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Investigation on a Novel Length-Based Local Linear Subdivision Strategy for Triangular Meshes (2310.01445v1)

Published 1 Oct 2023 in cs.GR and cs.CG

Abstract: Triangular meshes are a widely used representation in the field of 3D modeling. In this paper, we present a novel approach for edge length-based linear subdivision on triangular meshes, along with two auxiliary techniques. We conduct a comprehensive comparison of different subdivision methods in terms of computational capabilities and mesh-enhancing abilities. Our proposed approach demonstrates improved computational efficiency and generates fewer elements with higher quality compared to existing methods. The improvement in computational efficiency and mesh augmentation capability of our method is further enhanced when working with the two auxiliary techniques presented in this paper. Our novel strategy represents a significant contribution to the field and has important implications for local mesh refinement, computer-aided design, and isotropic remeshing.

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References (44)
  1. H. Zhang, O. Van Kaick, and R. Dyer, “Spectral mesh processing,” in Computer graphics forum, vol. 29, no. 6.   Wiley Online Library, 2010, pp. 1865–1894.
  2. O. Sorkine, “Differential representations for mesh processing,” in Computer Graphics Forum, vol. 25, no. 4.   Wiley Online Library, 2006, pp. 789–807.
  3. X. He, F. Gu, and A. Ball, “A review of numerical analysis of friction stir welding,” Progress in Materials Science, vol. 65, pp. 1–66, 2014.
  4. M. Sosnowski, J. Krzywanski, K. Grabowska, and R. Gnatowska, “Polyhedral meshing in numerical analysis of conjugate heat transfer,” in EPJ Web of Conferences, vol. 180.   EDP Sciences, 2018, p. 02096.
  5. C. Petres, Y. Pailhas, P. Patron, Y. Petillot, J. Evans, and D. Lane, “Path planning for autonomous underwater vehicles,” IEEE Transactions on Robotics, vol. 23, no. 2, pp. 331–341, 2007.
  6. A. Bircher, M. Kamel, K. Alexis, H. Oleynikova, and R. Siegwart, “Receding horizon path planning for 3d exploration and surface inspection,” Autonomous Robots, vol. 42, pp. 291–306, 2018.
  7. K. H. Raj, R. S. Sharma, S. Srivastava, and C. Patvardhan, “Modeling of manufacturing processes with anns for intelligent manufacturing,” International Journal of Machine Tools and Manufacture, vol. 40, no. 6, pp. 851–868, 2000.
  8. D. Zhao and W. Guo, “Mixed-layer adaptive slicing for robotic additive manufacturing (am) based on decomposing and regrouping,” Journal of Intelligent Manufacturing, vol. 31, no. 4, pp. 985–1002, 2020.
  9. J. Bolz and P. Schröder, “Rapid evaluation of catmull-clark subdivision surfaces,” in Proceedings of the seventh international conference on 3D Web technology, 2002, pp. 11–17.
  10. J. Guo, F. Ding, X. Jia, and D.-M. Yan, “Automatic and high-quality surface mesh generation for cad models,” Computer-Aided Design, vol. 109, pp. 49–59, 2019.
  11. P. Alliez, E. C. De Verdire, O. Devillers, and M. Isenburg, “Isotropic surface remeshing,” in 2003 Shape Modeling International.   IEEE, 2003, pp. 49–58.
  12. J.-Y. Wu and R. Lee, “The advantages of triangular and tetrahedral edge elements for electromagnetic modeling with the finite-element method,” IEEE Transactions on Antennas and Propagation, vol. 45, no. 9, pp. 1431–1437, 1997.
  13. D. R. Lindquist and M. B. Gilest, “A comparison of numerical schemes on triangular and quadrilateral meshes,” in 11th International Conference on Numerical Methods in Fluid Dynamics.   Springer, 2005, pp. 369–373.
  14. R. Jain, S. K. Pal, and S. B. Singh, “Numerical modeling methodologies for friction stir welding process,” in Computational Methods and Production Engineering.   Elsevier, 2017, pp. 125–169.
  15. H. Chen, W. Sheng, N. Xi, M. Song, and Y. Chen, “Automated robot trajectory planning for spray painting of free-form surfaces in automotive manufacturing,” in Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No. 02CH37292), vol. 1.   IEEE, 2002, pp. 450–455.
  16. Q. Du, D. Wang, and L. Zhu, “On mesh geometry and stiffness matrix conditioning for general finite element spaces,” SIAM journal on numerical analysis, vol. 47, no. 2, pp. 1421–1444, 2009.
  17. M. W. Beall, J. Walsh, and M. S. Shephard, “Accessing cad geometry for mesh generation.” in Imr, 2003, pp. 33–42.
  18. M. Bern and D. Eppstein, “Mesh generation and optimal triangulation,” in Computing in Euclidean geometry.   World Scientific, 1995, pp. 47–123.
  19. K. Shimada, “Current issues and trends in meshing and geometric processing for computational engineering analyses,” 2011.
  20. G. Foucault, J.-C. Cuillière, V. François, J.-C. Léon, and R. Maranzana, “Adaptation of cad model topology for finite element analysis,” Computer-Aided Design, vol. 40, no. 2, pp. 176–196, 2008.
  21. R. Jamieson and H. Hacker, “Direct slicing of cad models for rapid prototyping,” Rapid Prototyping Journal, vol. 1, no. 2, pp. 4–12, 1995.
  22. S. R. K. Ledalla, B. Tirupathi, and V. Sriram, “Performance evaluation of various stl file mesh refining algorithms applied for fdm-rp process,” Journal of The Institution of Engineers (India): Series C, vol. 99, pp. 339–346, 2018.
  23. M. L. King, M. J. Fisher, and C. G. Jensen, “A cad-centric approach to cfd analysis with discrete features,” Computer-Aided Design and Applications, vol. 3, no. 1-4, pp. 279–288, 2006.
  24. P. J. Flynn and A. K. Jain, “Cad-based computer vision: from cad models to relational graphs,” in Conference Proceedings., IEEE International Conference on Systems, Man and Cybernetics.   IEEE, 1989, pp. 162–167.
  25. J. Schöberl, “Netgen an advancing front 2d/3d-mesh generator based on abstract rules,” Computing and visualization in science, vol. 1, no. 1, pp. 41–52, 1997.
  26. C. Geuzaine and J.-F. Remacle, “Gmsh: A 3-d finite element mesh generator with built-in pre-and post-processing facilities,” International journal for numerical methods in engineering, vol. 79, no. 11, pp. 1309–1331, 2009.
  27. V. Sunil and S. Pande, “Automatic recognition of features from freeform surface cad models,” Computer-Aided Design, vol. 40, no. 4, pp. 502–517, 2008.
  28. A. Severn and F. Samavati, “Fast intersections for subdivision surfaces,” in International Conference on Computational Science and Its Applications.   Springer, 2006, pp. 91–100.
  29. H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, “Mesh optimization,” in Proceedings of the 20th annual conference on Computer graphics and interactive techniques, 1993, pp. 19–26.
  30. P. Cignoni, C. Montani, and R. Scopigno, “A comparison of mesh simplification algorithms,” Computers & Graphics, vol. 22, no. 1, pp. 37–54, 1998.
  31. P. Alliez, G. Ucelli, C. Gotsman, and M. Attene, “Recent advances in remeshing of surfaces,” Shape analysis and structuring, pp. 53–82, 2008.
  32. N. Noii, F. Aldakheel, T. Wick, and P. Wriggers, “An adaptive global–local approach for phase-field modeling of anisotropic brittle fracture,” Computer Methods in Applied Mechanics and Engineering, vol. 361, p. 112744, 2020.
  33. E. Catmull and J. Clark, “Recursively generated b-spline surfaces on arbitrary topological meshes,” in Seminal graphics: pioneering efforts that shaped the field, 1998, pp. 183–188.
  34. D. Rypl and Z. Bittnar, “Generation of computational surface meshes of stl models,” Journal of Computational and Applied Mathematics, vol. 192, no. 1, pp. 148–151, 2006.
  35. C. Loop, “Smooth subdivision surfaces based on triangles,” 1987.
  36. T. Jacquemin, P. Suchde, and S. P. Bordas, “Smart cloud collocation: geometry-aware adaptivity directly from cad,” Computer-Aided Design, vol. 154, p. 103409, 2023.
  37. V. Surazhsky, P. Alliez, and C. Gotsman, “Isotropic remeshing of surfaces: a local parameterization approach,” Ph.D. dissertation, INRIA, 2003.
  38. C. Sullivan and A. Kaszynski, “Pyvista: 3d plotting and mesh analysis through a streamlined interface for the visualization toolkit (vtk),” Journal of Open Source Software, vol. 4, no. 37, p. 1450, 2019.
  39. R. E. Bank, A. H. Sherman, and A. Weiser, “Some refinement algorithms and data structures for regular local mesh refinement,” Scientific Computing, Applications of Mathematics and Computing to the Physical Sciences, vol. 1, pp. 3–17, 1983.
  40. M. W. Bern and P. E. Plassmann, “Mesh generation.” Handbook of computational geometry, vol. 38, 2000.
  41. K. Müller and S. Havemann, “Subdivision surface tesselation on the fly using a versatile mesh data structure,” in Computer Graphics Forum, vol. 19, no. 3.   Wiley Online Library, 2000, pp. 151–159.
  42. K. Pulli and M. Segal, “Fast rendering of subdivision surfaces,” in Rendering Techniques’ 96: Proceedings of the Eurographics Workshop in Porto, Portugal, June 17–19, 1996 7.   Springer, 1996, pp. 61–70.
  43. D. A. Field, “Qualitative measures for initial meshes,” International Journal for Numerical Methods in Engineering, vol. 47, no. 4, pp. 887–906, 2000.
  44. P.-O. Persson and G. Strang, “A simple mesh generator in matlab,” SIAM review, vol. 46, no. 2, pp. 329–345, 2004.

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