i 
I 
is 
| 
3 
" 
  
  
   
     
    
   
  
      
   
  
   
  
   
   
  
  
193515453 1401931 1 44 11-3:119:5.9:5-9/5 1515.99 :.917. 703. 2009 
1111113111l1331732 1558351955] 5552702227777 
GT DELIS EIUS isst 
11/11 LkAQ)T 124014 s s s[s]s 5 sis 5 31:202.2. 21 
1111111Y11333131111,55[535 59555 77 717 
1254313540333 u5[S 5555555 77 7|? 
PLAILLELid MNAdgS. 51355 9.915 7 Ty 
1111311111131171 55555555517 73 
Drag ra 5555555557 13 
143.1,53,1:313 1:34 555553555511 7.7 
6646611111 5555355555 2057293 
666666 6.1678 «5555/55 5 2°2 2222 
66666666 444 4's 55 2222222 
666666 «ce 4444 2/2 222227272 
566666 6 4444 4444 2232222222 
6 6 6 6 6 4 4 € 4 444 2222232222 
6 6 C6666J4444 44 2 Hia ss 
66 666640464 44 229272 32 2 2? 
6 6 666614 4 4 4 332 22222232 
6 6UpTET V. 6.66€ 6,4 À 4 3 8.3'2.2,2-2:2:2,212 
66666666444 4 3339] 1 2^ t 
6 666666 6148 4 4 3333343122222 
666666666444 33.3-3:13. 33.312,22 
66€ 666 6/8 844 333333333372 
666666688888 se 
66666 888888 35.345133..3..31343. 3.3.3 
666688888898 3399333333 3.3 
6688888882868 J 3333335393333 
670888888888 | 3533434333 303.3.3,2 
88888888888 ; 33333333333 
  
€ The constraint edges are represented by 4-paths 
in both arrays. All L-pixels have a unique code in 
the distance array. In the feature array the L-pix- 
els of each edge are cut in half and get the code of 
the nearest P-pixel. 
In this way the constraints are still retained and the 
operation will, however, take place regardless of any 
constraint. That means, the computational time here 
remains as the same as the case that only points are 
triangulated. Figure 1 demonstrates the principle of 
the encoding method. 
23 Deriving a TIN from OVD 
Once the QVD of the given sets of points and lines is 
available, a TIN can be derived from it by using a suit- 
able operator. Two strategies can be applied to for- 
ming the TIN: 
€ constituting triangular edges individually by locat- 
ing Voronoi edges; 
€ constituting triangles individually by locating Vo- 
ronoi nodes. 
24211815121110 910111215182120171411 8 7 6 7 8111416151413121314 
2320171411 8 7 6 7 81114172019161310 7 4 3 4 7101315121110 91011 
2219161310 7 4 3 4 710131619181512 9 6 3 O 3 6 9121411 8°7 6 2^8 
21181512 9 6 3 0 3 6 912151821181512 1 4 3 4 110131310 7 4 3(4/7 
22191613107 4 3 4 710131619221916 1 17 6 7 8111412 9 6 3 0 3 6 
2320171411 8 7:6 7 8111417202320 1 11110 9101112151310 7 4 3 4 7 
24211815121110 9101112151821 ! ! 115141312131415161411 ! ! 6 7 8 
25221916151413121314151619 ! 12219181716151617181815 t 110 91011 
262320191817161516171819 ! 12623222120191819202119 1! 11413121314 
2724232221201918192021 ! 1302726252423222122232322 1181716151617 
24232221222322212223 ! 1343130292827262524252626 | 1201918181920 
212019181920212225 ! 1303130313231302928272829 ! 118171615161718 
1817161516171827 1 1262928272829303132313031 t 11615141312131415 
151413121314 ! t 122252625242526272829303132 11815121110 9101112 
121110 910 ! 11518212423222122232425262728 ! 11371411 8 
11.8 L6. 11114172021201918192021222324 ! 119161310 7 
963036 9121516151413121314151619 1242219161310 7 
107 43 4 710131615121110 910111215 ! 1212019171411 8 
7.6 7. 811 
4 3 4 710 
107^«4-3 4 710131619181716151617181920 t 121181512 9 6 3 0 3 6 9 
4 3 4 710 
76 7 811 
11 8 7 6-7 81114171411 8 7-6 7 811 ! 1191817161515121110 9101112 
121110 910111215161310 7 4 
15141312131415161512 9 6 3 
1817161516171819161310 7 4 
2120191819202119161411 8 7 
242322212223211815121110 9 
27262524252320171411 8 7 6 
30292827252219161310 7 3 
333230272421181512 9 6 0 
36343128252219161310 7 3 
38353229262320171411 8 6 
~N a wa 
  
(a) (b) 
  
(c) 
  
  
Figure 1. Principle of the encoding method for crea- 
ting the QVD of points and lines. 
(a) The QVD - the feature array after the DT; 
(b) The distance array after the DT using the cham- 
fer(3,4) distance; 
(c) The constrained Delaunay triangulation and the 
bounded Voronoi diagram. 
In the QVD a Voronoi edge can be of one of the fol- 
lowing three shapes: (a) a horizontal line; (b) a verti- 
cal line; (c) a terraced line (cf. Figure 2). Therefore, 
an operator which is suitable for edge detection can 
be used to locate the triangular edges in the QVD. 
i1 1411 1°1 112 2 2 2 
1 1 111 1 1:1 1]252 2 2 
1:1 3303 1:31 1:1 1/2 2:2 2 
2.222272 1 1 1l2 2:2 2 
222222 1.1.1]2. 2 2 2 
22 2:2 2.2 11 11222 2 
  
(3) (b) (c) 
Figure 2. Voronoi edges in the QVD. 
The cases where a Voronoi node can appear in the 
QVD are illustrated in Figure 3. In order to locate a 
Voronoi node in the QVD, an operator of 2x2 pixels 
(cf. Figure 4) is used. Positioning this operator on a 
pixel in the QVD, three neighbours of the pixel are in- 
volved in it. Hence, it is called the N3-operator. Using 
it, the procedure for locating Voronoi nodes in the 
568 
3.47 1 11916151413121314141312131415 
0 3 6 1211815121110 91011121515161718 
3 4 1 120171411 8 7 6 7 8111417192021 
6 1 11619161310 7 4 3 4 7101316192224 
| 11215181512 9 6 3 0 3 6 91215182124 
1.8111417161310 7 4 3 4 7101316192225 
4 7101316171411 8 7 6 7 8111417202326 
3 6 912151815121110 91011121518212427 
4 71013161916151413121314151619222528 
7 81114172019181716151617181920232629