International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
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Figure 10 Swap Operator 
4. [Extending the Terrain Surface 
We have re-formulated the traditional incremental algorithm for 
creating a TIN model. In order to add extra features to our TIN, 
a topologically connected TIN model is built using Euler 
Operators, and then an additional operator is used to modify and 
extend it. The operator “Make Edge Hole Kill Face" (MEHKF) 
which has exactly the same program code as “MEF” (Tse & 
Gold, 2001) is used to create bridges or tunnels. A TIN is built 
up and two unconnected triangles (Triangles A & B in fig 11) 
on the TIN surface are selected. Their edges are running in an 
anti-clockwise order. 
  
  
  
  
Figure 11 Two unconnected triangles 
Fig 12 shows the result of the first step using “MEHKF” to 
create a hole, a face and an edge between these two 
unconnected triangles. The two triangles concerned are deleted, 
an edge is formed between the two triangles, and a new face is 
formed that loops through each of the deleted triangles and both 
sides of the new edge (Tse & Gold, 2002). Edge "NI" is the 
new edge created between two unconnected triangles A and B. 
The connection of the edges will be al => a2=>a3 =>N1 =>b3 
=>b2 =>b1 =>N1 =>al (Face 1). The connectivity of edges in 
face 1 is in an anti-clockwise order. 
  
  
  
  
  
  
  
  
: New Edges 
; The edges 
I — —-P 
1 Face 1 
1 
! Face 1 
I 
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I 
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Figure 12 Make Hole Edge Kill Face Operator 
The *MEF" operator is used to split the face inside the tunnel 
shown in fig 13. A new edge “N2” is created to split the face 
into two pieces and one new face is made, and the connectivity 
of the edges are al =>N2 =>b2 => N1=> al (Face 2). Face | is 
split into two pieces using *MEF" again in fig 14. One face 
“Face 3” and edge “N3” are created. There are three rectangular 
faces inside the hole: face 1, 2 and 3, therefore three more 
“MEF” operators are used to split them into triangles. We have 
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