New Discrete Curvature Error Metric for the Generation of LOD Meshes

LOD 메쉬 생성을 위한 새로운 이산 곡률 오차 척도

  • Published : 2000.03.15


This paper proposes a new discrete curvature error metric to generate LOD meshes. For mesh simplification, discrete curvatures are defined with geometric attributes, such as angles and areas of triangular polygonal model, and dihedral angles without any smooth approximation. They can represent characteristics of polygonal surface well. The new error metric based on them, discrete curvature error metric, increases the accuracy of simplified model by preserving the geometric information of original model and can be used as a global error metric. Also we suggest that LOD should be generated not by a simplification ratio but by an error metric. Because LOD means the degree of closeness between original and each level's simplified model. Therefore discrete curvature error metric needs relatively more computations than known other error metrics, but it can efficiently generate and control LOD meshes which preserve overall appearance of original shape and are recognizable explicitly with each level.



  1. V. Borrelli. Courbures Discretes. Master's thesis, Universite Claude Bernard-Lyon 1, 1993
  2. A. Ciampalini, P. Cignoni, C. Montani, and R Scopigno. Multiresolution Decimation Based on Global Error. Technical Report C96-021, CNUCE-C.N.R., Pisa, Italy, July 1996
  3. P. Cignoni, C. Montani, and R. Scopigno. A Comparison of Mesh Simplification Algorithms COLOR TABLES. Technical Report 97-08, Istituto CNUCE-C.N.R., Pisa, Italy, June 1997
  4. J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F. Brooks, and W. Wright. Simplification Envelopes. Computer Graphics (SIGGRAPH '96 Proceedings), pages 119-128, August 1996
  5. M. Eck, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle. Multiresolution Analysis of Arbitrary Meshes. Computer Graphics (SIGGRAPH '95 Proceedings), pages 173-182, August 1995
  6. C. Erikson. Polygonal Simplification: An Overview. Technical Report TR-96-016, University of North Carolina - Chapel Hill, 1996
  7. B. Falcidieno and M. Spagnuolo. Geometric Reasoning for the Extraction of Surface Shape Properties. In D. Thalmann and N. M. Thalmann, editors, Communication with Virtual Worlds (Proc.CGI'93), pages 166-178. Springer-Verlag, 1993
  8. M. Garland and P. Heckbert. Simplifying Surfaces with Color and Texture Using Quadric Error Metrics. IEEE Visualization '98 Proceedings, pp. 263-169, 1998
  9. B. Hamann. A Data Reduction Scheme for Triangulated Surfaces. Computer Aided Geometric Design, 11(2):197-214, April 1994
  10. P. S. Heckbert and M. Garland. Survey of Polygonal Surface Simplification Algorithms. Technical Report, Carnegie Mellon University, 1997
  11. P, Hinker and C. Hansen. Geometric Optimization. In Proc. Visualization '93, pages 189-195, San Jose, CA, October 1993
  12. H. Hoppe. Surface Reconstruction from Unorganized Points. Ph.D. thesis, University of Washington, 1994
  13. H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stultzle. Mesh Optimization. Computer Graphics(SIGGRAPH '93 Proceedings), pages 19-26, August 1993
  14. A. D. Kalvin and R. H. Taylor. Superlaccs: Polygonal Mesh Simplification with Bounded Error. TR RC 19808(#877702), IBM Research Division, T. J. Watson Research Center, Yorktown Height, NY 10958, 1994
  15. R. Klein, G. Liebich, and W. Strasser. Mesh Reduction with Error Control. In R. Yagel, editor, Visualization 96. ACM, November 1996
  16. A. W. F. Lee, W. Sweldens, P. Schroeder, L. Cowsar, and D. Dobkin. MAPS: Multiresolution Adaptive Parameterization of Surfaces. SIGGRAPH '98, pages 105- 114, 1998
  17. B. O'Neill. Elementary Differential Geometry. Second Edition, Academic Press, USA, 1997
  18. E. Puppo and R. Scopigno. Simplification, LOD and Multiresolution - Principles and Applications. In EUROGRAPHICS '97 Tutorial Notes(ISSN 1017-4656), Eurographics Association, Aire-la-Ville(CH), 1997 (PS97 TN4)
  19. J. R. Rossignac and P. Borrel. Multiresolution 3 D Approximations for Rendering Complex Scenes. TR RC 17697(#77951), IBM Research Division, T. J. Watson Research Center, Yorktown Heights, NY 10958, 1992
  20. W. J. Schroeder, J. A. Zarge, and W. E. Lorensen. Decimation of Triangle Meshes. Computer Graphics (SIGGRAPH '92 Proceedings). 26(2):65-70, July 1992
  21. G. Turk. Re-Tiling Polygonal Surfaces. Computer Graphics(SIGGRAPH '92 Proceedings), 26(2):55-64, July 1992
  22. P. Veron and J. C. Leon. Static Polyhedron Simplification Using Error Measurements. Computer-Aided Design, Vol. 29. No.4, pp. 287-298, Elsevier Science Ltd., 1997
  23. W. Welch. Serious Putty: Topological Design for Variational Curves and Surfaces. Ph.D. thesis, Computer Science Department, Carnegie Mellon University, Pittsburgh, Pennsylvania, 1995