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
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.
