Counting cases in substitope algorithms

IEEE Transactions on Visualization and Computer Graphics

Volumn 10, Issue 4, 2004, Pages 371-384

  Banks, David C ^a   Linton, Stephen A ^b   Stockmeyer, Paul K ^c  

^a Florida State University   (United States)

^b UNIVERSITY OF ST ANDREWS   (United Kingdom)

^c The College of William and Mary   (United States)

Author keywords

Geometric substitution; Group action; Isosurface; Level set; Marching Cubes; Orbit; P lya counting; Separating surface; Substitope

Indexed keywords

GEOMETRIC SUBSTITUTION; GROUP ACTION; ISOSURFACES; LEVEL SETS; MARCHING CUBES (MC) ALGORITHMS; PÓLYA COUNTING; SEPARATING SURFACES; SUBSTITOPE;

ALGORITHMS; COMPUTATIONAL GEOMETRY; FUNCTIONS; ITERATIVE METHODS; PROBLEM SOLVING; SET THEORY;

COMPUTER GRAPHICS;

ALGORITHM; ARTICLE; COMPUTER ASSISTED DIAGNOSIS; COMPUTER GRAPHICS; IMAGE ENHANCEMENT; METHODOLOGY; THREE DIMENSIONAL IMAGING;

ALGORITHMS; COMPUTER GRAPHICS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL;

EID: 3042691805     PISSN: 10772626     EISSN: None     Source Type: Journal    
DOI: 10.1109/TVCG.2004.6     Document Type: Conference Paper

References (39)

1. W.E. Lorensen and H.E. Cline, "Marching Cubes: A High Resolution 3D Surface Construction Algorithm," Proc. SIGGRAPH 1987, pp. 163-169, 1987.
2. H.S.M. Coxeter, Regular Polytopes. Dover Publications, 1973.
3. D.C. Banks and S. Linton, "Counting Cases in Marching Cubes: Toward a Generic Algorithm for Producing Substitopes," Proc. Visualization 2003, 2003.
4. J. Bloomenthal, "Polygonization of Implicit Surfaces," Computer-Aided Geometric Design, vol. 5, pp. 341-355, 1988.
5. H.-W. Shen and C.R. Johnson, "Sweeping Simplices: A Fast IsoSurface Extraction Algorithm for Unstructured Grids," Proc. IEEE Visualization 1995, pp. 143-151, 1995.
6. S.F. Kirchberg, "Marching Hypercubes - ein Verfahren zur Konstruktion von Hyperflächen aus 4D-Rasterdaten," Universität Dortmund, doplomarbeit am Lehrstuhl 7, 1993.
7. J.C. Roberts and S. Hill, "Piecewise Linear Hypersurfaces Using the Marching Cubes Algorithm," Visual Data Exploration and Analysis VI, Proc. SPIE, R. Erbacher and A. Pang, eds., pp. 170-181, Jan. 1999.
8. P. Bhaniramka, R. Wenger, and R. Crawfis, "Isosurfacing in Higher Dimensions," Proc. IEEE Visualization 2000, pp. 267-273, 2000.
9. G.M. Nielson and J. Sung, "Interval Volume Tetrahedrization," Proc. IEEE Visualization 1997, pp. 221-228, 1997.
10. C. Weigle and D.C. Banks, "Complex-Valued Contour Meshing," Proc. IEEE Visualization 1996, pp. 173-180, 1996.
11. H.-C. Hege, M. Seebass, D. Stalling, and M. Zöckler, "A Generalized Marching Cubes Algorithm Based on Non-Binary Classifications," Technical Report SC 97-05, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Dec. 1997.
12. D. Stalling, M. Zöckler, O. Sander, and H.-C. Hege, "Weighted Labels for 3D Image Segmentation," Technical Report SC 98-39, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Dec. 1998.
13. Module: GMC, Template Graphics Software (User manual entry for amira visualization software), 2000.
14. K. Montgomery, C. Bruyns, and S. Wildermuth, "A Virtual Environment for Simulated Rat Dissection: A Case Study of Visualization for Astronaut Training," Proc. IEEE Visualization 2001, pp. 509-512, 2001.
15. H.-C. Hege, "Enumeration of Symmetry Classes in Mesh Generation," Report on Dagstuhl Seminar 9821: Hierarchical Methods in Computer Graphics, M. Gross, H. Müller, P. Schröder, and H.P. Seidel, eds., pp. 9-10, May 1998.
16. G.M. Nielson and R. Franke, "Computing the Separating Surface for Segmented Data," Proc. IEEE Visualization 1997, pp. 229-233, 1997.
17. H.-W. Shen, C.D. Hansen, Y. Livnat, and C.R. Johnson, "Isosurfacing in. Span Space with Utmost Efficiency (ISSUE)," Proc. IEEE Visualization 1996, pp. 287-294, 1996.
18. J. Wilhelms and A.V. Gelder, "Octrees for Faster Isosurface Generation," ACM Trans. Graphics, vol. 11, no. 3, pp. 201-227, July 1992.
19. P. Cignoni, P. Marino, C. Montani, E. Puppo, and R. Scopigno, "Speeding Up Isosurface Extraction Using Interval Trees," J. Symbolic Logic, vol. 3, no. 2, pp. 158-170, 1997.
20. R.S. Gallagher, "Span Filter: An Optimization Scheme for Volume Visualization of Large Finite Element Models," Proc. IEEE Visualization, 1991.
21. A. Lindenmayer, "Developmental Systems without Cellular Interaction, Their Languages and Grammars," J. Theoretical Biology, vol. 30, pp. 455-484, 1971.
22. P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants, 1990.
23. A. Glassner, "A Tutorial on Geometric Replacements," IEEE Computer Graphics and Applications, vol. 12, no. 1, pp. 22-36, Jan. 1992.
24. M. Lounsbery, T.D. DeRose, and J. Warren, "Multiresolution Analysis for Surfaces of Arbitrary Topological Type," ACM Trans. Graphics, vol. 16, no. 1, pp. 34-73, 1997.
25. L. Kobbelt, S. Campagna, and H.-P. Seidel, "A General Frame-work for Mesh Decimation," Proc. Graphics Interface, pp. 43-50, 1998.
26. n = 1," Philosophical Magazine, vol. 7, pp. 40-47, 1854.
27. J.G. Fraleigh, A First Course in Abstract Algebra, sixth ed. Addison-Wesley, 1998.
28. P.M. Cohn, Algebra, volume 1, second ed. Wiley, 1984.
29. A. Seress, "An Introduction to Computational Group Theory," Notices of the AMS, vol. 44, no. 6, pp. 671-679, June/July 1997.
30. M. Schönert, GAP - Groups, Algorithms and Programming, Lehrstuhl D für Mathematik, RTWH, Aachen, 1994.
31. W.S. Jevons, "Solution of the Inverse or Inductive Problem, Involving Two Classes," Proc. Manchester Literary and Philosophical Soc., vol. xi, pp. 65-68, Dec. 1871.
32. W.S. Jevons, The Principles of Science: A Treatise on Logic and Scientific Method. 1874, second edition, reprinted with corrections, 1879, 1883, 1887, 1892, 1900, 1905, 1907, 1913.
33. W.K. Clifford, Mathematical Papers, R. Tucker, ed. London: MacMillan and Co., 1882, introduction by H.J. Stephen Smith; reprinted by Chelsea, N.Y., 1968.
34. G. Pólya, "Sur les Types des Propositions Composées," J. Symbolic Logic, vol. 5, no. 3, pp. 98-103, Sept. 1940.
35. W. Burnside, Theory of Groups of Finite Order, second ed. London: Cambridge Univ. Press, 1911.
36. G. Pólya, "Kombinatorische Anzahlbesimmungen für Gruppen, Graphen und Chemische Verbindungen," Acta Math., vol. 68, pp. 145-254, 1937.
37. G. Pólya and R.C. Read, Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds. New York: Springer-Verlag, 1987.
38. "GAP-Groups, Algorithms, and Programming, Version 4.3," The GAP Group, 2002, http://www.gap-system.org.
39. W.K. Clifford, "On the Types of Compound Statement Involving Four Classes," Proc. Manchester Literary and Philosophical Soc., vol. xvi, pp. 88-101, Jan. 1877.