ISPRS, Vol.34, Part 2W2, "Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
175 
Table 5: Spatial relations between areas and lines 
f d 
-Ili!''''' 
a b 
disjoint 
Table 6: Topological relations between points and lines 
fc 
ayj b 
a r\b 
a\b 
alb 
a Ah 
Semantic 
© 
-0 
0 
-0 
-0 
-0 
disjoint 
-0 
-0 
-0 
0 
■0 
contain 
« 
■0 
-0 
0 
-0 
-.0 
contained 
Table 7: Spatial relations between points and areas 
fc 
a uj b 
a r\b 
a\b 
alb 
a Ah 
Semantic 
-0 
0 
-0 
-0 
-0 
disjoint 
-0 
-0 
-0 
0 
-0 
contain 
• 
-0 
-0 
0 
-0 
-0 
contained 
5.4 Topological relations between complex objects 
The description of spatial relations among loop line objects has 
been a difficult task and there is a lack of efficient solution. But 
this kind of relations may also be distinguished with the new 
approach. In order to describe this kind of relations, the value 
of combination of dimension and connected number of (a 0b) 
as well as the value of connected number of (a v 6b v ) is 
employed. The result is shown in Table 8. 
Table 8: Topological relations between loop line objects 
(Fd,F„) 
au b 
ar\h 
a\b 
alb 
a Ah 
Semantic 
Fn 
a 1 w h 1 ' 
a r r\ b 1 ' 
! 
a 1 ' / b‘ 
a 1 ' A h 1 ' 
<ci 
U,2) 
(-/.-0 
O, h 
0,1) 
0,2) 
disjoint 
3 
/ 
2 
2 
4 
0,1) 
(0,1) 
O■ 1) 
(U) 
0,2) 
interior meet 
3 
1 
2 
2 
4 
0,i) 
(0,1) 
0,1) 
0,1) 
0,2) 
3 
2 
2 
2 
4 
<:?>£> 
O.l) 
(0,2) 
0,2) 
0,2) 
(/,4) 
5 
3 
3 
3 
6 
QD 
0,1) 
(0,2) 
0,2) 
0,2) 
OA) 
5 
5 
4 
4 
8 
CO 
0. h 
(/. /) 
0,1) 
(/. 1) 
(1. 2) 
overlap 
3 
2 
2 
2 
4 
o 
(>-U) 
(’-¡.I) 
(-A/) 
(-/./) 
(-1.1) 
equal 
2 
2 
-/ 
-/ 
-1 
Using the new approach without other extension, the distinction 
of complex relations between area objects can also be realised, 
including various ‘inside’ relations. They are illustrated in 
Figure 5. 
(a) 
(b) 
(c) 
(d) 
Figure 5: Topological relations between area objects with 
complex shapes 
6. METRIC RELATIONS WITH THE SPATIAL ALGEBRA 
Statistically speaking, ‘disjoint 1 relations prevail over other 
relations. This kind of relations can, in fact, be considered as a 
type of spatial order relations for the detailed description. In 
most of existing models, there is no further distinction of 
'disjoint' relation except for Chen et al. (20001). In fact, higher 
resolution of 'disjoint' relation will be helpful for efficient 
extraction of the desired spatial information from geographical 
spatial databases. The 'disjoint' relation could be classified into 
K-order neighbour relation according to the number of Voronoi 
regions between two objects. Such K-order neighbour relation 
is shown in Table 8. The operator to get the number for K is 
called neighbour order denoted by l/', which indicates at least 
how many Voronoi regions of objects an object reaches 
another one.