The usual interpolation rules can all be written as 
z*(x,y) = 3 8121 (5) 
because all these rules estimate z* as a linear combination of the 
sample points. 
With respect to the unknown true value z at the location (x,y), the 
error of the interpolated height is 
e(x,y) = z-z* *Z- E 815 (6) 
and the standard deviation of the interpolation error og can be 
computed for the terrain using the variogram model in equation (2). 
The standard deviation is expressed in units of the constant k. It is 
assumed that the errorfree sample points are equally spaced with the 
spacing L and that intermediate points have to be interpolated. 
To demonstrate the accuracy estimation procedure the accuracy of in- 
terpolated heights is computed for prediction interpolation. 
For interpolation in profiles it holds 
cg?mean . ,8,.1 2 
ER AUTRE pie) > 
This accuracy result is plotted in Figure 1. 
The Figure relates the sample spacing - expressed in units of L - to 
the accuracy of interpolation - expressed in units of k - for diffe- 
rent values of the terrain characteristic parameter B. 
Further details are described and other interpolation procedures in- 
vestigated in (Frederiksen, Jacobi and Kubik, 1983). 
When planning the sample spacing, one enters the Figure with the re- 
quired accuracy of interpolation along the vertical axis, draws a 
horizontal line to the proper line for 8 and reads off the value L 
from the horizontal axis. 
In order to find the accuracy for a given sample spacing, the Figure 
is used reversely. 
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SZ