International Archives of the Photogrammetry, 
and propose the extension of this database by a 3-D primitive. 
Its topology, however, is only internal; there are no topological 
relations between primitives. (Stoter & van Oosterom, 2002) 
propose an implementation which is similar to ours, but they 
consider two different models: one using oracle spatial data 
types for Geometry, and another with topological relations. Our 
approach combines both in a single model. In addition, (Stoter 
& van Oosterom, 2002) do not deal with recursive aggregates. 
This paper is organized as follows: In the second section, the 
spatial and object-relational properties of the database system 
Oracle 9i are discussed. The representation of a 3-D city model 
in this spatial object-relational database is the topic of the third 
section. The next section discusses how this model may be 
queried and to what extend these queries are suitable to 
consider the third dimension, including performance issues. The 
paper ends with some concluding remarks and a discussion of 
open questions. 
2. SPATIAL OBJECT-RELATIONAL DATABASES - 
ORACLE 91 
Oracle 9i is a sophisticated, widespread commercial database 
system, which provides a spatial extension, called Oracle 
Spatial, and object-relational properties. Both are discussed in 
this section, which is based on (Oracle, 2002a) and (Oracle, 
2002b). 
2.1 Geometric properties 
Oracle Spatial provides a data type, called SDO GEOMETRY, 
for representing spatial data, and associated operators and 
functions, which allow storing, editing, updating and querying 
these data. Two mechanisms for indexing spatial data are used, 
Quadtrees and R-trges (Guttman, 1984). For querying 3-D data 
by Oracle Spatial, however, only R-trees may be employed. 
The geometry types supported by Oracle Spatial are based on 
the ‘OGC Simple Features Specification for SQL’ issued by the 
Open GIS Consortium (Open GIS Consortium, 1999). 
According to this standard, a geometry may be a point or a 
multi point, i.e. a point cluster, a line string or a multi line 
string, a polygon or a multi polygon. In addition to the Simple 
Feature specification, arc line strings, arc polygons, and 
collections of arbitrary geometries are offered. A geometry IS 
defined in a spatial coordinate reference system. According to 
the Simple Features specification, the explicit representation of 
topological relations between geometric objects is not provided. 
The coordinates of the geometric objects may be two or three 
dimensional, thus allowing polygons and lines positioned 
arbitrarily in 3-D space. The polygon boundaries may be non- 
planar, but the specification of interpolation rules for their 
interiors is not provided. For the representation of 3-D solids 
according to the Boundary Representation (B-Rep) (Foley et al., 
1995: Mäntylä, 1988), no data type is offered by Oracle Spatial. 
ec 
A database table may contain more than onc column of type 
SDO GEOMETRY. Thus it is possible, for example, to assign 
different levels of detail to a single object. This property is 
crucial for managing 3-D city models. 
For manipulating and querying spatial data, two mechanisms 
are offered, which differ in particular in their 3-D properties: 
operators and functions. 
Remote Sensing and Spatial Information Sciences, Vol XXXV, 
Part B4. Istanbul 2004 
Operators retrieve spatial data from the database according to 
geometrical criteria, using the R-tree index. One specific 
operator, called SDO FILTER. selects geometries, which 
interact with a given fixed geometry, or pairs of geometries, 
which interact pair-wise. The first case is called window-query, 
while the second is a join-query. The operator does not consider 
the exact geometry of objects, but approximates it by a minimal 
bounding rectangle or a minimal bounding box, depending on 
the dimension of thg geometries. The rectangles and boxes are 
parallel to the x-, y-, and z-axis of the coordinate reference 
system. 
The approximation of geometries by bounding boxes, however, 
yields inexact results. Consider, for example, the two 
geometries in Figure 1b), which are disjoint. The bounding 
boxes overlap, thus the operator SDO FILTER recognizes that 
both are not disjoint. In Figure la), the operator SDO FILTER 
is able to identify the two geometries' bounding boxes as 
disjoint. 
  
Approximation of geometries by minimal bounding 
boxes, yielding inexact results. In Figure a), both 
objects can be distinguished from cach other, while 
in b), the two geometries do not touch each other, 
but their bounding boxes do so. 
Figure 1: 
The other operators apart from SDO_F ILTER select geometries 
within a given distance, nearest neighbor geometries, or 
geometries with topological relations according to the well- 
known 4-intersection model (Egenhofer & Herring, 1990). 
These operators are evaluated using a so-called ‘two-tier 
model’, which applies SDO FILTER first, and the more exact 
operator to the result afterwards. All operators apart from 
SDO FILTER may not be applied to data with more than two 
dimensions, and thus are not discussed any further. 
In contrast to operators, functions do not use a filter step and a 
spatial index, and are applicable to 3-D data, but they ignore the 
7-coordinate. Oracle Spatial provides functions to select 
geometries according to the 4-intersection model, to compute 
areas, distances, or to construct convex hulls. centroids, buffers, 
and so on. In addition, the union, difference or intersection of a 
pair of geometries may be derived. 
Figure 2 depicts the different spatial relations distinguished by 
the function SDO GEOM.RELATE, which implements the 4- 
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