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On Marching Cubes
July-September 2003 (vol. 9 no. 3)
pp. 283-297

Abstract—A characterization and classification of the isosurfaces of trilinear functions is presented. Based upon these results, a new algorithm for computing a triangular mesh approximation to isosurfaces for data given on a 3D rectilinear grid is presented. The original marching cubes algorithm is based upon linear interpolation along edges of the voxels. The asymptotic decider method is based upon bilinear interpolation on faces of the voxels. The algorithm of this paper carries this theme forward to using trilinear interpolation on the interior of voxels. The algorithm described here will produce a triangular mesh surface approximation to an isosurface which preserves the same connectivity/separation of vertices as given by the isosurface of trilinear interpolation.

[1] W.E. Lorensen and H.E. Cline, Marching Cubes: A High Resolution 3D Surface Construction Algorithm SIGGRAPH '87 Proc., vol. 21, pp. 163-169, 1987.
[2] G.M. Nielson and B. Hamann, The Asymptotic Decider: Removing the Ambiguity in Marching Cubes Proc. Visualization '91, pp. 83-91, 1991.

Index Terms:
Isosurface, volume rendering, marching cubes, contour surfaces, asymptotic decider.
Gregory M. Nielson, "On Marching Cubes," IEEE Transactions on Visualization and Computer Graphics, vol. 9, no. 3, pp. 283-297, July-Sept. 2003, doi:10.1109/TVCG.2003.1207437
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