Pietroni N, Puppo E, Marcias G, Scopigno R, Cignoni P (2016) Tracing field-coherent quad layouts. In: Computer graphics forum, vol 35. Wiley Online Library, pp 485–496

  32. Reberol M, Chemin A, Remacle JF (2019) Multiple approaches to frame field correction for cad models. arXiv pp. arXiv-1912

  33. Sun R, Gao S, Zhao W (2010) An approach to b-rep model simplification based on region suppression. Comput Graph 34(5):556–564

    Article  Google Scholar 

  34. Takayama K (2019) Dual sheet meshing: an interactive approach to robust hexahedralization. In: Computer graphics forum, vol 38. Wiley Online Library, pp 37–48

  35. Wang R, Shen C, Chen J, Wu H, Gao S (2017) Sheet operation based block decomposition of solid models for hex meshing. Comput Aided Des 85:123–137

    Article  Google Scholar 

  36. Wang W, Zhang Y, Liu L, Hughes TJ (2013) Trivariate solid t-spline construction from boundary triangulations with arbitrary genus topology. Comput Aided Des 45(2):351–360

    Article  MathSciNet  Google Scholar 

  37. Xiao Z, He S, Xu G, Chen J, Wu Q (2020) A boundary element-based automatic domain partitioning approach for semi-structured quad mesh generation. Eng Anal Bound Elem 113:133–144

    Article  MathSciNet  MATH  Google Scholar 

  38. Xie J, Xu J, Dong Z, Xu G, Deng C, Mourrain B, Zhang YJ (2020) Interpolatory Catmull–Clark volumetric subdivision over unstructured hexahedral meshes for modeling and simulation applications. Comput Aided Geom Des 80:101867

    Article  MathSciNet  MATH  Google Scholar 

  39. Xu G, Ling R, Zhang YJ, Xiao Z, Ji Z, Rabczuk T (2021) Singularity structure simplification of hexahedral meshes via weighted ranking. Comput Aided Des 130:102946

    Article  MathSciNet  Google Scholar 

  40. Yu Y, Liu JG, Zhang YJ (2021) Hexdom: polycube-based hexahedral-dominant mesh generation. arXiv preprint arXiv:2103.04183

  41. Yu Y, Wei X, Li A, Liu JG, He J, Zhang YJ (2020) Hexgen and hex2spline: polycube-based hexahedral mesh generation and unstructured spline construction for isogeometric analysis framework in ls-dyna. In: Springer INdAM Serie: proceedings of INdAM Workshop “geometric challenges in isogeometric analysis”

  42. Zhang M, Huang J, Liu X, Bao H (2012) A divide-and-conquer approach to quad remeshing. IEEE Trans Vis Comput Graph 19(6):941–952

    Article  Google Scholar 

  43. Zheng Z, Wang R, Gao S, Liao Y, Ding M (2018) Dual surface based approach to block decomposition of solid models. In: International meshing roundtable. Springer, pp 149–167

  44. Zheng Z, Wang R, Gao S, Liao Y, Ding M (2020) Automatic block decomposition based on dual surfaces. Comput Aided Des 127:102883

    Article  MathSciNet  Google Scholar 

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Acknowledgements

We thank all reviewers for their valuable comments. This research is supported by the QiangJi Program (TC190A4DA/3).

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Authors and Affiliations

  1. State Key Lab of CAD & CG, Zhejiang University, Hangzhou, 310058, People’s Republic of China

    Zhihao Zheng & Shuming Gao

  2. Computer and Computer Science, Zhejiang University City College, Hangzhou, 310015, People’s Republic of China

    Chun Shen

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  1. Zhihao Zheng
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  2. Shuming Gao
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  3. Chun Shen
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Correspondence to Shuming Gao.

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Zheng, Z., Gao, S. & Shen, C. A progressive algorithm for block decomposition of solid models. Engineering with Computers 38, 4349–4366 (2022). https://doi.org/10.1007/s00366-021-01574-6

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