A simplex-based approach to implement dimension independent spatial analyses

Computers and Geosciences

Volumn 36, Issue 9, 2010, Pages 1123-1134

  Karimipour, Farid ^a,b   Delavar, Mahmoud R ^a   Frank, Andrew U ^b  

^a UNIVERSITY OF TEHRAN   (Iran)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

3D GIS; Delaunay triangulation; List data structure; N Dimensional spatial analyses; Simplexes

Indexed keywords

3D GIS; DELAUNAY TRIANGULATION; LIST DATA STRUCTURE; SIMPLEXES; SPATIAL ANALYSIS;

ALGORITHMS; COMPUTATIONAL GEOMETRY; CONTENT BASED RETRIEVAL; DATA STRUCTURES; RESEARCH; RESERVOIRS (WATER); TRIANGULATION; WATER LEVELS;

THREE DIMENSIONAL;

ALGORITHM; GEOMETRY; GIS; SPATIAL ANALYSIS; THREE-DIMENSIONAL MODELING; TRIANGULATION; TWO-DIMENSIONAL MODELING;

EID: 77955927989     PISSN: 00983004     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cageo.2010.03.002     Document Type: Article

References (37)

1. Abdul-Rahman A., Pilouk M. Spatial Data Modeling for 3D GIS 2008, Springer-Verlag, Berlin, Heidelberg, 289pp.
2. Alexandroff P. Elementary Concepts of Topology 1961, Dover Publications, New York, 57pp.
3. Apel, M., 2004. A 3D geoscience information system framework. Ph.D. Dissertation, Technische Universitaet Freiberg, Freiberg, Germany, 105pp.
4. Aurenhammer F. Voronoi diagrams-a survey of a fundamental geometric data structure. ACM Computing Surveys 1991, 23(3):345-405.
5. Bird R., Wadler P. Introduction to Functional Programming 1988, Prentice Hall, Hertfordshire, UK, 293pp.
6. Bowyer A. Computing Dirichlet tessellation. The Computer Journal 1981, 24(2):162-166.
7. Bulbul, R., Karimipour, F., Frank, A.U., 2009. A simplex-based dimension independent approach for convex decomposition of nonconvex polytopes. In: Proceedings 10th International Conference on GeoComputation, Sydney, Australia, 8pp. http://www.biodiverse.unsw.edu.au/geocomputation/proceedings/PDF/Bulbul_et_al.pdf.
8. Delaunay B.N. Sur la Sphere Vide (On the empty sphere). Izvestia Akademia Nauk SSSR, Otdelenie Matematicheskii i Estestvennyka Nauk 1934, 7:793-800.
9. Field, D.A., 1986. Implementing Watson's algorithm in three dimension. In: Proceedings 2nd Annual Symposium on Computational Geometry, New York, USA, pp. 246-259.
10. Frank A.U. One step up the abstraction ladder: combining algebras-from functional pieces to a whole. Proceedings International Conference COSIT'99, Stade, Germany, Lecture Notes in Computer Sciences 1999, vol. 1661:95-107. Springer-Verlag.
11. Frank A.U., Kuhn W. Cell graphs: a provable correct method for the storage of geometry. Proceedings 2nd International Symposium on Spatial Data Handling 1986, 411-436. D. Marble (Ed.).
12. Guibas L., Stolfi J. Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Transactions on Graphics 1985, 4(2):74-123.
13. Hatcher A. Algebraic Topology 2002, Cambridge University Press, Cambridge, UK, 544pp. accessed 30 April 2010.
14. Houlding S.W. 3D Geoscience Modeling: Computer Techniques for Geological Characterization 1994, Springer-Verlag, Berlin, 309pp.
15. Karimipour, F., Delavar, M.R., Frank, A.U., 2008a. A mathematical tool to extend 2D spatial operations to higher dimensions. In: Proceedings of the International Conference on Computational Science and Its Applications (ICCSA 2008), Perugia, Italy, Lecture Notes in Computer Science, vol. 5072, Springer-Verlag, pp. 153-164.
16. Karimipour, F., Frank, A.U., Delavar, M.R., 2008b. An operation-independent approach to extend 2D spatial operations to 3D and moving objects. In: Proceedings of the 16th ACM (Association for Computing Machinery) SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM GIS 2008), Irvine, CA, USA, pp. 51-56.
17. Lattuada, R., Raper, J., 1995. Applications of 3D Delaunay triangulation algorithms in geoscientific modeling. In: Proceedings of the 3rd National Conference on GIS Research UK, Newcastle, UK, pp. 150-153. (accessed 30 April 2010). http://geog.bbk.ac.uk.
18. Ledoux, H., 2006. Modelling three-dimensional fields in geo-science with the Voronoi diagram and its dual. Ph.D. Dissertation, University of Glamorgan, Pontypridd, Wales, UK, 168pp.
19. Ledoux, H., 2007. Computing the 3D Voronoi diagram robustly: an easy explanation. In: Proceedings of the 4th International Symposium on Voronoi Diagrams in Science and Engineering, Pontypridd, Wales, UK, pp. 117-129.
20. Ledoux, H., Gold, C., 2007. The 3D Voronoi diagram: a tool for the modelling of geoscientific datasets. In: Proceedings of the GeoCongres 2007, Quebec, Canada, 13pp. http://www.gdmc.nl/publications/2007/3D_Voronoi_Diagram_Tool.pdf.
21. Monga O., Ngom F.N., Delerue J.F. Representing geometric structures in 3D tomography soil images: application to pore-space modeling. Computers & Geosciences 2007, 33:1140-1161.
22. Mostafavi M.A., Gold C., Dakowicz M. Delete and insert operations in Voronoi/Delaunay methods and applications. Computers & Geosciences 2003, 29:523-530.
23. Nonato L.G., Minghim R., Oliveira M.C.F., Tavares G. A novel approach for Delaunay 3D reconstruction with a comparative analysis in the light of applications. Journal of Computer Graphics 2001, 20(2):1-14.
24. Okabe A., Boots B., Sugihara K., Chiu S.N. Spatial Tessellations: Concepts and Applications of Voronoi Diagrams 2000, John Wiley, Chichester, UK, 671pp. second ed.
25. O'Rourke J. Computational Geometry in C 1998, Cambridge University Press, Cambridge, UK, 350pp. second ed.
26. Penninga F., van Oosterom P.V. A simplicial complex-based DBMS approach to 3D topographic data modeling. International Journal of Geographical Information Science 2008, 22(7):751-779.
27. Pouliot J., Bedard K., Kirkwood D., Lachance B. Reasoning about geological space: coupling 3D geomodels and topological queries as an aid to spatial data selection. Computers & Geosciences 2008, 34:529-541.
28. Preparata F.P., Hong S.J. Convex hulls of finite sets of points in two and three dimensions. Communications of the ACM 1997, 20(2):87-93.
29. Raper J. Multidimensional Geographic Information Science 2000, Taylor & Francis, London, 317pp.
30. Schneider M. Spatial Data Types For Database Systems-Finite Resolution Geometry For Geographic Information Systems, Lecture Notes in Computer Sciences. Berlin-Heidelburg 1997, 1288. Springer-Verlag, 275pp.
31. Stolfi, J., 1989. Primitives for computational geometry. Ph.D. Dissertation, Computer Science Department, Stanford University, Palo Alto, CA, 228pp.
32. Thompson S. Haskell: The Craft of Functional Programming 1999, Addison-Wesley, Dorchester, UK, 500pp.
33. Three Dimensional Modelling with Geoscientific Information Systems 1992, Kluwer Academic Publishers, Dordrecht, The Netherlands. K. Turner (Ed.).
34. Tzenkov T., Gospodinov S. Geometric analysis of geodetic data for investigation of 3D landslide deformations. Natural Hazards Reviews 2003, 4(2):78-81.
35. Watson D.F. Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes. The Computer Journal 1981, 24:167-172.
36. Yanbing, W., Lixin, W., Wenzhong, S., Xiaomeng, L., 2007. On 3D GIS spatial modeling. In: Proceedings of the ISPRS Workshop on Updating Geo-spatial Databases with Imagery and the 5th ISPRS Workshop on DMGISs, Urumchi, Xinjiang, China, pp. 237-240.
37. Yong X., Sun M., Ma A. On the reconstruction of three-dimensional complex geological objects using Delaunay triangulation. Journal of Future Generation Computer Systems 2004, 20:1227-1234.