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Robust Boolean operations algorithm on regularized triangular mesh and implementation

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Abstract

Boolean operations are an essential tool for creating complex entities in many fields. In order to implement complex entity modeling, we proposed a method based on robust Boolean operations that focused on the robustness of geometric calculations caused by computational errors and data error. This method used a uniform logical judgment to analyze the specific conditions of the intersection of vertices or edges in advance, and avoided the inconsistency between logical judgment results and geometric relations. We correspondingly obtained the positions of the two triangles, the validity of the intersection and the intersection edges from tetrahedral-volume calculations, the triangle-area calculations, and the topology information to mark the triangles instead of intersecting lines tracking and the judgment of the triangles inside the entities. Finally, the experimental results indicate that this method realized the three-dimensional modeling of any complex geological body.

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References

  1. Aghdaii N, Younesy H, Hao Z (2012) 5c6c7 meshes: remeshing and analysis. Comput Graph 36(8):1072–1083

    Article  Google Scholar 

  2. Aibo GK, Lichao Z, Congjun W, Shuhuai H (2006) Implementation of Boolean operations on stl models. J Huazho Univ Sci Tech (Nat Sci Edn) 34(7):96–99

    Google Scholar 

  3. Arruda MCD, Lira WWM, Martha LF (2012) Boolean operations on multi-region solids for mesh generation. Eng Comput 28(3):225–239

    Article  Google Scholar 

  4. Attene M (2014) Direct repair of self-intersecting meshes. Graph Model 76 (6):658–668

    Article  Google Scholar 

  5. Dianzhu S, Xincheng L, Zhongchao T, Yanrui L (2009) Accelerated Boolean operations on triangular mesh models based on dynamic spatial indexing. J Comput-Aided Des Comput Graph 21(9):1232–1237

    Google Scholar 

  6. Du Q, Wang D (2006) Recent progress in robust and quality delaunay mesh generation. J Comput Appl Math 195(1):8–23

    Article  MathSciNet  Google Scholar 

  7. Feito FR, Ogayar CJ, Segura RJ, Rivero ML (2013) Fast and accurate evaluation of regularized Boolean operations on triangulated solids. CAD Comput Aided Des 45(3):705–716

    Article  Google Scholar 

  8. Ferley E, Cani MP, Gascuel JD (2000) Practical volumetric sculpting. Vis Comput 16(8):469–480

    Article  Google Scholar 

  9. Frisken SF, Perry RN, Rockwood AP, Jones TR (2000) Adaptively sampled distance fields: a general representation of shape for computer graphics, pp 249–254

  10. Guocan W, Yixian X, Xujun C, Jisheng G, Junjian Y, Yiming G, Long X, Xiuguo L, Weihua H (2015) Three-dimensional geological mapping and visualization of complex orogenic belt. Earth Sci-J Chin Univ Geosci 40(3):397–406

    Google Scholar 

  11. Hichem B, Guennebaud G, Sebti F (2015) Exact, robust, and efficient regularized Booleans on general 3d meshes. Comput Math Appl 70(6):1235–1254

    Article  MathSciNet  Google Scholar 

  12. Jessell M, Aillres L, Kemp ED, Lindsay M, Wellmann F, Hillier M, Laurent G, Carmichael T, Martin R (2016) Next generation three-dimensional geologic modeling and inversion. Soc Econ Geol Spec Publ 18:261–272

    Google Scholar 

  13. Karamete BK, Dey S, Mestreau EL, Aubry R, Bulat-Jara FA (2013) An algorithm for discrete Booleans with applications to finite element modeling of complex systems. Finite Elem Anal Des 68(88):10–27

    Article  Google Scholar 

  14. Krishnan S, Manocha D, Gopi M, Culver T, Keyser J (2001) Boole: a boundary evaluation system for Boolean combinations of sculptured solids. Int J Comput Geom Appl 11(01):105–144

    Article  Google Scholar 

  15. Landier S (2017) Boolean operations on arbitrary polygonal and polyhedral meshes. Comput Aided Des 85:138–153

    Article  Google Scholar 

  16. Li J, Wang W (2017) Fast and robust gpu-based point-in-polyhedron determination. Comput Aided Des 87:20–28

    Article  Google Scholar 

  17. Li Y, Zhang E, Kobayashi Y, Wonka P (2010) Editing operations for irregular vertices in triangle meshes. Acm Trans Graph 29(6):1–12

    Google Scholar 

  18. Lin B, Liguan W, Jianhong C, Xinlong F (2008) Spacial Boolean operations of3d mesh model. J Huazhong Univ Sci Tech (Nat Sci Edn) 36(5):82–85

    Google Scholar 

  19. Lo SH (2013) Automatic merging of tetrahedral meshes. Int J Numer Methods Eng 93(11):1191C1215

    Article  MathSciNet  Google Scholar 

  20. Mclaurin D, Marcum D, Remotigue M, Blades E (2013) Repairing unstructured triangular mesh intersections. Int J Numer Methods Eng 93(3):266–275

    Article  MathSciNet  Google Scholar 

  21. Pan M, Zhaoliang LI, Gao Z, Yang Y, Gengyu WU (2012) 3-d geological modeling-concept,methods and key techniques. Acta Geologica Sinica (English Edition) 86(4):1031–1036

    Article  Google Scholar 

  22. Tournois J, Alliez P, Devillers O (2008) Interleaving delaunay refinement and optimization for 2d triangle mesh generation. In: International meshing roundtable, October 14-17, 2007. Seattle, Washington, Usa, Proceedings, pp 83–101

  23. Turner AK (2006) Challenges and trends for geological modelling and visualisation. Bull Eng Geol Environ 65(2):109–127

    Article  Google Scholar 

  24. Updegrove A, Wilson NM, Shadden SC (2016) Boolean and smoothing of discrete polygonal surfaces. Adv Eng Softw 95:16–27

    Article  Google Scholar 

  25. Vartziotis D, Athanasiadis T (2008) Mesh smoothing using the geometric element transformation method. Comput Methods Appl Mech Eng 197(45):3760–3767

    Article  Google Scholar 

  26. Wang CCL (2010) Approximate Boolean operations on large polyhedral solids with partial mesh reconstruction. IEEE Trans Vis Comput Graph 17(6):836–849

    Article  Google Scholar 

  27. Xiang-rong L, Mao P, Zhan-gang W, Hong-gang Q, Zhi-dong S, Jing M (2008) Algorithm on3d models based on tin and implementation on3d geological modeling. Geograph Geo-Inf Sci 24(4):6–10

    Google Scholar 

  28. Xiao Z, Chen J, Zheng Y, Zheng J, Wang D (2016) Booleans of triangulated solids by a boundary conforming tetrahedral mesh generation approach. Comput Graph 59(C):13–27

    Article  Google Scholar 

  29. Xu S, Keyser J (2013) Fast and robust Booleans on polyhedra. Cad Computer Aided Design 45(2):529–534

    Article  MathSciNet  Google Scholar 

  30. Zhaoliang L, Mao P, Dakuang H, Wenling L, Shuiqing H, Peigang L, Mei Y (2016) Three dimensional structural modeling technique. Earth Sci 41 (12):2136–2146

    Google Scholar 

  31. Zhou L, Lu X, Wang H, Zhang W, Peng Y, Pan D (2018) Adaptive algorithm for three-dimensional mesh generation based on constrained delaunay. Int J Pattern Recogn Artif Intell 32(09):1855,017

    Article  MathSciNet  Google Scholar 

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Acknowledgments

The author(s) discloses the following financial support for the research, authorship, and/or publication of this article: This paper is supported by the National Key Research and Development Program of China (2016YFC0801406), Shandong Province Key Research and Development Plan Project(2016GSF120012), Shandong Key Research and Development program (2018GGX109013), Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (2016RCJJ033).

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Authors and Affiliations

  1. Department of Information Engineer, Shandong University of Science and Technology, Taian, China

    Hongjuan Wang

  2. College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao, China

    Shuting Kan, Xingli Zhang, Xinming Lu & Longquan Zhou

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  1. Hongjuan Wang
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  2. Shuting Kan
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Correspondence to Hongjuan Wang.

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Wang, H., Kan, S., Zhang, X. et al. Robust Boolean operations algorithm on regularized triangular mesh and implementation. Multimed Tools Appl 79, 5301–5320 (2020). https://doi.org/10.1007/s11042-018-6479-2

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  • DOI: https://doi.org/10.1007/s11042-018-6479-2

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