Improvement of Mesh Simplification Using Normal Vector Diversity

Document Type : Research Paper


Faculty of Electrical and Computer Engineering (ECE), Semnan University,Semnan,Iran


3D mesh simplification is an important challenge in various fields. While different simplification methods have been proposed in recent years, the focus has shifted to keeping properties such as ridges and valleys along with mesh simplification. While most of the proposed models have used curvature, some challenges exist, such as the computational complexity and sensitivity to the neighborhood size. The latter can be solved by averaging several neighborhoods. This paper proposes a simple yet fast method with less sensitivity to the neighborhood size. To this end, we use the normal vector and the parameters of a probability distribution of its variations to detect the elevations, depressions (geometrical changes), and curve parts. We combine this method with the Quadric Error Metric (QEM) method to produce a hybrid method for 3D mesh simplification, preserving its elevations and depressions. Evaluation results show that our method has a lower error than the other methods.  


Main Subjects

  1. Yuk Ming Tang, H.L. Ho, 3D Modeling and Computer Graphics in Virtual Reality, Mixed Reality and Three-Dimensional Computer Graphics, 2020, 10.5772/intechopen.91443.
  2. Swantje Bargmann, Benjamin Klusemann, Jürgen Markmann, Jan Eike Schnabel, Konrad Schneider, Celal Soyarslan, Jana Wilmers, Generation of 3D representative volume elements for heterogeneous materials: A review, Progress in Materials Science, Volume 96, July 2018, Pages 322-384.
  3. Mauro Mazzei and Davide Quaroni, Development of a 3D WebGIS Application for the Visualization of Seismic Risk on Infrastructural Work, Int. J. Geo-Inf. 2022, 11(1), 22;
  4. Rumeng Lv, Xiaobing Chen, and Bingying Zhang, A simplified algorithm for 3D mesh model considering the influence of edge features, Journal of Physics: Conference Series, 2021.
  5. Guangyou Zhou; Shangda Yuan; Sumei Luo, Mesh Simplification Algorithm Based on the Quadratic Error Metric and Triangle Collapse, IEEE Access, Vol. 8, pp. 196341–196350, 2020.
  6. Schroeder, William J., Jonathan A. Zarge, and William E. Lorensen. "Decimation of triangle meshes." ACM Siggraph Computer Graphics. Vol. 26. No. 2. ACM, 1992.
  7. Renze, Kevin J., and James H. Oliver. "Generalized unstructured decimation [computer graphics]." Computer Graphics and Applications, IEEE 16.6 (1996): 24-32.
  8. Hoppe, Hugues. "Progressive meshes." Proceedings of the 23rd annual conference on Computer graphics and interactive techniques. ACM, 1996.
  9. Garland, Michael, and Paul S. Heckbert. "Surface simplification using quadric error metrics." Proceedings of the 24th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., 1997.
  10. Cao, Weiqun, Hujun Bao, and Qunsheng Peng. "An algorithm for LOD by merging near coplanar faces based on gauss sphere." Journal of Computer Science and Technology 16.5 (2001): 450-457.
  11. DeHaemer Jr, Michael J., and Michael J. Zyda. "Simplification of objects rendered by polygonal approximations." Computers & Graphics 15.2 (1991): 175-184.
  12. Hamann, Bernd. "A data reduction scheme for triangulated surfaces." Computer aided geometric design 11.2 (1994): 197-214.
  13. Schaefer, Scott, and Joe Warren. "Adaptive vertex clustering using octrees." Geometric Design and Computing 2.5 (2003).
  14. Bayik, Tolga, and Mehmet B. Akhan. "3d object database simplification using a vertex clustering algorithm." University of West Bohemia, Plzen, Czech Republic. 1999.
  15. Turk, Greg. "Re-tiling polygonal surfaces." ACM SIGGRAPH Computer Graphics 26.2 (1992): 55-64.
  16. Campomanes-Álvarez, B. Rosario, Sergio Damas, and Oscar Cordón. "Mesh simplification for 3D modeling using evolutionary multi-objective optimization." Evolutionary Computation (CEC), 2012 IEEE Congress on. IEEE, 2012.
  17. Huang, Hui-Ling, and Shinn-Ying Ho. "Mesh optimization for surface approximation using an efficient coarse-to-fine evolutionary algorithm." Pattern Recognition 36.5 (2003): 1065-1081.
  18. Álvarez, Rafael, et al. "A mesh optimization algorithm based on neural networks." Information Sciences 177.23 (2007): 5347-5364.
  19. Hoppe, Hugues. "New quadric metric for simplifiying meshes with appearance attributes." Proceedings of the conference on Visualization'99: celebrating ten years. IEEE Computer Society Press, 1999.
  20. Wei, Jin, and Yu Lou. "Feature preserving mesh simplification using feature sensitive metric." Journal of Computer Science and Technology 25.3 (2010): 595-605.
  21. Lee, Chang Ha, Amitabh Varshney, and David W. Jacobs. "Mesh saliency." ACM Transactions on Graphics (TOG). Vol. 24. No. 3. ACM, 2005.
  22. Wu, Jinliang, et al. "Mesh saliency with global rarity." Graphical Models 75.5 (2013): 255-264.
  23. Chen, Xiaobai, et al. "Schelling points on 3D surface meshes." ACM Transactions on Graphics (TOG) 31.4 (2012): 29
  24. Hongle Li and SeongKi Kim, A Novel Mesh Simplification Method Based on Vertex Removal Using Surface Angle, International Journal of Engineering Research and Technology. Volume 12, Number 8 (2019), pp. 1313-1320.
  25. Guangyou Zhou, Shangda Yuan, and Sumei Luo, Mesh Simplification Algorithm Based on the Quadratic Error Metric and Triangle Collapse, IEEE Access, 2020. 10.1109/ACCESS.2020.3034075.
  26. Rolandos Alexandros Potamias, Stylianos Ploumpis, Stefanos Zafeiriou, Neural Mesh Simplification, CVPR, pp. 18583- 18592, 2022.
  27. Marie-Julie Rakotosaona, Paul Guerrero, Noam Aigerman, Niloy J Mitra, and Maks Ovsjanikov. Learning delaunay surface elements for mesh reconstruction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22–31, 2021.
  28. Thibault Lescoat, Hsueh-Ti Derek Liu, Jean-Marc Thiery, Alec Jacobson, Tamy Boubekeur, and Maks Ovsjanikov. Spectral mesh simplification. Computer Graphics Forum, 39(2):315–324, 2020.