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
