ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
174 
listed as follows: 
(1) Assumption 1: Spatial objects are embedded in 
Euclidean space; and 
(2) Assumption 2: A spatial object has only one 
connected component. 
5.2 Topological relations between simple area and line 
objects 
The topological relations between simple area objects are 
illustrated in Table 3. Table 3(a) list the use of content as the 
value of set operations. In Table 3(b), dimension is used and 
further discrimination between contain/cover and 
contained/covered can then be made. Table 3(c) illustrated the 
further discrimination of contain/cover and contained/covered 
with the general model. 
Table 3: Topological relations between simple solid area objects 
(a) Basic relations between solid area by empty/non-empty 
fc 
a<jb 
anh 
a\h 
alb 
а A h 
Semantic 
Ql 
-0 
0 
-0 
-0 
-0 
disjoint 
a © 
-0 
-0 
■0 
■0 
-0 
meet / overlap 
-0 
-0 
-0 
0 
-0 
contain / cover 
-0 
-0 
0 
■0 
■0 
contained / covered 
• 
-0 
■0 
0 
0 
0 
equal 
(b) further discrimination of mect/ovcrlap with the simple model by dimensions 
ÏD 
a\jb 
ar\h 
a\ b 
alb 
a Ah 
Semantic 
2 
0 
2 
2 
2 
0-D meet 
Cl© 
2 
I 
2 
2 
2 
1-D meet 
CD® 
2 
2 
2 
2 
2 
Overlap 
(c) further discrimination of conlain/cover and contained/covered with the general model 
Fc 
a^jb 
ar\b 
a\b 
alb 
a Ah 
a'\j b' 
a 1 о b v 
a v \b v 
ct / h' 
a 1 A h 1 
-0 
-0 
-0 
0 
-0 
cover 
X 
-0 
-0 
■0 
0 
-0 
-0 
-0 
-0 
0 
-0 
contain 
■0 
0 
-0 
0 
-0 
0 
-0 
0 
-0 
-0 
-0 
-0 
0 
-0 
-0 
-0 
-0 
0 
■0 
-0 
ШЮЁ 
■0 
0 
0 
-0 
-.0 
Table 4. Topological relations between simple lines 
(a) Level I : basic relations with the simple model by empty/non-empty 
fo 
a Kj b 
a n h 
a\b 
alb 
а Д b 
Semantic 
1 1 
>‘l 
-J 
>-/ 
>-/ 
>-/ 
Disjoint 
Dh 
>-/ 
0 
>-/ 
>-/ 
-/ 
meet / intersect 
>-/ 
l 
>0 
0 
Overlap 
>-/ 
'•1 
>-/ 
-/ 
>-/ 
Contain 
~— 
>-/ 
>-/ 
-1 
>-l 
>-/ 
Contained 
— 
>-/ 
>-/ 
-/ 
-/ 
-/ 
Equal 
(b) Level 2: the description of mcct/intcrsect with the general model 
The topological relations between simple lines are illustrated in 
Table 4 in the matrix form with multiple operators. Here, in 
order to distinguish the 'meet' and 'intersect' relations between 
lines, the value of connected components of (a v 6 b v ) is used. 
In fact, different typed of "meet' relations can also be 
distinguished by this operation. It is noted that this kind of 
relations listed in Table 4b is very difficult to be distinguished by 
other models. 
5.3 Topological relations between simple objects with 
different dimensions 
Topological relations between simple objects with different 
dimensions here mainly refer to those between areas and lines, 
areas and points and lines with points. In fact, the distinction of 
relations between lines and areas can be realised without the 
aid of such notions as interior, exterior and boundary-. This is 
an important characteristic of this model, which makes its 
realisation easy and practical in either raster space or rector 
space. 
These relations are illustrated in Tables 5 to 7.