ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
23 
1 ••• n disc) - diAB^IBC 
; U d2AB c °d2BC U ••• U 
diAB°°diBC 
¡tween target object B 
ation between target 
:tion relation between 
be deduced from the 
iWbc ). 
ic ) = Nab°°NVVbc U 
» NWbc U Eab^VVbc = 
jects 
her refined according 
C and Y coordinates, 
t B and C (Fig. 5), we 
less or equal to B’s 
ri the given direction 
t less A’s maximum X 
>t less X2)Xc < X2)f the 
target object D and 
ie composition of (N A b 
5CRIPTIONS 
■ations using our 41 
the constraints about 
(Goyal 1999), while 
9 different direction 
er 4I direction matrix 
on combinations that 
i in figure 6. This is 
II which direction tiles’ 
led direction matrixes 
^2,V 3 ,V 4 to mark the 
e object (Fig 6), then 
,V 4 -Vi, and 8 open 
>,V 4 -W, where \A-~N 
int and stretches in N 
to differentiate which 
meets; so that more 
uished. For example, 
ition relations can be 
:rix cannot. 
:e 
% N S 
NE Ip 
N A 
NE % 
N A 
NE 
W A Co J 
E 
w A 
GO 
E 
W A 
O .j 
E 
sw S A 
SE a 
SW 
S A 
SE a 
sw 
S A 
se a 
(a) (b) (c) 
OBJECT AS A REFERENCE 
For the direction relations between spatial objects with line 
object as a reference, If the reference object is parallel with to X 
or Y coordinate, it is a special case of the direction relations 
between spatial objects with area object as a reference (Fig 9). 
Thus the minimum bounding rectangles of reference object 
reduced to a line. We still use Equ. 1-9 to test the primary 
directions between objects. At this time N A , S A , or E A , W A are 
reduced to open lines. 
N a 
NE 
W A 
r N 
R 
sw 
S A 
se a 
(d) 
Fig.7 configurations that cannot be distinguished with 4- 
intersection directions mixes 
^B-NS 
R-B-WE 
ßnFj - N 
B^V 4 -S 
\SnF, -W 
BnV 4 -W 
B r\V 2 - N 
B r\V 3 - S 
Bc\V 2 -E 
BnV 3 -E 
(9) 
(10) 
Rß-AMBR - 
^B-AMBRP 
Br\V\ -V 2 BnV 2 -V 3 
BnV 3 -V 4 BnV 4 -V] 
~ Bc^V x BnV 2 ~ 
_BnV 4 BnV 3 
(11) 
(12) 
NW 
N 
NE 
v, 
v 2 
W 
E 
SW 
s 
SE 
NW 1 
1 NE 
v 3 
• 
W ( 
] E 
V 4 
SW 5 
SE 
(b) 
NW 
N 
NE 
v, 
F 
W 
U 
r 
SW 
s 
SE 
(c) 
NW > 
V 3 
1 NE 
W ( 
V 4 
SW 5 
SE 
(f) 
NW 
N 
.NE 
w 
\ 
E 
sw 
S 
SE 
(g) 
NW 
\NE 
w 
\ 
sw 
s 
SE 
(¡) 
Fig.9 8 directions model with line object as reference 
5 DIRECTION RELATION DESCRIPTIONS WITH POINT 
OBJECT AS A REFERENCE 
For the direction relations between spatial objects with point 
object as a reference, it is a special case of the direction 
relations between spatial objects with area object as a reference 
(Fig 8). In this way, the minimum bounding rectangles of 
reference object reduced to a point. We still use Equ. 1-9 to test 
into which direction tile the target object falls. At this time N A , E A , 
S A , W A are reduced to open lines. 
If the reference object is parallel with X coordinate, the detailed 
direction matrix is: 
^3 
Ce 
1 
£ 
II 
~Bnï\ 
-N 
BnV 2 
-N 
BnV^ 
-S 
BnV 2 
-S 
(8) 
R-b-we - 
[Br\V x 
-W 
BnV 2 
-E] 
(9) 
R B-AMBRI 
= [SnK, 
BnV } - 
F 
BnV 2 ] 
(10) 
If the reference object is parallel with Y coordinate, the detailed 
direction matrix is: 
B-WE - 
B n V 3 - W 
BnV 4 -W 
B r\V 3 -E 
BnV 4 -E 
(11) 
B-NS = 
BnV 3 -N 
Bn V 4 -S] 
(12) 
B-AMBRP ~[ßn\V 3 
BnV 3 - V 4 
ßnK 4 ] 
(13) 
Fig.8 8 directions model with point object as reference 
So detailed direction matrix is: 
RB-NSWE - 
R-b-ambrp = 
Br^O-N 
Br\0-W 
ßnö 
BnO-S 
Br\0-E 
(6) 
(7) 
6 THE DIRECTION RELATION DESCRIPTION WITH LINE 
Otherwise, the detailed direction matrix is Equ.9 -12 
7 Conclusions and further work 
Topological, direction, and distance these three spatial relations 
are not entirely independent each other, there exist certain 
relations between them. Egenhofer (Egenhofer, 1994) pointed