Summary
Time-varying scalar fields are produced by measurements or simulation of phys- ical processes over time, and must be interpreted with the assistance of computational tools. A useful tool in interpreting the data is graphical visualization, often through level sets, or isocontours of a continuous function derived from the data. In this paper we survey isocontour based visualization techniques for time-varying scalar fields. We focus on techniques that aid selection of meaningful isocontours, and algorithms to extract chosen isocontours.
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References
P. S. Alexandrov. Combinatorial Topology. Dover, Mineola, NY, 1998.
E. Artzy. Display of three-dimensional information in computed tomography. Computer Graphics and Image Processing, 9:196–198, 1979.
C. L. Bajaj, V. Pascucci, and D. Schikore. The contour spectrum. In IEEE Visualization, pages 167–174, 1997.
C. L. Bajaj, A. Shamir, and S. Bong-Soo. Progressive tracking of isosurfaces in time-varying scalar fields. Technical report, Univ. of Texas, Austin, 2002. http://www.ticam.utexas.edu/CCV/papers/Bongbong-Vis02.pdf.
T. F. Banchoff. Critical points for embedded polyhedral surfaces. The American Mathematical Monthly, 77:457–485, 1970.
K. G. Bemis, D. Silver, P. A. Rona, and C. Feng. Case study: a methodology for plume visualization with application to real-time acquisition and navigation. In Proc. IEEE Conf. Visualization, pages 481–494, 2000.
J. L. Bentley. Multidimensional binary search trees used for associative searching. Communications of the ACM, 18(9):509–517, 1975.
J. F. Blinn. A generalization of algebraic surface drawing. ACM Transactions on Graphics, 1(3):235–256, 1982.
R. L. Boyell and H. Ruston. Hybrid techniques for real-time radar simulation. In Proc. of 1963 Fall Joint Computer Conference (IEEE), pages 445–458, 1963.
H. Carr and J. Snoeyink. Path seeds and flexible isosurfaces: Using topology for exploratory visualization. In Proc. of Eurographics Visualization Symposium, pages 49–58, 285, 2003.
H. Carr, J. Snoeyink, and U. Axen. Computing contour trees in all dimensions. Computational Geometry, 24(2):75–94, 2003.
H. Carr, J. Snoeyink, and M. van de Panne. Simplifying flexible isosurfaces using local geometric measures. In Proc. of IEEE Visualization 2004, pages 497–504, 2004.
Y.-J. Chiang. Out-of-core isosurface extraction of time-varying fields over irregular grids. In Proc. IEEE Visualization 2003, pages 217–224, 2003.
Y.-J. Chiang, C. T. Silva, and W. J. Schroeder. Interactive out-of-core isosurface extraction. In Proc. of the Symp. for Volume Vis., pages 167–174, 1998.
T. Chiueh and K.-L. Ma. A parallel pipelined renderer for time-varying volume data. In Proc of Parallel Architecture, Algorithms, Networks, pages 9–15, 1997.
P. Cignoni, P. Marino, C. Montani, E. Puppo, and R. Scopigno. Speeding up isosurface extraction using interval trees. IEEE Transaction on Visualization and Computer Graphics, 3(2):158–170, 1997.
K. Cole-McLaughlin, H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci. Loops in Reeb graphs of 2-manifolds. In Proc. 14th Ann. Sympos. Comput. Geom., pages 344–350, 2003.
T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms, MIT, Cambridge, MA, 1994.
M. Cox and D. Ellsworth, Application controlled demand paging for out-of-core visualization. In IEEE Proc. of Vis. '97, pages 235–244, 1997.
C. J. A. Delfinado and H. Edelsbrunner. An incremental algorithm for betti numbers of simplicial complexes on the 3-sphere. Computer Aided Geometric Design, 12:771–784, 1995.
J. R. Driscoll, N. Sarnak, D. D. Sleator, and R. E. Tarjan. Making data structures persistent. Journal of Computer and System Sciences, 38:86–124, 1989.
M. J. Dürst. Additional reference to “marching cubes”. SIGGRAPH Computer Graphics, 22(5):243, 1988.
H. Edelsbrunner and J. Harer. Jacobi sets of multiple morse functions. In F. Cucker, R. DeVore, P. Olver, and E. Sueli, editors, Foundations of Computational Mathematics, pages 37–57. Cambridge University Press, Cambridge, 2002.
H. Edelsbrunner, J. Harer, A. Mascarenhas, and V. Pascucci. Time-varying Reeb graphs for continuous space-time data. In Proc. of the 20th Ann. Sympos. on Comp. geometry, pages 366–372. ACM Press, 2004.
H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci. Morse-smale complexes for piecewise linear 3-manifolds. In Proc. 19th Ann. Sympos. Comput. Geom., pages 361–370, 2003.
H. Edelsbrunner, J. Harer, and A. Zomorodian. Hierarchical morse complexes for piece-wise linear 2-manifolds. In Proceedings of the 17th Annual Symposium on Computational geometry, pages 70–79. ACM Press, 2001.
A. T. Fomenko and E. T. L. Kunii. Topological Methods for Visualization. Springer, Tokyo, 1997.
H. Fuchs, Z. Kedem, and S. Uselton. Optimal surface reconstruction from planar contours. Communications of the ACM, 20:693–702, 1977.
R. S. Gallagher. Span filtering: An efficient scheme for volume visualization of large finite element models. In G. M. Neilson and L. Rosenblum, editors, Proc. of Vis. '91, pages 68–75, Oct 1991.
A. V. Gelder and J. Wilhelms. Topological considerations in isosurface generation. ACM Transactions on Graphics, 13(4):337–375, 1994.
M. Golubitsky and V. Guillemin. Stable mappings and their singularities. Graduate Texts in Mathematics, Vol. 14. Springer, New York, 1973.
P. Hanrahan. Three-pass affine transforms for volume rendering. Computer Graphics, 24(5):71–78, 1990.
G. T. Herman and H. K. Lun. Three-dimensional display of human organs from computed tomograms. Computer Graphics and Image Processing, 9:1–21, 1979.
C. T. Howie and E. H. Black. The mesh propagation algorithm for isosurface construction. In Computer Graphics Forum 13, Eurographics '94 Conf. Issue, pages 65–74, 1994.
M. Isenburg and S. Gumhold. Out-of-core compression for gigantic polygon meshes. In Proc. of SIGGRAPH 2003, pages 935–942, July 2003.
M. Isenburg and P. Lindstrom. Streaming meshes. In Manuscript, April 2004.
M. Isenburg, P. Lindstrom, S. Gumhold, and J. Snoeyink. Large mesh simplification using processing sequences. In Proc. of Vis. 2003, pages 465–472, Oct 2003.
J. T. Kajiya and B. P. V. Herzen. Ray tracing volume densities. Computer Graphics, 18(3):165–174, 1984.
A. Kaufman and E. Shimony. 3d scan-conversion algorithms for voxel-based graphics. In 1986 Workshop on Interactive 3D Graphics, pages 45–75, 1986.
L. Kettner, J. Rossignac, and J. Snoeyink. The safari interface for visualizing time-dependent volume data using iso-surfaces and contour spectra. Computational Geometry: Theory and Applications, 25(1–2):97–116, 2003.
M. Levoy. Efficient ray tracing of volume data. ACM Transactions on Graphics, 9(3):245–261, 1990.
Y. Livnat, H. W. Shen, and C. R. Johnson. A near optimal iso-surface extraction algorithm for unstructured grids. IEEE Transaction on Visualization and Computer Graphics, 2(1):73–84, 1996.
W. E. Lorensen and H. E. Cline. Marching cubes: A high resolution 3d surface construction algorithm. In M. C. Stone, editor, Computer Graphics (SIGGRAPH '87 Proc.), volume 21, pages 163–169, July 1987.
Y. Matsumoto. An Introduction to Morse Theory (Translated from Japanese by K. Hudson and M. Saito). American Mathematical Society, 2002.
S. V. Matveyev. Approximation of isosurface in the marching cube: ambiguity problem. In Proceedings of the conference on Visualization '94, pages 288–292. IEEE Computer Society Press, 1994.
N. Max, R. Crawfis, and D. Williams. Visualization for climate modeling. In IEEE Computer Graphics Applications, pages 481–494, 2000.
B. H. McCormick, T. A. DeFanti, and M. D. Brown. Visualization in scientific computing. Computer Graphics, 21(6), 1987.
J. Milnor. Morse Theory. Princeton University Press, New Jersey, 1963.
C. Montani, R. Scateni, and R. Scopigno. Discretized marching cubes. In Proceedings of the conference on Visualization '94, pages 281–287. IEEE Computer Society Press, 1994.
J. R. Munkres. Elements of Algebraic Topology. Addison-Wesley, Redwood City, CA, 1984.
B. K. Natarajan. On generating topologically consistent isosurfaces from uniform samples. Visual Computer, 11(1):52–62, 1994.
G. M. Nielson and B. Hamann. The asymptotic decider: resolving the ambiguity in marching cubes. In Proceedings of the 2nd conference on Visualization '91, pages 83–91. IEEE Computer Society Press, 1991.
V. Pascucci and K. Cole-McLaughlin. Parallel computation of the topology of level sets. Algorithmica, 38(1):249–268, 2003.
G. Reeb. Sur les points singuliers d'une forme de pfaff complèment intégrable ou d'une fonction numérique. Comptes Rendus de L'Académie ses Séances, Paris, 222:847–849, 1946.
H. W. Shen. Iso-surface extraction in time-varying fields using a temporal hierarchical index tree. In IEEE Proc. of Vis. '98, pages 159–166, Oct 1998.
H. W. Shen, C. D. Hansen, Y. Livnat, and C. R. Johnson. Isosurfacing in span space with utmost efficiency (issue). In Proc. of Vis. '96, pages 287–294, 1996.
Y. Shinagawa and T. L. Kunii. Constructing a Reeb graph automatically from cross sections. IEEE Computer Graphics and Applications, 11:44–51, 1991.
B.-S. Sohn and C. L. Bajaj. Time-varying contour topology. In Manuscript, 2004.
P. Sutton and C. Hansen. Isosurface extraction in time-varying fields using a temporal branch-on-need tree(t-bon). In IEEE Proc. of Vis. '99, pages 147–153, 1999.
N. Thune and B. Olstad. Visualizing 4-D medical ultrasound data. In Proceedings of the 2nd conference on Visualization '91, pages 210–215. IEEE Computer Society Press, 1991.
M. van Kreveld. Efficient methods for isoline extraction from digital elevation model based on triangulated irregular networks. In Sixth Inter. Symp. on Spatial Data Handling, pages 835–847, 1994.
M. van Kreveld, R. von Oostrum, C. L. Bajaj, V. Pascucci, and D. R. Schikore. Contour trees and small seed sets for iso-surface traversal. In The 13th ACM Sym. on Computational Geometry, pages 212–220, 1997.
L. Westover. Interactive volume rendering. In Chapel Hill Workshop on Volume Visualization, pages 9–16, 1989.
J. Wilhelms and V. Gelder. Octrees for faster isosurface generation. ACM Transaction on Graphics, 11(3):201–227, 1992.
B. Wyvill, C. McPheeters, and G. Wyvill. Animating soft objects. Visual Computer, 2:235–242, 1986.
G. Wyvill, C. McPheeters, and B. Wyvill. Data structure for soft objects. Visual Computer, 2:227–234, 1986.
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Mascarenhas, A., Snoeyink, J. (2009). Isocontour based Visualization of Time-varying Scalar Fields. In: Möller, T., Hamann, B., Russell, R.D. (eds) Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b106657_3
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