John Congote, Aitor Moreno, Iñigo Barandiaran, Javier Barandiaran, Oscar E. Ruiz


This work proposes a variation on the Marching Cubes algorithm, where the goal is to represent implicit functions with higher resolution and better graphical quality using the same grid size. The proposed algorithm displaces the vertices of the cubes iteratively until the stop condition is achieved. After each iteration, the difference between the implicit and the explicit representations are reduced, and when the algorithm finishes, the implicit surface representation using the modified cubical grid is more detailed, as the results shall confirm. The proposed algorithm corrects some topological problems that may appear in the discretisation process using the original grid.


  1. Balmelli, L., Morris, C. J., Taubin, G., and Bernardini, F. (2002). Volume warping for adaptive isosurface extraction. In Proceedings of the conference on Visualization 02, pages 467-474. IEEE Computer Society.
  2. Carr, J. C., Beatson, R. K., Cherrie, J. B., Mitchell, T. J., Fright, W. R., McCallum, B. C., and Evans, T. R. (2001). Reconstruction and representation of 3d objects with radial basis functions. In SIGGRAPH 7801: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pages 67- 76, New York, NY, USA. ACM.
  3. Chernyaev, E. (1995). Marching cubes 33: Construction of topologically correct isosurfaces. Technical report, Technical Report CERN CN 95-17.
  4. Frisken, S. F., Frisken, S. F., Perry, R. N., Perry, R. N., Rockwood, A. P., Rockwood, A. P., Jones, T. R., and Jones, T. R. (2000). Adaptively sampled distance fields: A general representation of shape for computer graphics. pages 249-254.
  5. Kimura, A., Takama, Y., Yamazoe, Y., Tanaka, S., and Tanaka, H. T. (2004). Parallel volume segmentation with tetrahedral adaptive grid. ICPR, 02:281-286.
  6. Krek, P. (2005). Flow reduction marching cubes algorithm. In Proceedings of ICCVG 2004, pages 100- 106. Springer Verlag.
  7. Lewiner, T., Lopes, H., Vieira, A., and Tavares, G. (2003). Efficient implementation of marching cubes' cases with topological guarantees. Journal of Graphics Tools, 8(2):1-15.
  8. Lorensen, W. E. and Cline, H. E. (1987). Marching cubes: A high resolution 3d surface construction algorithm. SIGGRAPH Comput. Graph., 21(4):169-169.
  9. Morse, B. S., Yoo, T. S., Rheingans, P., Chen, D. T., and Subramanian, K. R. (2005). Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions. In SIGGRAPH 7805: ACM SIGGRAPH 2005 Courses, page 78, New York, NY, USA. ACM.
  10. Newman, T. S. and Yi, H. (2006). A survey of the marching cubes algorithm. Computers & Graphics, 30(5):854- 879.
  11. Oscar E. Ruiz, Miguel Granados, C. C. (2005). Fea-driven geometric modelling for meshless methods. In Virtual Concept 2005, pages 1-8.
  12. Paiva, A., Lopes, H., Lewiner, T., and de Figueiredo, L. H. (2006). Robust adaptive meshes for implicit surfaces. SIBGRAPI, 0:205-212.
  13. Schaefer, S. and Warren, J. (2004). Dual marching cubes: Primal contouring of dual grids. In PG 7804: Proceedings of the Computer Graphics and Applications, 12th Pacific Conference, pages 70-76, Washington, DC, USA. IEEE Computer Society.
  14. Shekhar, R., Fayyad, E., Yagel, R., and Cornhill, J. F. (1996). Octree-based decimation of marching cubes surfaces. In VIS 7896: Proceedings of the 7th conference on Visualization 7896, pages 335-ff., Los Alamitos, CA, USA. IEEE Computer Society Press.
  15. Weber, G. H., Kreylos, O., Ligocki, T. J., Shalf, J. M., Hamann, B., and Joy, K. I. (2001). Extraction of crack-free isosurfaces from adaptive mesh refinement data. In Data Visualization 2001 (Proceedings of VisSym 7801), pages 25-34. Springer Verlag.

Paper Citation

in Harvard Style

Congote J., Moreno A., Barandiaran I., Barandiaran J. and E. Ruiz O. (2009). ADAPTATIVE CUBICAL GRID FOR ISOSURFACE EXTRACTION . In Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009) ISBN 978-989-8111-67-8, pages 21-26. DOI: 10.5220/0001786200210026

in Bibtex Style

author={John Congote and Aitor Moreno and Iñigo Barandiaran and Javier Barandiaran and Oscar E. Ruiz},
booktitle={Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009)},

in EndNote Style

JO - Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2009)
SN - 978-989-8111-67-8
AU - Congote J.
AU - Moreno A.
AU - Barandiaran I.
AU - Barandiaran J.
AU - E. Ruiz O.
PY - 2009
SP - 21
EP - 26
DO - 10.5220/0001786200210026