„15 = 
In Sweden, Nordisk ADB has developed a DTM [1-5], [2-3] in which the 
interpolation in each area bounded by terrain lines is performed along the shortest 
line through the interpolated point which connects two different lines. Along 
this shortest line, the interpolation is linear. 
Schult [64] describes a method for the computation of the heights at the 
nodes of a regular grid from contour lines. In this method, the two grid lines 
on which a node is located are intersected with the two nearest contour lines. 
The height at the node is then computed as the weighted mean of the heights of the 
four intersected points. The weights attached to these heights are inversely 
proportional to the distances. In many instances, three of these intersections 
will lie on the same contour line while the fourth one will lie on the second line. 
mat should make the interpolation somewhat less accurate than the above inter- 
polations. 
Finally, Baetslé [17] has developed an interpolation method which fits 
under the present heading. The method serves to interpolate in an area enclosed 
by a traverse, which is a string of measured points. The height of an interpolated 
point is a weighted mean of the heights of the traverse points. The weight 
attached to the height of a traverse point is the sum of the tangents of half the 
angles under which the two adjoining traverse sides are observed, divided by the 
distance from interpolated point to traverse point. This weighting produces a 
linear interpolation on the traverse sides and, in this way, produces continuity 
with any surrounding interpolation areas. Reference heights in the interior of 
the area can be accommodated also. Their weights are simply the reciprocals of 
their distances. Baetslé shows that in the case of an enclosed triangle the weights 
are the barycentric coordinates of the interpolated point. This method will be 
most useful, because least laborious, if the total interpolation region is sub- 
divided into small areas enclosed by polygons with few sides. If the total area is 
enclosed by one polygon, there is little reason to enforce linear interpolation on 
the sides of this polygon and one might as well make all weights equal to the 
SEES of the distances. That reduces the method to a simple moving surface 
method. 
9. Construction of profiles 
  
Profiles are of interest especially for volume computations, as for 
instance in road design and open pit mining. Discreet points on a profile can be 
obtained either by measuring in a photogrammetric model or by intersecting the 
vertical plane of the profile with grid lines, contour lines, or any other 
characteristic lines. Almost generally, straight line connections between the 
discreet points are considered to give a sufficiently accurate terrain representa- 
tion. The small local positive and negative errors which this can produce will 
tend to cancel each other in the summation for the volume computation. 
Only two papers deal with a more complicated interpolation. Miller and 
Laflamme [61], in the first published paper on digital terrain models, give here 
their only mathematical formulation. They suggest connecting each two consecutive 
points by a third-degree polynomial and they give also the formula for the area 
under this curve. Killian and Meiss]l [40] use cubic spline curves, but do not 
give detailed formulas. They need the greater accuracy because their profiles are 
along fall lines and are used for the construction of additional contour lines 
between existing ones. 
10. Construction of contour lines 
  
10.1 Determination of discreet points 
The construction of a contour line requires the availability of a 
sufficiently large number of its points, given by their planimetric coordinates. 
These points can be measured sequentially by following the contour line in a photo- 
grammetric model. Recording can here take place at equal time or, perhaps, length 
intervals.