tailieunhanh - Advances in Database Technology- P8

Tham khảo tài liệu 'advances in database technology- p8', công nghệ thông tin, cơ sở dữ liệu phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 332 S. Skiadopoulos et al. Fig. 1. Reference tiles and relations In Fig. 1 regions a b and c are in REG also in REG and region d di U U dg is in REG . Notice that region d is disconnected and has a hole. Let us now consider two arbitrary regions a and 6 in REG . Let region a be related to region b through a cardinal direction relation . a is north of b . Region b will be called the reference region . the region which the relation refers to while region will be called the primary region . the region for which the relation is introduced . The axes forming the minimum bounding box of the reference region b divide the space into 9 areas which we call tiles Fig. 1a . The peripheral tiles correspond to the eight cardinal direction relations south southwest west northwest north northeast east and southeast. These tiles will be denoted by 5 b 5W b W b NW b N b NE b E b and SE b respectively. The central area corresponds to the region s minimum bounding box and is denoted by 5 b . By definition each one of these tiles includes the parts of the axes forming it. The union of all 9 tiles is If a primary region a is included in the set-theoretic sense in tile 5 b of some reference region b Fig. 1b then we say that a is south of b and we write a Sb. Similarly we can define southwest SW west W northwest NW north N northeast NE east E southeast SE and bounding box B relations. If a primary region lies partly in the area and partly in the area 5 b of some reference region b Fig. 1c then we say that a is partly northeast and partly east ofb and we write a N E E b. The general definition of a cardinal direction relation in our framework is as follows. Definition 1. A cardinal direction relation is an expression Rk where a k ft Rx . Rk e B S SW W NW N NE E SE and c Rif Rj for every i j such that 1 i j k and i j. A cardinal direction relation Rk is called single-tile if k 1 otherwise it is called multi-tile. Let a and b be two regions in REG . Single-tile cardinal