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Fig. 8: Setting up pairs of screen elements 
in the fourth quadrant 
When we look at the arrows, we see that they all obey the same rotation (from 
left to right) with respect to the viewing point. We will use this feature 
later. 
Now we have filled the whole DTM with screen elements. Unnecessary doubles 
are contained merely in the mesh-strips starting from the viewing point 
following the four directions of wind. No problems will arise if we handle 
this special case when initializing our index loops. 
As we have stated earlier, we don't want to compare individual screen ele- 
ments with one another. The following question becomes so more and more 
pressing: When putting up any one of the screen elements, what really is its 
counterpart deciding its visibility? 
4, THE HORIZON 
For this purpose we use the perspective image of the highest contour of all 
screen elements already set up. This contour serves as horizon: It hides 
Loue» objects, but an object appearing higher modifies its shape (fig. 9). 
This horizon will be called hiding polygon later on. 
What happens when we set up a pair of screen elements? 
At first normalized image coordinates of the upper two corners of the element 
are computed. Then this unique polygon side is searched for, the starting 
point belongs to. It is found, if this point is projected exactly above or 
beneath this side. Since the edges of screen elements appear to run from left 
to right the hiding polygon is then followed to the right too, until the 
image of this edge crosses the polygon or it ends. An intersection point is 
inserted into the hiding polygon as soon as it occurs. Points of the polygon 
bypassed beneath the edge are discarded from the hiding polygon. The point 
ending the edge ist inserted if it lies above the polygon. The hiding polygon 
requires therefore a highly dynamical data structure to ensure efficient be- 
haviour of the whole algorithm. The second member of the screen pair is hand- 
led similarly. It should be noted, that there may occur only an even number 
of intersections when setting up one screen pair. 
The screen edges respectively that parts of screen edges, which appear above 
the hiding polygon are output to a graphic device or written to a file as 
visible DTM: The normalized image coordinates are transformed into a ficti- 
tious user-camera, defined by inner orientation. This allows different inner- 
orientations for different - simultaneously serviced - graphic output devices. 
The complementary parts may be output too, but marked as invisible (e.g. as 
dashed line).