Abstract
Volume Visualization techniques have advanced considerably since the first international symposium held on this topic eight years ago.
This paper briefly reviews the techniques proposed for the visualization of irregular (or scattered) volume datasets. In particular, methods which adopt simplicial decompositions of E 3 space are considered, and this choice is justified both in terms of modeling and visualization. Simplicial complexes are powerful and robust geometric structures, and a number of efficient visualization algorithms have been proposed. We show that simplicial cells (or simply tetrahedral cells since our target is 3D space) may be conceived as being the unifying kernel primitive for the visualization of not-regular meshes.
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References
L. B. Chandrajit, V. Pascucci, and D. R. Schikore, Fast isocontouring for improved interactivity, 1996 IEEE Volume Visualization Symposium (1996), 39–46.
J. F. Blinn, Light reflection functions for simulation of clouds and dusty surfaces, Computer Graphics (SIGGRAPH ’82) 16:3 (1982), 21–29.
Y. Chiang and C. T. Silva, I/O optimal isosurface extraction, IEEE Visualization ’87 Proceedings, (R. YAGEL AND H. HAGEN, eds.), 1997.
P. Cignoni, L. de Floriani, C. Montani, E. Puppo, and R. Scopigno, Multiresolution modeling and rendering of volume data based on simplicial complexes, Proceedings of 1994 Symposium on Volume Visualization, ACM Press, 1994, 19–26.
P. Cignoni, C. Montani, E. Puppo, and R. Sgopigno, Multiresolution Representation and Visualization of Volume Data, Technical Report C97–05, Istituto CNUCE — C.N.R., Pisa, Italy, January 1997.
P. Cignoni, C. Montani, E. Puppo, and R. Scopigno, Speeding up isosurface extraction using interval trees, IEEE Trans. on Visualization and Comp. Graph. 3:2 (1997).
P. Cignoni, C. Montani, D. Sarti, and R. Scopigno, On the optimization of projective volume rendering, Visualization in Scientific Computing 1995, Springer, Wien, 1995, 58–71.
L. DE Floriani, P. Marzano, and E. Puppo, Multiresolution models for topographic surface description, The Visual Computer, 12:7 (1996), 317–345.
R. A. Drebin, L. Carpenter, and P. Hanrahan, Volume rendering, Computer Graphics (SIGGRAPH ’88 Proceedings) 22 (1988), 65–74.
H. Edelsbrunner, An acyclicity theorem for cell complexes in d dimensions, Combinatorica 10 (1990), 251–260.
S. F. Gibson, Beyond volume rendering: visualization, haptic exploration, and physical modeling of voxel-based objects, Visualization in Scientific Computing `95, Springer, Wien, 1995, 10–24.
R. S. Gallagher, Span filter: an optimization scheme for volume visualization of large finite element models, IEEE Visualization ’81 Proc. (1991), 68–75.
T. A. Galyean and J. F. Hughes, Sculpting: an interactive volumetric modeling technique, Computer Graphics 25:4 (1991), 264–274.
M. R. Garey and D. S. Johnson, Computers and intractability: A guide to the theory of NP-completeness. W. H. Freeman and Company, New York, 1979.
M. P. Garrity, Raytracing irregular volume data, Computer Graphics (San Diego Workshop on Volume Visualization), 24:5 (1990), 35–40.
C. Giertsen, Volume visualization on sparse irregular meshes, IEEE Computer Graphics & Applications (1992), 40–48.
B. Guo, A multiscale model for structured-based volume rendering, IEEE Trans. on Visualization and Computer Graphics 1:4 (1995), 291–301.
B. Hamann and J. L. Chen, Data point selection for piecewise trilinear approximation, Computer Aided Geometric Design 11 (1994), 477–489.
T. Itoh and K. Koyamada, Automatic isosurface propagation using an Extrema Graph and sorted boundary cell lists, IEEE Trans. on Vis. and Comp. Graph. 1:4 (1995), 319–327.
J. T. Kajiya and Brian P. von Herzen, Ray tracing volume densities, Computer Graphics (SIGGRAPH ’84 Proceedings) 18 (1984), 165–174.
A. Lerios, C. D. Garfinkle, and M. Levoy, Feature-based volume metamorphosis, Comp. Graph. (Siggraph ’85), ACM Press, 1995, 449–464.
M. Levoy, Display of surfaces from volume data, IEEE Computer Graphics and Applications 8:3 (1988), 29–37.
Y. Livnat, H. V. Shen, and C. R. Johnson, A near optimal isosurface extraction algorithm for structured and unstructured grids, IEEE Trans. on Vis. and Comp. Graph. 2:1 (1996), 73–84.
W. E. Lorensen and H. E. Cline, Marching cubes: A high resolution 3D surface construction algorithm, Computer Graphics (SIGGRAPH ’87 Proceedings) 21 (1987), 163–170.
N. Max, Optical models for direct volume rendering, IEEE Trans. on Vis. and Comp. Graph. 1:2 (1995), 99–108.
N. Max, P. Hanrahan, and R. Crawfis, Area and volume coherence for efficient visualization of 3D scalar functions, Computer Graphics (San Diego Workshop on Volume Visualization), 24:5 (1990), 27–33.
E. Puppo and R. Scopigno, Simplification, LOD,and Multiresolution - Principles and Applications, Technical Report C97–12, CNUCE, C.N.R., Pisa (Italy), June 1997. (also in: EUROGRAPHICS’97 Tutorial Notes, Eurographics Association, Aire-la-Ville (CH)).
K. J. Renze and J. H. Oliver, Generalized unstructured decimation, IEEE C.G.&A. 16:6 (1996), 24–32.
P. Sabella, A rendering algorithm for visualizing 3D scalar fields, Computer Graphics (SIGGRAPH ’88 Proceedings) 22:4 (1988), 51–58.
W. J. Schroeder, J. A. Zarge, and W. E. Lorensen, Decimation of triangle meshes, ACM Computer Graphics (SIGGRAPH ’82 Proceedings) 26 (1992), 65–70.
P. Shirley and A. Tuchman, A polygonal approximation to direct scalar volume rendering, Computer Graphics (San Diego Workshop on Volume Visualization), 24:5 (1990), 63–70.
C. T. Silva and J. S. B. Mitchell, The lazy sweep ray casting algorithm for rendering irregular grids, Technical Report 11794/3600, State University of New York, Stony Brook, 1997.
C.T. Silva, J. Mitchell, and A. Kaufman, Fast rendering of irregular grids, Proceedings 1996 Symp. on Volume Visualization (1996), 15–22.
D. Speray, S. Kennon, Volume probes: Interactive data exploration on arbitrary grids, Computer Graphics (San Diego Workshop on Volume Visualization), 24:5 (1990), 5–12.
C. Stein, B. Becker, and N. Max, Sorting and Hardware Assisted Rendering for Volume Visualization, Proceedings of 1994 Symposium on Volume Visualization, ACM Press, 1994, 83–90.
P. Su and R. L. S. Drysdale, A comparison of sequential delaunay triangulation algorithms, 11th ACM Computational Geometry Conf. Proc. (Vancouver, Canada), ACM Press, 1995, 61–70.
A. van Gelder and J. Wilhelms, Rapid exploration of curvilinear grids using direct volume rendering, IEEE Visualization ’83 Proceedings, 1993, 70–77.
J. Wilhelms and A. von Gelder, Octrees for faster isosurface generation, ACM Computer Graphics 24:5 (1990), 57–62.
J. Wilhelms, A. van Gelder, P. Tarantino, and J. Gibbs, Hierarchical and parallelizable direct volume rendering for irregular and multiple grids, Visualization ’86 Proceedings, IEEE Press, 1996, 57–64.
J. Wilhelms and A. von Gelder, Octrees for faster isosurface generation, ACM Transaction on Graphics 11:3 (1992), 201–227.
P. L. Williams, Visibility ordering of meshed polyhedra, ACM Transaction on Graphics 11:2 (1992), 103–126.
P. L. Williams, Interactive splatting of nonrectilinear volumes, A.E. Kaufman and G.M. Nielson, editors, Visualization ’82 Proceedings, IEEE Computer Society Press, 1992, 37–45.
P. L. Williams, Interactive Direct Volume Rendering of Curvilinear and Unstructured Data. PhD thesis, University of Illinois at Urbana-Champaign, 1993.
R. Yagel, D. M. Reed, A. Law, P. W. Shi, and N. Shareef, Hardware assisted volume rendering of unstructured grids by incremental slicing, Proceedings 1996 Symp. on Volume Visualization, 1996, 55–62.
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© 1998 Springer-Verlag Berlin Heidelberg
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Cignoni, P., Montani, C., Scopigno, R. (1998). Tetrahedra Based Volume Visualization. In: Hege, HC., Polthier, K. (eds) Mathematical Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03567-2_1
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DOI: https://doi.org/10.1007/978-3-662-03567-2_1
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