DH UN << (D 
m MM 
Te UC 
P$ MEETS-PART ! 
iff (P$ MEETS ]) AND 
(BOUNDARY(P8) OVERLAPS | ) 
   
MEETS-0 MEETS-1 
Figrue 4. Two specific cases of the MEETS relation. 
pg1 MEETS-0 pg2 
iff (pg1 MEETS pg2) AND 
(BOUNDARY(pg1) MEETS 
BOUNDARY(p¢2)) 
pg1 MEETS-1 pg2 
‘sa 3b 4a 4b iff (pel MEETS pg2) AND 
(BOUNDARY(pg1) OVERLAPS 
BOUNDARY(pe2)) 
  
Figure 3. Topological relations between a line and a polygon. 
The relation 3a is described by the operator E E 
6. Spatial queries 
S COS T SK el )AND Suppose that a spatial database consists of three 
(BOUNDARY(3) OVERLAPS 1 ) spatial relations: 
: : Towns(Pt:POINT, 
and the relation 3b is detected by the operator Name: TEXT, 
Population:INTEGER) 
P$ BOUND-COVERS | 
iff (pg COVERS 1) AND Roads(Li:LINE, 
(BOUNDARY(/8) COVERS 1) Class:INTEGER, 
No:INTEGER) 
The relations in group 4 can be respectively 
distinguished by the operators ENTERS and Provinces(Pg:POLYGON, 
PASSING defined as Name: TEXT, 
Population:INTEGER) 
l ENTERS P8 : 
iff (Pg OVERLAPS 1) AND Here, POINT, LINE and POLYGON are spatial data 
(P$ CONTAINS SP()) OR pres 
GS CONTAINS EPOD Query 1: Find towns inside province B passed by 
second class roads. 
I PASSING pg 
iff (PS OVERLAPS /) AND Roads2 «- *(a:Roads,b:Provinces) 
(P8 DISJOINT SP(]))) AND WHERE[(a.Class = 2) AND 
(P$ DISJOINT EP()) (b.Name = 'B') AND 
((b.Pg OVERLAPS a.Li) OR 
Example 7: Operators for checking topological (b.Pg COVERS a.Li) OR 
relations between two polygons pgl and pg2. (b.Pg CONTAINS a.Li))] 
All the topological relations in table 1 are defined as [Lia li Noa Nok 
fund 1 
undamental operators for two polygons. Two Towns1 <- *(a:Towns,b:Provinces) 
polygons, however, can meet, cover, or overlap in WHERE[(b.Name = 'B') AND 
different ways. These specific relationships can be (b.Pg CONTAINS a.Pt)] 
distinguished by combinations of fundamental 
operators and other predefined operators and [Pt:a. Pt, Name:a.Name, 
functions. The following is the meets-0 and meets-1 Population:a.Population]; 
examples (Figure 4). 
Towns2 <- *(a:Towns1,b:Roads2) 
WHERE[b.Li COVERS a.Pt] 
[Pt:a.Pt,Name:a.Name, 
Population:a.Population]; 
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