CAUSTA: Clifford algebra-based unified spatio-temporal analysis

Transactions in GIS

Volumn 14, Issue SUPPL. 1, 2010, Pages 59-83

  Yuan, Linwang ^a,b   Yu, Zhaoyuan ^a   Chen, Shaofei ^b   Luo, Wen ^a   Wang, Yongjun ^a   Lü, Guonian ^a  

^a NANJING NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF TEXAS AT DALLAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TRANSFORMATIONS; SOFTWARE PROTOTYPING; SPATIAL VARIABLES MEASUREMENT;

CLIFFORD ALGEBRA; DATA OBJECTS; HYPER-CUBES; MATHEMATICAL FOUNDATIONS; MULTIVECTORS; POINT-CLOUDS; SPATIAL TEMPORAL ANALYSIS; SPATIO-TEMPORAL; SPATIOTEMPORAL ANALYSIS; SPATIOTEMPORAL DATA MODEL;

ALGEBRA;

ALGORITHM; GIS; NUMERICAL MODEL; SOFTWARE; SPATIAL DATA; SPATIOTEMPORAL ANALYSIS;

EID: 77954359277     PISSN: 13611682     EISSN: 14679671     Source Type: Journal    
DOI: 10.1111/j.1467-9671.2010.01221.x     Document Type: Article

References (52)

1. Armstrong M P. Temporality in spatial databases: Proceedings of GIS/LIS'88. 1988, 880-9. In, San Antonio, Texas
2. Cazals F, Giesen J. Delaunay triangulation based surface reconstruction. Effective Computational Geometry for Curves and Surfaces 2006, 231-76. Boissonnat J D, Teillaud M. In, eds, Berlin, Springer
3. Chen J D, Meng X F. Update-efficient indexing of moving objects in road networks. GeoInformatica 2009, 13:397-424.
4. Cheng T, Li Z, Gong J. An activity-based spatio-temporal data model for epidemic transmission analysis. Advances in Spatio-Temporal Analysis 2007, 135-46. Tang X, Liu Y, Zhang JKainz W. In, eds, London, Taylor and Francis
5. Clifford W K. Applications of Grassmann's extensive algebra. American Journal of Math 1878, 1:350-8.
6. Curtin K M. Network analysis in geographic information science: Review, assessment, and projections. Cartography and Geographic Information Science 2007, 34:103-11.
7. Doran C, Lasenby A. Geometric Algebra for Physicists 2003, Cambridge, Cambridge University Press
8. Dorst L, Fontijne D, Mann S. Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry 2007, San Fransisco, CA, Morgan Kaufmann
9. Goodchild M F. Combining space and time: New potential for temporal GIS. Placing History: How Maps, Spatial Data, and GIS Are Changing Historical Scholarship 2008, 179-98. Knowles A K. In, ed, Redlands, CA, ESRI Press
10. Grassmann H G. Die Lineale Ausdehnungslehre: Ein neuer Zweig der Mathematik 1844, Leipzig, Verlag von Otto Wigand
11. Gull S F, Lasenby A N, Doran C J L. Imaginary numbers are not real: The geometric algebra of spacetime. Foundations of Physics 1993, 23:1175-201.
12. Güting R H, Schneider M. Moving Objects Databases 2005, San Fransisco, CA, Morgan Kaufmann
13. Hestenes D. Space Time Algebra 1966, New York, Gordon and Breach
14. Hestenes D. New Foundations for Classical Mechanics 2002, Dordrecht, Kluwer
15. Hestenes D. Spacetime physics with geometric algebra. American Journal of Physics 2003a, 71:691-714.
16. Hestenes D. Curvature calculations with spacetime algebra. International Journal of Theoretical Physics 2003b, 25:581-8.
17. Hestenes D, Sobczyk G. Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics 1984, Dordrecht, Reidel
18. Hornsby K, Egenhofer M. Identity-based change: A foundation for spatio-temporal knowledge representation. International Journal of Geographical Information Science 2000, 14:207-24.
19. Hucks J. Hyperbolic complex structures in physics. Journal of Mathematical Physics 1993, 34:5986-6008.
20. Kalay U, Kalipsiz O. A comparison study of moving object index structures. Journal of Computer Science and Technology 2009, 24:1098-108.
21. Kim K Y, Wu Q. A comparison study of EOF techniques: Analysis of nonstationary data with periodic statistics. Journal of Climate 1999, 12:185-99.
22. Langran G. States, events, and evidence: The principal entities of a temporal GIS: Proceedings of GIS/LIS '92. 1992, 416-25. In, San Antonio, Texas
23. Langran G, Chrisman N. A framework for temporal geographical information systems. Cartographica 1988, 25:1-14.
24. Le Y. A prototype temporal GIS for multiple spatio-temporal representations. Cartography and Geographic Information Science 2005, 32:315-29.
25. Lee I, Gahegan M. Interactive analysis using Voronoi diagrams: Algorithms to support dynamic update from a generic triangle-based data structure. Transactions in GIS 2002, 6:89-114.
26. Li H. Invariant Algebras and Geometric Reasoning 2008, Singapore, World Scientific Publishing
27. Li W M, Yang F. N-dimensional space-time unit spheres and Lorentz transformation. Advances in Applied Clifford Algebras 2003, 13:57-64.
28. Liu Y, Goodchild M F, Guo Q, Tian L, Wu L. Towards a general field model and its order in GIS. International Journal of Geographical Information Science 2008, 22:623-43.
29. Longley P A, Goodchild M F, Maguire D J, Rhind D W. Geographic Information Systems and Science 2005, 2nd, edn., New York, John Wiley and Sons
30. McIntosh J, Yuan M. A framework to enhance semantic flexibility for analysis of distributed phenomena. International Journal of Geographic Information Science 2005, 19:999-1018.
31. McMaster R, Usery E L. A Research Agenda for Geographic Information Science 2004, Boca Raton, FL, CRC Press
32. Nascimento M A, Silva J R. Towards historical R-trees: Proceedings of the ACM Symposium on Applied Computing (ACM-SAC '98). 1998, 235-40. In, Atlanta, Georgia
33. Pavšič M. Clifford space as a generalization of spacetime: Prospects for QFT of point particles and strings. Foundations 2005, 35:1617-42.
34. Perwass C. Geometric Algebra with Applications in Engineering 2009, Berlin, Springer-Verlag
35. Peuquet D J. Making space for time: Issues in space-time data representation. GeoInformatica 2001, 5:11-32.
36. Peuquet D J, Duan N. An Event-based Spatio-Temporal Data Model (ESTDM) for temporal analysis of geographical data. International Journal of Geographical Information Systems 1995, 9:7-24.
37. Pultar E, Raubal M, Cova T J, Goodchild M F. Dynamic GIS case studies: Wildfire evacuation and volunteered geographic information. Transactions in GIS 2009, 13:85-104.
38. Qu J. Outlier detection based on Voronoi diagram. Data Mning Advances and Applications 2008, 5139:516-23. Li XWang SDong Z Y. In, eds, Berlin, Springer Lecture Notes of Computer Science, Vol
39. Raper J, Livingstone D. Development of a geomorphological spatial model using object-oriented design. International Journal of Geographical Information Systems 1995, 9:359-83.
40. Samet H. Foundations of Multidimensional and Metric Data Structures 2006, San Fransisco, CA, Morgan Kaufmann
41. Schott R, Staples G S. Reductions in computational complexity using Clifford algebras. Advances in Clifford Algebras 2010, 20:121-40.
42. Scotese C R, Rees P M. The Spatial-Temporal Information Matrix (STIM) cube: An efficient way to store geological information: Proceedings of the Annual Meeting of the Geological Society of America. 2004, In, Denver, Colorado
43. Tao Y F, Papadias D. Efficient historical R-trees: Proceedings of the Thirteenth IEEE Conference on Scientific and Statistical Database Management (SSDBM). 2001, 223-32. In, Fairfax, Virginia
44. Theodoridis T, Vazirgiannis M, Sellis T. Spatio-temporal indexing for large multimedia applications: Proceedings of the Third IEEE Conference on Multimedia Computing and Systems (ICMCS '96). 1996, 441-8. In, Hiroshima, Japan
45. Wachowicz M, Healey R G. Towards Temporality in GIS 1994, London, Taylor and Francis
46. Wolfson O, Xu B, Chamberlain S, Jiang L. Moving objects databases: Issues and solutions: Proceedings of the Tenth International Conference on Scientific and Statistical Database Management (SSDM98). 1998, 111-22. In, Capri, Italy
47. Worboys M. A unified model for spatial and temporal information. Computer Journal 1994, 37:26-34.
48. Wu W G, Chen H, Wu Y, Liu Y. A novel spatio-temporal attributes index-based query for wireless sensor networks. International Journal of Distributed Sensor Networks 2009, 5:67-67.
49. Wu Y B, Deng X M, Zhao G M, Li S, Lv J B, Yang X Y. Hyperbolic phase transformation group and its application to four dimensional relativistic spacetime. Acta Physica Sinica 2005, 54:4994-5005. in Chinese
50. Xu X, Han J, Lu W. RT-tree: An improved R-tree index structure for spatiotemporal databases: Proceedings of the Fourth International Symposium on Spatial Data Handling. 1990, 1040-9. In, Zurich, Switzerland
51. Yuan M. Use of a three-domain representation to enhance GIS support for complex spatiotemporal queries. Transaction in GIS 1999, 3:137-59.
52. Yuan M. Knowledge discovery of geographic dynamics in spatiotemporal data. Geographic Data Mining and Knowledge Discovery 2009, 347-66. Miller H JHan J. In, eds, Second, edn., London, Taylor and Francis