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International Archives of the Photogrammetry, Remote Sensing
Definition 3 Degree of Proximity. If the count of linking edge
whose two nodes are on contour lines c; and C» respectively is
Nj», the count of valid nodes of €, to cz is N,,» and the count of
valid nodes of c» to €, is N,>,, then the degree of proximity of c,
to c5 is:
Dict 62) 7 Nu»! Nus
And the degree of proximity of c; to ¢ is:
D(c», cj) * N,»/ Na,
And the degree of proximity of contour pair (c», c;) is:
Dc:;c,-Max(D(c,, c5), D(c», c;))
2.3 Construction of Topological Relation of Contour Lines
By construction of topological relation of contour lines, we
mean the relation should be stored explicitly or can be retrieved
directly. We take contour lines as the nodes of contour tree
structure. After the CDT is constructed on the contour map, this
relation is not difficult to be obtained by traversing the
triangulation network and counting the third type edges. The
node structure corresponding contour line which is used to
record the topological relation in the implementation is as
below. It has three array items which record the contour lines
who have relation Nj, N., and N, with this contour line
respectively. Some pairs of contour lines who are 0-order
proximal may not be detected directly by traversal, e.g. the
contour lines with one elevation interval difference above the
saddle regions. According to previous section, this relation can
be derived from existing ones. Just as in figure 3, figure 3(b) is
the recorded relation table of figure 3(a), and there is not third
type CDT edges between set Node
contour e and f, however we {
can see that it is true that long *HighNeighbor:
Ní(d)-e, Ni(d)-f e and f long *LowNeighbor;
are on the same side of d, long *EquaNeighbor:;
then we have
No(e)=/ }
No(f)=e.
J
(a)
HighNeighbor | LowNeighbor EquaNeighbor
da bc
b d a c
c a b
d ef b
e d f
f d e
H(e)-H(d)=H(d)-H(b)=H(b)-H(a)= AH
H(e)=H(1). H(b)=H(c)
Figure 3 Construction and management of topological relation
of contour lines
1199
and Spatial Information Sciences, Vol XXXV , Part B4. Istanbul 2004
As mentioned above, contour lines are directional. Any
meaningful operation on contour should be based on the
consistency of the direction of contour lines over the entire map.
As a matter of fact the direction is a relative concept on this
point and in order to adjust the contour lines to “left high and
right low”, the default direction setting in this paper, there must
be a reference contour line. The reference contour line either
has different elevation or has the same elevation and has been
adjusted to the default direction. Regarding this property the
algorithm implemented in our research has two stages which
handle different situations sequentially. The detailed algorithm
is demonstrated in figure 4.
Input: contour map and CDT on it. Output: contour map
with the right direction.
I Set a is the contour that need be adjusted. If a is
null then go to II, otherwise go to 2;
2 Set P,, and P, are two sequential nodes on a. If
Pis null then a is passed waiting for process in II,
otherwise go to 3;
3 ParPaz is a CDT object edge. Set P,, and P;> are
two nodes who form triangles with P,P, on either
I side and on other contour lines;
4 If Py; or Py is on contour line ^ and 5 satisfies
No(a) #b(assuming P;;), go to 5, otherwise go back
to 2:
5 If Ni(a)-b and P4, is on the right of B B SOIN.
ı(a)=b and Py; is on the left of Palaz 20:10. 06,
otherwise go back to |;
6 Reverse the order of points chain of a. go back to
step Lt:
| Set a is the contour that need be adjusted. If a is
null then break iteration and exit, otherwise eo to 2:
2 Find two sequential nodes P,, and P,» on a where
exists a third node P,, on a processed contour line ^
forming triangle with edge P,,P,. If find nothing
then go back to 1;
I| 3 Find two sequential nodes P,, and P,; on b where
exist a third node P,,, on a forming triangle with edge
Py; Py. If find nothing then go back to 1;
4 If Py, is on the left (right) of P,P, and Pan IS-0Ù
the left (right) of P,,P,; then set a as processed,
otherwise reverse the order of points chain of a. go
back to II -1.
Figure 4 The two-step process of adjusting contour lines to
default direction
+= d:40
— b:40
Pb; | Pa, §
Figure 5 Adjustment of equal-elevation contour lines’ direction
