Qualitative Spatial Reasoning about Cardinal

Spatial reasoning is very important for cartography and GISs. Most known methods translate a spatial problem to an analytical formulation to solve quantitatively. This paper shows a method for formal, qualitative reasoning about cardinal directions. The problem addressed is how to deduce the direction from A to C, given the direction from A to B and B to C. It first analyzes the properties formal cardinal direction system should have. It then constructs an algebra with the direction symbols (e.g., {N, E, S, W}) and a combination operation which connects two directions. Two examples for such algebras are given, one formalizing the well-known triangular concept of directions (here called cone-shaped directions) and a projectionbased concept. It is shown that completing the algebra to form a group by introducing an identity element to represent the direction from a point to itself simplifies reasoning and increases power. The results of the deductions for the two systems agree, but the projection bases system produces more 'Euclidean exact' results, in a sense defined in the paper.