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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
could be traced directly. In the following, a method developed 
by Aumann et al. (1991) is described. 
Firstly, it is necessary to obtain an optimum triangulated 
irregular network (TIN) of contours. Since the contours in form 
of ‘polyline’ are the primary data only (Figure 2), it must be 
taken care of intersections between contours and triangle edges. 
Such an optimum TIN could be obtained by constrained 
Delaunay triangulation. However, it is hardly to gain a 
satisfactory result in this case. Horizontal triangles of which 
vertices have same height may occur in the TIN. They lead to 
an incorrect description of terrain surface from the aspect of 
modeling. On the other hand, they are the important clues, i.e. 
they mark the regions of skeleton lines, because they occur 
where the land forms chance considerably. The areas of 
horizontal triangles are called critical areas. Skeleton lines are 
derived in the critical areas (Figure 3). 
Figure 2. Contours 
Figure 3. Critical areas of horizontal triangles in TIN 
Figure 4. Steepest slope vectors at contour points 
619 
Types of the skeleton lines to be derived are determined in 
accordance with the steepest slope vectors at contour points 
(Figure 4). A steepest slope vector at a contour point is assumed 
as the bisector unit vector. It means the bisector between two 
consecutive contour segments at the contour point. 
It is formerly decided that the bisectors are determined whether 
lower or higher side of the contours. All bisectors are computed 
at the same side of the contours. For instance, if all the bisectors 
are computed at lower sides and they indicate each other in a 
critical area, the skeleton line to be derived in that area is a 
valley line. 
Skeleton lines are derived by tracing process. It starts with 
selection of the beginning point of the skeleton line to be 
derived. A point on the highest contour in the critical area of 
horizontal triangles is selected as the beginning point, if the 
skeleton line to be derived is a valley line. Otherwise, i.e. if it is 
a ridge line, the lowest point in the critical area is selected as 
the beginning point. A beginning point is the one that yields the 
longest steepest slope line in the critical area. After that, 
beginning from this point, a series of vector are computed 
consecutively. These vectors are called skeleton line vectors. 
Length and direction of a skeleton line vector is one unit and 
steepest slope direction respectively. The value of one unit is 
calculated with the following formula. 
ST, z (lx MP (1) 
Here, MP is the arithmetic mean of all contour segments 
(Aumann, 1994). Direction of a skeleton line vector is 
computed with the followings: 
e Directions of the steepest slope vectors at the vertices 
of the triangle containing the beginning point of the 
skeleton line vector 
e x andy components of the steepest slope vector 
e x and y components of the skeleton line vector 
direction by means of linear interpolation with the x 
and y components of the steepest slope vectors at the 
vertices of the triangle (Figure 5). 
Figure 5. Components (x, y) of the steepest slope vectors 
Tracing process for a skeleton line is finished when it is reached 
to end of the critical region (Figure 6). Finally, it is assigned 
heights to the skeleton line points by means of linear 
interpolation using the related contour elevations. A