Cardinal directions between complex regions

  • Authors:

  • Markus Schneider;Tao Chen;Ganesh Viswanathan;Wenjie Yuan

  • Affiliations:

  • University of Florida, Gainesville, FL;University of Florida, Gainesville, FL;University of Florida, Gainesville, FL;University of Florida, Gainesville, FL

  • Venue:
  • ACM Transactions on Database Systems (TODS)
  • Year:
  • 2012

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Abstract

Besides topological relationships and approximate relationships, cardinal directions like north and southwest have turned out to be an important class of qualitative spatial relationships. They are of interdisciplinary interest in fields like cognitive science, robotics, artificial intelligence, and qualitative spatial reasoning. In spatial databases and Geographic Information Systems (GIS) they are frequently used as join and selection criteria in spatial queries. However, the available computational models of cardinal directions suffer a number of problems like the use of too coarse approximations of the two spatial operand objects in terms of single representative points or minimum bounding rectangles, the lacking property of converseness of the cardinal directions computed, and the limited applicability to simple instead of complex regions only. This article proposes and formally defines a novel two-phase model, called the Objects Interaction Matrix (OIM) model, that solves these problems, and determines cardinal directions for even complex regions. The model consists of a tiling phase and an interpretation phase. In the tiling phase, a tiling strategy first determines the zones belonging to the nine cardinal directions of each individual region object and then intersects them. The result leads to a bounded grid called objects interaction grid. For each grid cell the information about the region objects that intersect it is stored in an objects interaction matrix. In the subsequent interpretation phase, a well-defined interpretation method is applied to such a matrix and determines the cardinal direction. Spatial example queries illustrate our new cardinal direction concept that is embedded in a spatial extension of SQL and provides user-defined cardinal direction predicates.