Direction as a Spatial Object

Date of Submission: 
March 1, 1998
Report Number: 
98-021
Abstract: 
Direction is an important spatial relation that is used in many fields such as geographic information system (GIS) and image interpretation. It is also frequently used as a selection condition in spatial queries. Previous work has modeled direction as a relationship predicate between spatial objects. Conversely, in this paper, we model direction as a new kind of spatial object using the concepts of vectors, points and angles. The basic approach is to model direction as a unit vector. Given an ordered pair (p1, p2) of spatial pints, one can define a direction, which can take the values of North, Northwest, 3 o'clock, etc. to represent the corresponding qualitative directional predicates on (p1,p2) in previous work. Direction objects can also have quantitative operations such as direction-addition, direction-subtraction. This novel view of direction has several obvious advantages: First, it allows us to define the orientation of spatial objects; Second, a richer set of predicates and operators on direction and orientation can be defined; Third, new spatial data types such as oriented spatial objects and unbounded spatial objects can be defined. Finally, the object view of direction makes it easy to do quantitive direction reasoning, which is useful in spatial query processing and optimization. Its applicability is demonstrated with geographic examples.