ISPRS, Vol.34, Part 2W2, "Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
235 
l, administration, 
in a 3D GIS, we 
CTS 
nt component of 
techniques for 
dely known and 
ions, they were 
in GIS. However 
itions of GIS the 
:ts in computers, 
lis mapping can 
astraction of the 
tation establishs 
ogether with the 
ations. The goal 
1 manage solid 
ie requirements 
wing five criteria 
objects, which 
ted 
ality (accuracy, 
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}ject exactly one 
and to each 
exactly one 
eeded. 
5 for creation, 
messing. 
ire compromises 
ion of storage 
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ree classes can 
adels and solid 
todels are unapt 
3 fund 1999) this 
solid models all 
ither 3D-models 
applications, to 
! only „complete" 
;epted, systems 
able to answer 
itout interactive 
hat it should not 
faces. 
d by voxels of 
ue to the pixel, 
it lattice and are 
jrdinates of the 
arrangement of 
ion of the model 
il enumeration is 
j other boolean 
well as for 
visualisation. On the other hand the geometrical items point, 
edge and surface can be calculated only inaccurately and at 
much expenditure, since they cannot be stored explicitly. 
The memory expenditure for cell models behaves cubically 
compared to the desired resolution with the number of 
attributes as fourth dimension and becomes for large project 
enormous for good approximations. 
Number _ of _ voxels = 
x max~ x min ymax~ymin 
x_resolution y _resolution 
Zmin Y Attributes 
z_ resolution 
Since however voxel in direct neighbourhood have often the 
same value, an octree coding can be used. This way the 
memory expenditure and in addition the access times can be 
reduced, since octree coding corresponds to a spatial 
indexing. 
3.1.2 Constructive Solid Geometry (CSG) 
A further common method for the modelling of objects is the 
construction by means of space-primitives. Primitives are basic 
geometrical elements such as cuboids, cones, spheres, 
cylinders etc. An object is determined by a combination of 
primitives and the appropriate logical operations (union, 
difference, average) and transformations (translation, rotation, 
scaling). 
CSG-structures are usually stored in binary trees. Each 
volume primitive is a leave which determine the geometry of 
an object gradually and the operators applied to the primitives 
are the nodes. 
Computer internally CSG models contain neither effective 
edges nor surfaces of the modelled body in an explicit form 
and are therefore for analysis or other applications not directly 
usable. E.g. edges, which are definde by an intersection of the 
surfaces of two space primitives will not be stored in a CSG 
model. They must be computed every time they are required. 
3.1.3 Boundary Representation (B-Rep) 
B-rep models are an often used form of the three-dimensional 
modeling. They use three-dimensional polygon surfaces, in 
order to define the boundaries of an object. The surface 
modeling is a simple and generally accepted method for the 
representation of three-dimensional objects. It represents an 
accurate description for a multiplicity of bodies and enables in 
the other cases a good approximation. Details can be made 
visible by making several smaller surfaces. 
Conventionally, the B-Rep model consists of three object 
types: nodes, edges and surfaces. The need to model solid 
objects and assign them attributes makes a further object type 
necessary: Bodies. The topological model therefore consists of 
four object types (Fig.3): Bodies are defined by surfaces, 
surfaces by edges, edges by nodes and nodes finally consists 
of three coordinates. The B-Rep is thus a logical extension of 
the in the most vector GIS implemented node-edge-surface 
data model. 
A simple but often used data structure in order to define the 
EDGE_LOOP 
LOOP_FACE 
m VERT£X_EDGE_ID 
rr* VERTEX ID 
m edgejd 
PREV_VE_ID 
next_ve id 
edge_loop_id 
edgejd 
LOOPJD 
PREV_ELJD 
NEXT_EL ID 
LOOPJD 
FACEJD 
LOOPJTYPE 
FACEJD 
BODYJD 
BODY 
VERTEXJD 
XCOORD 
Y_COORD 
Z_COORD 
EDGE ID 
FIRSTJ/ERTEX 
LAST_ VERTEX 
LOOPJD 
BODYJD 
FACE_POL YGON 
EDGEJJNE ID 
EDGEJD 
LINEJD 
PREF_ELJD 
NEXT_ELJD 
FACEJD 
POLYGONJD 
BODYJEHTTTY 
BODY_ENTITY ID 
BODYJD 
ATTRIBUTES 
x 
■m 
■-i: 
f ' '' 
m 
i 
¡Li. 
h. 
ras 
POLYQONENT1TY 
POi^EHTTTY 
POINT JENTITYJD 
VERTEXJD 
ATTRIBUTES 
POLYGONJD 
ATTRIBUTES 
'... 
Geometric data types 
Thematic entities 
Fig 4: Relational data model of a 3D-GIS