A.I. Abdelmoty and M.H. Williams. “Approaches to the representation of qualitative spatial relations for geographic databases,” Geodesy, Vol. 40:204–216, 1994.Google Scholar
T. Bittner. “On ontology and epistemology of rough location. Spatial information theory.” Cognitive and Computational Foundations of Geographic Information Science COSIT' 99, in C. Freksa and D. Mark (Eds.), Lecture Notes in Computer Science, Vol. 1661:433–448, 1999.
S. Cicerone and P. De Felice. “Cardinal directions between spatial objects: the pairwiseconsistency problem,” Information Science
, Vol. 164(1–4):165–188, 2004.CrossRefGoogle Scholar
Clementini et al. “Qualitative representation of positional information,” Artificial Intelligence
, Vol. 95:317–356, 1997.CrossRefGoogle Scholar
A. Cohn. “Calculi for qualitative spatial reasoning”. Artificial intelligence and symbolic mathematical computation, in J. Calmet, J. Campbell, and J. Pfalzgraf (Eds.), Lecture Notes in Computer Science, Vol. 1138:124–143, Springer-Verlag, New York, 1996.
M. Egenhofer and R. Franzosa. “Point-set topological spatial relations,” International Journal of Geographical Information System
, Vol. 5(2):161–174, 1991.Google Scholar
M. Egenhofer and R. Shariff. “Metric details for natural-language spatial relations,” ACM Transactions on Information Systems
, Vol. 16(4):295–321, 1998.CrossRefGoogle Scholar
A.U. Frank. “Qualitative spatial reasoning about distances and directions in geographic space,” Journal of Visual Languages and Computing
, Vol. 3(2):343–371, 1992.CrossRefGoogle Scholar
A.U. Frank. “Qualitative spatial reasoning: cardinal directions as an example,” 1International Journal of Geographic Information Systems
, Vol. 10(3):269–290, 1996CrossRefGoogle Scholar
C. Freksa. “Using orientation information for qualitative spatial reasoning”. Theories and methods of spatio-temporal reasoning in geographic space, in A. Frank, I. Campari, and U. Formentini (Eds.), Lecture Notes in Computer Science, Pisa, Italy, 639:162–178, 1992.
R.K. Goyal. “Similarity assessment for cardinal directions between extended spatial objects”. PHD Thesis. The University of Maine, 2000.
H. Guesgen. “Spatial reasoning based on allen's temporal logic”. Technical Report: TR-89-049, International Computer Science Institute, Berkley, CA, 1989.
R. Haar. “Computational models of spatial relations,” Technical Report: TR-478, MSC-72-03610, Computer Science, University of Maryland, College Park, MD, 1976.
D. Hernandez. “Qualitative representation of spatial knowledge,” Springer Verlag: New York, 1994.Google Scholar
J. Hong. “Qualitative distance and direction reasoning in geographic space,” PHD Thesis. University of Maine, 1994.
B. Kim and K. Um. “2D+ string: A spatial metadata to reason topological and direction relations,” 11th International Conference on Scientific and Statistical Database Management, 112–P122, Cleveland, Ohio, 1999.
L.J. Latecki, and R. Rőhrig. “Orientation and qualitative angle for spatial reasoning,” International Joint Conference on Artificial Intelligence, Chambëry, France, 1993.
Z. Li, R. Zhao, and J. Chen. “A voronoi-based spatial algebra for spatial relations,” Progress in Natural Science
, Vol. 12(6):43–51, 2002.Google Scholar
G. Ligozat. “Reasoning about cardinal directions,” Journal of Visual Languages and Computing
, Vol. 9(1):23– 44, 1998.CrossRefGoogle Scholar
S.L. Liu and X. Chen. “Measuring distance between spatial objects in 2D GIS,” 2nd international symposium on spatial data quality. Hongkong, China, in W.Z. Shi, M.F. Goodchild, and P.F., Fisher (Eds.), 51–60, 2003.
D. Mitra. “A class of star-algebras for point-based qualitative reasoning in two dimension space,” in D. Mitra (Ed.), Proceedings of the FLAIRS-2002, Pendacola Beach, Florida, 2002.
D. Mitra. “Qualitative reasoning with arbitrary angular directions,” Spatial and temporal reasoning workshop note, AAAI, Edmonton, Canada, 2002.
M. Nabil, et al. “2D projection interval relations: A symbolic representation of spatial relations,” Advances in Spatial Databases-4th International Symposium, Portland, in M. Egenhofer and J. Herring (Eds.), Lecture Notes in Computer Science, Vol. 951:292–309, Springer-Verlag: Berlin, 1995.
D. Papadias, Y. Theodoridis, and T. Sellis. “The retrieval of direction relations using R-Trees,” Database and Expert Systems Applications-5th International Conference, DEXA '94. Athens, Greece. in D. Karagiannis (Ed.), Lecture Notes in Computer Science, Vol. 856:173–182, Springer-Verlag: New York, 1994.
D. Peuquet and C.X. Zhan. “An algorithm to determine the directional relation between arbitrarily-shaped polygons in the plane,” Pattern Recognition
, Vol. 201:65–74, 1987.CrossRefGoogle Scholar
S. Pigot. “A topological model for 3D spatial information system,” Auto Carto
, 10:368–392, 1992.Google Scholar
N. Pissinou, I. Radev, K. Macki, and W.G. Campbell. “A topological-directional model for the spatio-temporal composition of the video objects,” Eighth international workshop on research issues on data engineering. in A. Silberschatz, A. Zhang, and S. Mehrotra (Eds.), Continuous-Media Databases and Applications, 17–24, Orlando, FL, 1998.
M. Safar and C. Shahabi. “2D topological and direction relations in the World of Minimum Bounding Circles,” in Proceedings of the 1999 International Database Engineering and Applications Symposium, 1999.
C. Schlieder. “Reasoning about ordering [A],” A Theoretical Basis for GIS International Conference COSIT'95 Semmering, 314–349, Springer-Verlag: Berlin, 1995.
J. Sharma. “Integrated spatial reasoning in geographic information systems: Combining topology and direction,” PHD Thesis, University of Maine, 1996.
S. Shekhar and X. Liu. “Direction as a spatial object: A summary of results,” The Sixth International Symposium on Advances in Geographic Information Systems, 69–75, Washington, 1998.
R. Weibel. “A topology of constraints to line simplification,” in M.J. Kraak and M. Molenaar (Eds.), Advances on GIS I
I, 9A.1–9A.14, London, Taylor & Francis, 1996.Google Scholar
M. Wertheimer. “Law of organization in perceptual forms.” in W. D. Ellis (Kegan Paul, Trench, Trubner) (Ed.), A Source Book of Gestalt Psychology, 71–88, 1923.
H.W. Yan and R.Z. Guo. “Research on a formal description model for direction relations based on voronoi diagrams,” Geoinformatics and Information Science of Wuhan University
, Vol. 28(4):468–472, 2003.Google Scholar
H.W. Yan and R.Z. Guo. “Theorization of directional relation description based on voronoi diagram,” Geoinformatics and Information Science of Wuhan University
, Vol. 27(3):306–310, 2002.Google Scholar
K. Zimmermann and C. Freksa. “Qualitative spatial reasoning using orientation, distance, and path knowledge,” Applied Intelligence
, Vol. 6(1):49–58, 2003.CrossRefGoogle Scholar