Pointerless implementation of hierarchical simplicial meshes and efficient neighbor finding in arbitrary dimensions

International Journal of Computational Geometry and Applications

Volumn 17, Issue 6, 2007, Pages 595-631

  Atalay, F Betul ^a   Mount, David M ^b  

^a SAINT JOSEPH S UNIVERSITY   (United States)

^b Institute of Advanced Computer Science   (United States)

Author keywords

Hierarchical simplicial meshes; Neighbor finding; Pointerless data structures

Indexed keywords

EID: 37749053116     PISSN: 02181959     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218195907002495     Document Type: Article

References (37)

1. R. E. Bank, A. H. Sherman and A. Weiser, Refinement algorithms and data structures for regular local mesh refinement, J. Sci. Comput. (1983) 3-17.
2. W. F. Mitchell, Optimal multilevel iterative methods for adaptive grids, SIAM J. Sci. Stat. Comp. 13 (1992) 146-167.
3. D. N. Arnold, A. Mukherjee and L. Pouly, Locally adapted tetrahedral meshes using bisection, SIAM J. Sci. Comput. 22(2), (2001) 431-448.
4. J. Bey, Tetrahedral grid refinement, Comput. 55 (1995) 355-378.
5. A. Liu and B. Joe, Quality local refinement of tetrahedral meshes based on bisection, SIAM J. Sci. Comput. 16 (1995) 1269-1291.
6. A. Liu and B. Joe, Quality local refinement of tetrahedral meshes based on 8-subtetrahedron subdivision, Math. Comput. 65(215) (1996) 1183-1200.
7. J. M. Maubach, Local bisection refinement for N-simplicial grids generated by reflection, SIAM J. Sci. Stat. Comp. 16 (1995) 210-227.
8. M. C. Rivara, Local modification of meshes for adaptive and/or multigrid finiteelement methods, J. Comput. Appl. Math. 36 (1991) 79-89.
9. H. Edelsbrunner, Algorithms in Combinatorial Geometry, EATCS Monographs on Theoretical Computer Science, Vol. 10 (Springer-Verlag, 1987).
10. J. R. Munkres, Topology: A First Course (Prentice Hall, Englewood Cliffs, NJ, 1975).
11. Y. Zhou, B. Chen and A. Kaufman, Multiresolution tetrahedral framework for visualizing regular volume data, Proc. IEEE Visualization'97, 1997, pp. 135-142.
12. T. Gerstner and M. Rumpf, Multiresolutional parallel isosurface extraction based on tetrahedral bisection, Proc. Symp. Volume Visualization, 1999.
13. M. Ohlberger and M. Rumpf, Hierarchical and adaptive visualization on nested grids, Computing 56 (1997) 365-385.
14. D. J. Hebert, Symbolic local refinement of tetrahedral grids, J. Symb. Comput. 17 (1994) 457-472.
15. A. S. Glassner, An Introduction to Ray Tracing (Academic Press, San Diego, 1989).
16. F. B. Atalay and D. M. Mount, Ray interpolants for fast ray-tracing reflections and refractions, J. WSCG 10(3) (2002) 1-8,
17. Proc. Int. Conf. Central Europe on Computer Graphics, Visualization and Computer Vision.
18. F. B. Atalay and D. M. Mount, Interpolation over light fields with applications in computer graphics, Proc. 5th Workshop on Algorithm Engineering and Experiments (ALENEX 2003) (SIAM, 2003), pp. 56-68.
19. M. Bern, D. Eppstein and J. Gilbert, Provably good mesh generation, J. Comput. Syst. Sci. 48 (1994) 384-409.
20. R. Pajarola, Overview of quadtree-based terrain triangulation and visualization, Technical report, UCI-ICS-02-01, Information & Computer Science, University of California Irvine, 2002.
21. R. Sivan and H. Samet, Algorithms for constructing quadtree surface maps, Proc. 5th Int. Symp. Spatial Data Handling, 1992, pp. 361-370
22. H. Samet, Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS (Addision-Wesley, 1990).
23. M. Lee and H. Samet, Navigating through triangle meshes implemented as linear quadtrees, ACM Trans. Comput. Graph. 19 (2000) 79-121.
24. T. Chilimbi, M. D. Hill and J. R. Larus, Cache-conscious structure layout, in Programming Languages Design and Implementation, 1999.
25. A. Aggarwal and J. S. Vitter, The input/output complexity of sorting and related problems, Commun. ACM 31 (1988) 1116-1127.
26. L. Arge, External memory data structures, in Handbook of Massive Data Sets, eds. J. Abello, P. M. Pardalos and M. G. C. Resende (Kluwer Academic Publishers, 2002), pp. 313-358.
27. E. D. Demaine, Cache-oblivious algorithms and data structures, in Lecture Notes from the EEF Summer School on Massive Data Sets, 2002.
28. I. Gargantini, An effective way to represent quad-trees, Commun. ACM25(12) (1982) 905-910.
29. W. Evans, D. Kirkpatrick and G. Townsend, Right-triangulated irregular networks, Algorithmica 30(2) (2001) 264-286.
30. M. Lee, L. De Floriani and H. Samet, Constant-time neighbor finding in hierarchical tetrahedral meshes, Proc. Int. Conf. Shape Modelling, 2001, pp. 286-295.
31. D. K. Blandford, G. E. Blelloch, D. E. Cardoze and C. Kadow, Compact representations of simplicial meshes in two and three dimensions, Proc. 12th Int. Meshing Roundable, 2003.
32. A. Szymczaka and J. Rossignac, Grow & fold: compressing the connectivity of tetrahedral meshes, Comput. Aided Desig. 32 (2000) 527-537.
33. J. M. Maubach, The efficient location of neighbors for locally refined n-simplicial grids, Proc. 5th Int. Meshing Roundable, 1996.
34. E. Allgower and K. Georg, Generation of triangulations by reflection, Utilitas Mathematica 16 (1979) 123-129.
35. D. E. Knuth, Sorting and Searching, The Art of Computer Programming, Vol. 3 (1973).
36. S. R. Lay, Convex Sets and Their Applications (John Wiley Sz Sons, New York, NY, 1982).
37. F. B. Atalay and D. M. Mount, Pointerless implementation of hierarchical simplicial meshes and efficient neighbor finding in arbitrary dimensions, Proc. 13th Int. Meshing Roundable, 2004, pp. 15-26.