This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Near Optimal Isosurface Extraction Algorithm Using the Span Space
March 1996 (vol. 2 no. 1)
pp. 73-84

Abstract—We present the "Near Optimal IsoSurface Extraction" (NOISE) algorithm for rapidly extracting isosurfaces from structured and unstructured grids. Using the span space, a new representation of the underlying domain, we develop n isosurface extraction algorithm with a worst case complexity of $O\left ({\sqrt n} + k\right )$ for the search phase, where n is the size of the data set and k is the number of cells intersected by the isosurface. The memory requirement is kept at O(n) while the preprocessing step is O(n log n). We utilize the span space representation as a tool for comparing isosurface extraction methods on structured and unstructured grids. We also present a fast triangulation scheme for generating and displaying unstructured tetrahedral grids.

[1] 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.
[2] J. Wilhelms and A. Van Gelder, "Octrees for Faster Isosurface Generation," ACM Trans. Graphics, vol. 11, no. 3, July 1992, pp. 201-227.
[3] T. Itoh and K. Koyyamada,"Isosurface Generation by Using Extrema Graphs," Proc. Visualization '94.Los Alamitos, Calif.: IEEE Press, 1994, pp. 77-83.
[4] M. Giles and R. Haimes, “Advanced Interactive Visualization for CFD,” Computer Systems in Eng., vol. 1, no. 1, pp. 51-62, 1990.
[5] R.S. Gallagher, “Span Filtering: An Optimization Scheme for Volume Visualization of Large Finite Element Models,” Proc. IEEE Visualization '91, pp. 68-74, 1991.
[6] 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.
[7] J.L. Bentley, "Multidimensional Binary Search Trees Used for Associative Searching," Comm. ACM, vol. 18, no. 9, pp. 509-517, 1975.
[8] M. Blum,R.W. Floyd,V. Pratt,R.L. Rivest, and R.E. Tarjan,"Time Bounds for Selection," J. Computer and System Science, vol. 7, pp. 448-461, 1973.
[9] R. Sedgewick, Algorithms in C++. Addison-Wesley, 1992.
[10] D.T. Lee and C.K. Wong,"Worst-Case Analysis for Region and Partial Region Searches in Multidimensional Binary Search Trees and Balanced Quad Trees," Acta Informatica, vol. 9, no. 23, pp. 23-29, 1977.
[11] J.L. Bentley and D.F. Stanat,"Analysis of Range Searches in Quad Trees," Info. Proc. Lett., vol. 3, no. 6, pp. 170-173, 1975.

Index Terms:
Isosurface extraction, unstructured grids, span space, kd-trees.
Citation:
Yarden Livnat, Han-Wei Shen, Christopher R. Johnson, "A Near Optimal Isosurface Extraction Algorithm Using the Span Space," IEEE Transactions on Visualization and Computer Graphics, vol. 2, no. 1, pp. 73-84, March 1996, doi:10.1109/2945.489388
Usage of this product signifies your acceptance of the Terms of Use.