Volume computation has to start from a grid of height 
differences and from different line information (limit of the 
area of interest, intersection line, break lines, form lines, DEM 
border lines). Fig. 4.1 shows the initial lines for a small part of 
a difference model. 
The lines build up irregular polygons. For each grid mesh a 
triangular network is derived from the irregular polygons (see 
fig. 4.2). Thus, the volume computation can be reduced to 
triangular prisms which have to be related to either cutting or 
filling, depending on the sign of the height differences. 
5. GENERAL VIEW OF THE COMBINATION 
AND INTERSECTION METHODS 
The methods used for volume computation shall in the 
following be used as an example for a more general view of 
the arithmetic operations on DEM data. 
5.1 DEM combination 
Building up a difference model from two DEMs is a functional 
DEM computation by using a simple subtraction as a 
combination function. 
Zaiff. = ZDEM1 - ZDEM2 
SCOP.INTERSECT is now extended for the use of any 
mathematical function of the form 
Zfunct. = f( Z1 Z, ) 
The function f is described by the fundamental arithmetic 
operations and by a discrete description of more complex 
functions. 
The functional values Zfynct, are stored in a SCOP model with 
the grid structure of either the Z; or the Z, SCOP model and 
the line information of both models. 
  
SCOP model 1 SCOP model 2 
L J 
  
functional model 
Fig. 5: Data structure of the functional model 
  
880 
Each point of the functional model needs its values Z; and Z, 
before performing the computation of the functional Z value. 
In most cases only one of the Z values is directly stored either 
in the Z4 or in the Z; model. The corresponding Z value of the 
other model is automatically determined by an interpolation 
within the respective grid mesh. 
5.2 DEM Intersection 
Volume computation is a special case of DEM intersection for 
which the DEM is a difference model. It is intersected with 
areas of interest. Each area of interest is subdivided by the 
isolines of height difference zero into areas of cutting and 
filling. The intersection results are volumes of cutting and 
filling. 
In general the DEM can be any SCOP model (DEM, slope 
model or any functional model). The areas of interest may be 
any polygon areas. And the height difference zero for dividing 
cutting and filling may be replaced by any class limits. 
The intersection classifies the polygon area and computes the 
intersection results which may be classified areas, volumes or 
surfaces. Applications of a DEM intersection are described in 
chapter 7 and in table 1. 
5.3 Polygon Overlays 
In many cases the input data for a functional combination of 
surface data or for an intersection do not exist in form of a 
DEM, but have to be digitized from maps in form of polygon 
areas. Each polygon area has a corresponding value Z. 
Such polygon areas may be converted with 
SCOP.INTERSECT into a SCOP model, and are then available 
for a functional combination with other surface data or for an 
intersection. 
The conversion into a SCOP model is done by overlaying the 
polygon areas with a regular grid. Each grid and polygon point 
is stored with the Z value of the referring polygon area. The 
result is a surface description which consists of adjacent 
horizontal terraces. 
After a conversion of polygon areas into a SCOP model 
SCOP.INTERSECT is able to solve a conventional polygon 
overlay by intersecting a second set of polygon areas with the 
SCOP model. 
6. OTHER APPLICATIONS FOR A DEM 
COMBINATION 
The two following examples show how other arithmetic or 
boolean operations can be used for a combination of digital 
elevation models. 
6.1 Integration of planned structures into a DEM 
A simple boolean function can be used for the integration of 
planned terrain surfaces (roads, railways, embankments etc.) 
into a DEM of the existing terrain. 
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