International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
6.1 Surface normal calculation for contour data 
It is necessary to use all available information from maps that 
could improve terrain surface reconstruction. Some of these 
information are given implicitly by contours (Schneider, 
1998). This information could be generated by using rules 
applied during map making process and by respecting the very 
nature of contours. Some of these are: limited terrain height in 
areas bounded by contour(s) of given height(s), existence of 
terrain form lines in areas where set of contours abruptly 
change direction, maximum slope direction is perpendicular on 
contour segments, etc. 
Surflng’s algorithm for building high quality DTM is based on 
TIN and bicubic Bezier’s surface patches over triangles. No 
special data filtering is currently supported, i.e. calculated 
terrain surface interpolates data points. Therefore, this method 
is very sensitive to distribution of data points and their height 
values, so this must be taken into consideration. Also, 
estimation of surface normals at these points is highly critical, 
as this has a great influence on calculated terrain surface. 
Generally, surface uses Akima’s method for estimating surface 
normals, by averaging surface normals of all TIN triangles 
joining at given data point. However, this method is not 
suitable for contour points. Another approach is used. It is 
based on assumption that direction of steepest slope is 
perpendicular to the contour. Slope is estimated by calculating 
profile containing given contour point in the direction of the 
steepest slope (Figure 4).. 
> 
Figure 4. Calculation of surface normals for contour points 
  
Profile is calculated using intersection between neighboring 
contours and the profile line. Slope could be estimated by 
using smooth curve set through given point and all intersecting 
points, or simply averaging slopes for upper and lower contour 
profile intersections. The similar approach is proposed in 
(Schneider, 1998). This method provides much better results 
for contour data than original Akima's method 
6.2 Extraction of specific geomorphological elements from 
contour data 
The second problem that is typical for TIN based terrain 
surface reconstruction using contour data is related to regions 
with flat triangles. It is well known, that these reagions are 
actually implicating that there are some special terrain forms 
(local minimum and maximum, ridge, drainage, saddle). There 
are several published algorithms for automatic extraction of 
specific geomorphological elements using contour data and 
TIN (Auman 1990; Heitzinger, 2001; Peng 1996; Schneider, 
1998; Thibault, 2000). Some of these algorithms based on 
vector data processing techiques are implemented within 
Surfing. 
The most promising and also simple for implementation is the 
one based on skeleton construction, i.e. Medial Axis transform 
(Thibault, 2000). This approach is based on Delaunay 
triangulation (Figure 5, green lines) and it's dual Voronoi 
diagram (Figure 5, red lines). Requirement for algorithm is 
that data are well-sampled. This means that all contour 
segments (Figure 5, brown, thick lines) are preserved within 
Delaunay triangulation without special constraints, i.e. the 
result should be conforming Delaunay triangulation. If contour 
data is undersampled, additional densification of contour 
points (splitting of sontour segments) is necessary. Ridge, 
drainage and saddle lines are constituting skeleton (Thibault, 
2000). Problem of finding skeleton is reduced to local test of 
each Voronoi/Delaunay edge pairs. For each pair, it is either 
that Voronoi edge is part of the skeleton (Figure 5, red thick 
lines) or Delaunay edge is part of the crust (Figure 5, brown 
thick lines), but not both. Criterium is the following: if there is 
circle set through Delaunay edge vertices that does not contain 
any Voronoi vertices then Delaunay edge is part of the crust 
(Figure 5, green, dotted circle case). Otherwise, Voronoi edge 
is part of the skeleton (Figure 5, blue circle case). 
  
Figure 5. Criterium for extracting skeleton (red) and crust 
(brown) 
The results of the algorithm implemented within SurfIng are 
shown on Figure 6, where extracted terrain lines are shown in 
red. 
Figure 6. Detected structure lines (red) and digitized contours 
(brown) 
Heights for extracted line points are calculated by linear 
interpolation between points where given line crosses the 
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