This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Improving the Robustness and Accuracy of the Marching Cubes Algorithm for Isosurfacing
January-March 2003 (vol. 9 no. 1)
pp. 16-29

Abstract—This paper proposes a modification of the Marching Cubes algorithm for isosurfacing, with the intent of improving the representation of the surface in the interior of each grid cell. Our objective is to create a representation which correctly models the topology of the trilinear interpolant within the cell and which is robust under perturbations of the data and threshold value. To achieve this, we identify a small number of key points in the cell interior that are critical to the surface definition. This allows us to efficiently represent the different topologies that can occur, including the possibility of “tunnels.” The representation is robust in the sense that the surface is visually continuous as the data and threshold change in value. Each interior point lies on the isosurface. Finally, a major feature of our new approach is the systematic method of triangulating the polygon in the cell interior.

[1] W. Lorensen and H. Cline, “Marching Cubes: A High Resolution 3D Surface Reconstruction Algorithm,” Computer Graphics, vol. 21, no. 4, pp. 163-169, 1987.
[2] G. Nielson and B. Hamann, “The Asymptotic Decider: Resolving the Ambiguity in Marching Cubes,” Proc. IEEE Visualization '92, pp. 83-91, 1992.
[3] B. Natarajan, “On Generating Topologically Consistent Isosurfaces from Uniform Samples,” The Visual Computer, vol. 11, pp. 52-62, 1994.
[4] E. Chernyaev, “Marching Cubes 33: Construction of Topologically Correct Isosurfaces,” Technical Report CN/95-17, CERN, 1995, http://wwwinfo.cern.ch/asdoc/psdirmc.ps.gz .
[5] P. Cignoni, F. Ganovelli, C. Montani, and R. Scopigno, “Reconstruction of Topologically Correct and Adaptive Trilinear Surfaces,” Computers and Graphics, vol. 24, no. 3, pp. 399-418, 2000.
[6] M. Dürst, “Letters: Additional Reference to Marching Cubes,” Computer Graphics, vol. 22, no. 2, pp. 72-73, 1988.
[7] S. Matveyev, “Approximation of Isosurface in the Marching Cube: Ambiguity Problem,” Proc. IEEE Visualization '94, pp. 288-292, 1994.
[8] A. van Gelder and J. Wilhelms, “Topological Considerations in Isosurface Generation,” ACM Trans. Graphics, vol. 13, no. 4, pp. 337-375, 1994.
[9] M. Bailey, “Manufacturing Isovolumes,” Volume Graphics, M. Chen, A. Kaufman, and R. Yagel, eds., pp. 79-93, Springer, 2000.
[10] A. Lopes, “Accuracy in Scientific Visualization,” PhD thesis, Univ. of Leeds, Leeds, U.K., 1999.
[11] A. Lopes and K. Brodlie, “Accuracy in Contour Drawing,” Eurographics UK 98 Conf. Proc., 1998.
[12] D. Cohen-Or, A. Kadosh, D. Levin, and R. Yagel, “Smooth Boundary Surfaces from 3D Datasets,” Volume Graphics, M. Chen, A.E. Kaufman, and R. Yagel, eds., pp. 71-78, Springer, 2000.
[13] B. Hamann, I. Trotts, and G. Farin, “On Approximating Contours of the Piecewise Trilinear Interpolant Using Triangular Rational-Quadratic Bezier Patches,” IEEE Trans. Visualization and Computer Graphics, vol. 3, no. 3, pp. 215-227, 1997.
[14] H.-W. Shen, C. Hansen, Y. Livnat, and C. Johnson, “Isosurfacing in Span Space with Utmost Efficiency,” Proc. IEEE Visualization '96, pp. 287-294, 1996.
[15] P. Cignoni, P. Marino, C. Montani, E. Puppo, and R. Scopigno, “Speeding Up Isosurface Extraction Using Interval Trees,” IEEE Trans. Visualization and Computer Graphics, vol. 3, no. 2, pp. 158-170, Apr.-June 1997.
[16] K. Brodlie and J. Wood, “Recent Advances in Volume Visualization,” Computer Graphics Forum, vol. 20, no. 2, pp. 125-148, 2001.

Index Terms:
Isosurface, marching cubes, robustness, accuracy, trilinear interpolation.
Citation:
Adriano Lopes, Ken Brodlie, "Improving the Robustness and Accuracy of the Marching Cubes Algorithm for Isosurfacing," IEEE Transactions on Visualization and Computer Graphics, vol. 9, no. 1, pp. 16-29, Jan.-March 2003, doi:10.1109/TVCG.2003.1175094
Usage of this product signifies your acceptance of the Terms of Use.