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THREE-DIMENSIONAL REPRESENTATION OF SPATIAL OBJECT AND TOPOLOGICAL 
RELATIONSHIPS 
GUO 
National Key Lab. for Information Engineering in Surveying, Mapping and Remote Sensing 
Wuhan Technical University of Surveying and Mapping 
39 Luoyu Road, Wuhan 430070 P.R. CHINA 
Tel: +86-27-7881292 
Fax: +86-27-7884185 
Commission III, Working Group III/IV 
KEY WORDS: Three-dimensional spatial representation method. topologic model, Topological relationship. 
ABSTRACT 
Extension of GIS from 2D to 3D is a difficult but necessary step for many GIS applications. Most functions of GIS 
should be designed based on a data model which is a digital form to represent terrain objects of the real world. Hence it 
is important to investigate the concept of data modeling for 3D GIS. This paper discusses issues concerning the 
development of 3D GIS. such as current techniques for representation of spatial object, a topologic model for 3D GIS, 
the formal description of topological relationships and the implementation of 3D GIS modeling environment on the 
micro-computer. 
1. INTRODUCTION 
A Geographic Information Systems (GIS) can bc uscd to 
store and handle data representing terrain. Although the 
world we live is three-dimension. The representation of 
spatial object in GIS is in gencral restricted to two- 
dimensional. These 2D data are in digital forms and can 
be handled, to some extent, efficiently. However, there 
are many problems that cannot be solved properly by 
using the 'traditional' 2D GIS software. First of all, 
successful interpretation of the hydrogeologic setting of a 
hazardous waste site (HES) requires data detailing 3D 
distribution of the natural surgical soils and manmade 
fill material, geologic strata and structure, and ground 
water conditions both locally and regionally (Fostered 
al. ,1987), followed by the branch of mine surveyors 
(Kavouras, 1985; Sarkozy,1985), geological modeling 
(Jones,1989),urban space modeling (Shibasaki,1992; 
Shaobo,1992), etc. So it is necessary to develop and 
investigate 3D GIS systems. 
In the context of 3D GIS, representation of spatial object 
and topological relationships play a central role both at 
the organization of spatial data and at the design of query 
methods. But the lack of a practical spatial data model 
and compressive theory of spatial relationships have been 
a major impediment to 3D GIS implementation. 
This paper discusses issues concerning the concept of 
data modeling for 3D GIS. The remainder of this paper is 
organized as follows. Section 2 describes current 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
techniques and 3D spatial representation methods. In 
section 3, a topological model for 3D GIS is presented. 
In section 4, the formal description of topological 
relationships has been introduced and a 3D GIS 
architecture ways has been given. Section 5 then 
concludes this paper and suggests the future works. 
2. 3D SPATIAL REPRESENTATION METHOD 
Current techniques for 3D GIS rely heavily on the power 
of computer graphics capability and stress geometry over 
interaction between geo-objects, but do attempt to provide 
solutions for creation, visualization, and analysis of 
complex geo-object, spatial, and entity-data relationships 
found in the real world (Fisher and Wales, 1991b). 
Geoscientific objects are geometrically complete and, 
thus, the abstract representation of such objects must 
have similar properties. Most of current 3D spatial 
representation methods may be categorized as either 
volume or surface representations ( see Fig. 1). 
2.1 Volume Representations 
Volume representation are octrees and their variations, 
polytrees (polyhedral trees) and G-( gery-scale ) octrees; 
geo-cellular models; 3D grids and isosurfaces. They 
represents an object by the union of a set of cells where 
the cell is a primitive shape which can be either regular 
or irregular. Cells are adjacent, connected and do not 
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