International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
4.3 In Triangular Node (T) 
The spherical object within a triangle can be classified into 4 
categories at next level according to their locations. They are 
defined as follows (shown as Figure 3): 
« [n Sub-triangle: The object is completely within a 
sub-triangle (expressed as S;(i=0,1,2,3) , totally 4). 
* Edge-neighbour: The object covers two edge-neighbour 
sub-triangles (expressed as Eg; (i=1,2,3), totally 3). 
* Angle-neighbours: The object covers two or more 
angle-neighbour sub-triangles which have one common 
vertex (expressed as Aoi», A023s A013» totally 3). 
* NO-neighbour (Objects): The object traverses the four 
sub-triangles. It is O Node and the pointer which point to 
the object is stored in this node. It is expressed as Oi 
(i=1,2,...,n). 
  
  
Fig.3 Sub-/ Nodes categories from in-triangle and their 
representations 
4.4 Edge-neighbour Node (E) 
Spherical objects, which cover two edge-neighbour 
sub-triangles, can be classified into 3 categories according to 
their locations as follows (Figure 4): 
Edge neighbour: The object covers only two 
edge-neighbour sub-triangles (expressed as Ey Ej, totally 
2) 
* Angle-neighbours: The object covers two or more 
angle-neighbour sub-triangles which have one common 
vertex (expressed as A», totally 1) 
* NO-neighbour (Objects): The object covers the 
no-neighbour sub-triangles, it is O Node which store a 
pointer pointing to this object ( expressed as Oy), 
C) En 
7 LE 
  
Fig.4 Sub-/ Nodes categories from Edge-neighbour 
node and representations 
4.5 Angle-neighbour Triangles Node (A) 
Spherical objects which covers two or more angle-neighbour 
sub-triangles with one common vertex can be classified into 2 
categories according to their locations as follows (shown as 
Figure 5): 
* Angle-neighbours: The object covers two or more 
angle-neighbour sub-triangles with one common vertex 
(expressed as A, totally 1). 
* NO-neighbour (Objects): The object covers no-neighbour 
sub-triangles, it is O Node which stores a pointer pointing 
to this object (expressed as 09. 
(C) An 
T 
  
Fig.5 Sub-/ Ndes categories from Angle-neighbour 
node and representations 
5 DYNAMIC MANIPULATION OF LOCAL SPATIAL 
DATA IN VDTS 
A change in local area may result in the reconstruction of 
topological relationship in a larger area [Gold 1992]. This 
process obstructs the real-time updating of the local spatial data 
and limits applications greatly. In this section, we utilize the 
property of dynamic stability of Voronoi data structure to update 
the individual objects while this process only influences the 
neighbour objects and keeps the relationship structure of other 
objects stability or changeless. 
5.1 Insertion and Deletion of Spatial Objects 
Insertion and deletion of spatial objects are the two main 
dynamic manipulations in local data updating. In this section, 
we discuss how to insert an object to its right node location in 
VTDS in details. 
Each object can be expressed by QTM address codes in VTDS. 
Let the triangular address codes of object U be represented by 
where k is the levels of VTDS data structure; n is the total 
number of address codes in object U in level k («84^ 
Digitals in U * (kz1,2,...) include *0,:517,:*2" and '3' and U 
include digitals *0'-^7' in primitive level 0. We use code f, €, 
and a’ to represent /_Nodes in level i whose object is completely 
within one triangle, covering two edge neighbour triangles, and 
covering more than two angle neighbour triangles which have 
one common vertex respectively. Code E' represents I Nodes in 
level i whose object traverses two edge neighbour triangles in 
different octant triangles. Code A! represents / Nodes in level i 
whose object traverses more than two angle neighbour triangles 
in different octant triangles in which have one common vertex. 
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