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Speeding Up Isosurface Extraction Using Interval Trees
April-June 1997 (vol. 3 no. 2)
pp. 158-170

Abstract—The interval tree is an optimally efficient search structure proposed by Edelsbrunner [5] to retrieve intervals on the real line that contain a given query value. We propose the application of such a data structure to the fast location of cells intersected by an isosurface in a volume dataset. The resulting search method can be applied to both structured and unstructured volume datasets, and it can be applied incrementally to exploit coherence between isosurfaces. We also address issues about storage requirements, and operations other than the location of cells, whose impact is relevant in the whole isosurface extraction task.

In the case of unstructured grids, the overhead, due to the search structure, is compatible with the storage cost of the dataset, and local coherence in the computation of isosurface patches is exploited through a hash table. In the case of a structured dataset, a new conceptual organization is adopted, called the chess-board approach, which exploits the regular structure of the dataset to reduce memory usage and to exploit local coherence. In both cases, efficiency in the computation of surface normals on the isosurface is obtained by a precomputation of the gradients at the vertices of the mesh.

Experiments on different kinds of input show that the practical performance of the method reflects its theoretical optimality.

[1] C.L. Bajaj, V. Pascucci, and D.R. Schikore, “Fast Isocontouring for Improved Interactivity,” Proc. ACM Symp. Volume Visualization '96, 1996.
[2] P. Cignoni, C. Montani, E. Puppo, and R. Scopigno, "Multiresolution Modeling and Visualization of Volume Data," Technical Report 95-22, Istituto CNUCE-CNR, Pisa, Italy, July 1995.
[3] P. Cignoni, C. Montani, E. Puppo, and R. Scopigno, "Optimal Isosurface Extraction From Irregular Volume Data," Proc. 1996 Volume Visualization Symp., pp. 31-38, 1996.
[4] P. Criscione, C. Montani, R. Scateni, and R. Scopigno, "DiscMC: An Interactive System for Fast Fitting Isosurfaces on Volume Data," Proc. Virtual Environments and Scientific Visualization '96, M. Goebel, J. David, P. Slavik and J.J. van Wijk, eds., pp. 178-190. Springer Wien, 1996.
[5] H. Edelsbrunner, "Dynamic Data Structures for Orthogonal Intersection Queries," Technical Report F59, Inst. Informationsverarb., Tech. Univ. Graz, Graz, Austria, 1980.
[6] R.S. Gallagher, “Span Filtering: An Optimization Scheme for Volume Visualization of Large Finite Element Models,” Proc. IEEE Visualization '91, pp. 68-74, 1991.
[7] M. Giles and R. Haimes, “Advanced Interactive Visualization for CFD,” Computer Systems in Eng., vol. 1, no. 1, pp. 51-62, 1990.
[8] T. Itoh, Y. Yamaguchi, and K. Koyamada, “Volume Thinning for Automatic Isosurface Propagation,” Proc. IEEE Visualization '96, pp. 303-310, 1996.
[9] T. Itoh and K. Koyamada, “Automatic Isosurface Propagation by Using an Extrema Graph and Sorted Boundary Cell Lists,” IEEE Trans. Visualization and Computer Graphics, vol. 1, no. 4, pp. 319-327, Dec. 1995.
[10] M. Laszlo, "Fast Generation and Display of Isosurfaces Wireframe," CVIGP: Graphical Models and Image Processing, vol. 54, no. 6, pp. 473-483, 1992.
[11] Y. Livnat, H. Shen, and C.R. Johnson, "A Near Optimal Isosurface Extraction Algorithm Using the Span Space," IEEE Trans. Visualization and Computer Graphics, vol. 2, no. 1, Mar. 1996, pp. 73-84.
[12] W.E. Lorensen and H.E. Cline, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” Computer Graphics (SIGGRAPH '87 Proc.), vol. 21, pp. 163-169, 1987.
[13] C. Montani, R. Scateni, and R. Scopigno, "Discretized Marching Cubes," IEEE Visualization '94 Proc., pp. 281-287,Washington, D.C., 1994.
[14] F.P. Preparata and M.I. Shamos, Computational Geometry. Springer-Verlag, 1985.
[15] H. Shen, C.D. Hansen, Y. Livnat, and C.R. Johnson, “Isosurfacing in Span Space with Utmost Efficiency (ISSUE),” Proc. IEEE Visualization '96, pp. 287-294, 1996.
[16] H. Shen and C.R. Johnson, “Sweeping Simplices: A Fast Iso-Surface Extraction Algorithm for Unstructured Grids,” Proc. IEEE Visualization '95, pp. 143-150, 1995.
[17] D. Speray and S. Kennon, “Volume Probe: Interactive Data Exploration on Arbitrary Grids,” Computer Graphics, vol. 24, no. 5, pp. 5-12, 1990.
[18] M. van Kreveld, "Efficient Methods for Isoline Extraction from a Digital Elevation Model Based on Triangulated Irregular Networks," Proc. Sixth Int'l Symp. Spatial Data Handling, pp. 835-847, 1994.
[19] J. Wilhelms and A. Van Gelder, "Octrees for Faster Isosurface Generation," ACM Trans. Graphics, vol. 11, no. 3, July 1992, pp. 201-227.
[20] G. Wyvill, C. McPheeters, and B. Wyvill, "Data Structures for Soft Objects," The Visual Computer, vol. 2, no. 4, pp. 227-234.

Index Terms:
Volume visualization, isosurface extraction, marching cubes, interval tree.
Paolo Cignoni, Paola Marino, Claudio Montani, Enrico Puppo, Roberto Scopigno, "Speeding Up Isosurface Extraction Using Interval Trees," IEEE Transactions on Visualization and Computer Graphics, vol. 3, no. 2, pp. 158-170, April-June 1997, doi:10.1109/2945.597798
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