This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Material Interface Reconstruction
October-December 2003 (vol. 9 no. 4)
pp. 500-511
Kathleen S. Bonnell, IEEE Computer Society
Mark A. Duchaineau, IEEE Computer Society
Daniel R. Schikore, IEEE Computer Society
Bernd Hamann, IEEE Computer Society
Kenneth I. Joy, IEEE Computer Society

Abstract—This paper presents an algorithm for material interface reconstruction for data sets where fractional material information is given as a percentage for each element of the underlying grid. The reconstruction problem is transformed to a problem that analyzes a dual grid, where each vertex in the dual grid has an associated barycentric coordinate tuple that represents the fraction of each material present. Material boundaries are constructed by analyzing the barycentric coordinate tuples of a tetrahedron in material space and calculating intersections with Voronoi cells that represent the regions where one material dominates. These intersections are used to calculate intersections in the Euclidean coordinates of the tetrahedron. By triangulating these intersection points, one creates the material boundary. The algorithm can treat data sets containing any number of materials. The algorithm can also create nonmanifold boundary surfaces if necessary. By clipping the generated material boundaries against the original cells, one can examine the error in the algorithm. Error analysis shows that the algorithm preserves volume fractions within an error range of 0.5 percent per material.

[1] G.M. Nielson, Tools for Triangulations and Tetrahedrizations and Constructing Functions Defined over Them Scientific Visualization: Overviews, Methodologies, and Techniques, G.M. Nielson, H. Hagen, and H. Müller, eds., pp. 429-525, 1997.
[2] A. Okabe, B. Boots, and K. Sugihara, Spatial Tesselations—Concepts and Applications of Voronoi Diagrams. Chichester: Wiley, 1992.
[3] 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.
[4] G.M. Nielson and B. Hamann, The Asymptotic Decider: Removing the Ambiguity in Marching Cubes Proc. Visualization '91, pp. 83-91, 1991.
[5] Y. Zhou, B. Chen, and A. Kaufman, Multiresolution Tetrahedral Framework for Visualizing Regular Volume Data Proc. IEEE Visualization '97, R. Yagel and H. Hagen, eds., pp. 135-142, 1997.
[6] W.F. Noh and P. Woodward, SLIC (Simple Line Interface Calculation) Lecture Notes in Physics, A.I. van der Vooren and P.J. Zandbergen, eds., pp. 330-340, Springer-Verlag, 1976.
[7] D.L. Youngs, Time-Dependent Multi-Material Flow with Large Fluid Distortion Numerical Methods for Fluid Dynamics, K.W. Morton and J.J. Baines, eds., pp. 273-285, Academic Press, 1982.
[8] D. Gueyffier, J. Li, A. Nadim, R. Scardovelli, and S. Zaleski, Volume-of-Fluid Interface Tracking with Smoothed Surface Stress Methods for Three-Dimensional Flows J. Computational Physics, vol. 152, pp. 423-456, 1999.
[9] J.E. Pilliod and E.G. Puckett, Second-Order Accurate Volume-of-Fluid Algorithms for Tracking Material Interfaces technical report, Lawrence Berkeley Nat'l Laboratory, 2000.
[10] G.M. Nielson and R. Franke, Computing the Separating Surface for Segmented Data Proc. IEEE Visualization '97, R. Yagel and H. Hagen, eds., pp. 229-234, Oct. 1997.
[11] K. Bonnell, D. Schikore, M. Duchaineau, B. Hamann, and K.I. Joy, Constructing Material Interfaces from Data Sets with Volume-Fraction Information Proc. IEEE Visualization 2000, T. Ertl, B. Hamann, and A. Varshney, eds., pp. 367-372, Oct. 2000.
[12] A. Hanson,"Geometry for N-Dimensional Graphics," Graphics Gems IV, P. Heckbert, ed., Academic Press, 1994, p. 167.
[13] K. Bonnell, On Material Boundary Surfaces MS thesis, Dept. of Computer Science, Univ. of California, Davis, June 2000.

Index Terms:
Eulerian flow, material boundaries, material interfaces, finite elements, barycentric coordinates, volume fraction, isosurface extraction.
Citation:
Kathleen S. Bonnell, Mark A. Duchaineau, Daniel R. Schikore, Bernd Hamann, Kenneth I. Joy, "Material Interface Reconstruction," IEEE Transactions on Visualization and Computer Graphics, vol. 9, no. 4, pp. 500-511, Oct.-Dec. 2003, doi:10.1109/TVCG.2003.1260744
Usage of this product signifies your acceptance of the Terms of Use.