ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
53 
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o force which 
produces power, or movement. In GIS, it is normally used to 
“imply some kind of change, movement and analysis of force“ 
(Chrisman, 1999). 
There seem to be three types of meaning by "dynamic". One 
implies that the nature of the object is dynamic, e.g.. coastal 
line. In this case, the “dynamic” is associated with “fuzzy". 
The other means the spatial process is dynamic, e.g. soil 
erosion process. In this case, the "dynamic" is associated with 
"temporal". The third is related to the dynamic spatial data 
structure of GIS, such as the Voronoi diagram-based spatial 
data modelling, mobile spatial data modelling. 
Spatial objects in the real world can, according the speed of 
change, be categorized into the following three classes (see 
Zhang and Hunter, 2000): 
• those that are static; 
• those that change slowly (and imperceptibly); and 
• those that are dynamic. 
Zhang and Hunter (2000) reasoned: "Objects in the first 
category do not change measurably over the lifespan of the 
feature being observed, for example, geological structures and 
major landforms. In the second category, objects vary slowly, 
for instance, vegetation cover and sea-level changes. While 
they cannot be considered static, movement is not normally an 
essential element of these phenomena. The objects in the 
third category represent dynamic situations and the way in 
which they vary can be further subdivided into three sub 
categories 
• positional change; 
• size change; and 
• shape change. 
For change in position, the vital elements are time, velocity 
and acceleration. For change in size, it is not motion but rather 
growth and shrinkage that become important, while for change 
in shape it is deformation rather than motion that is of key 
interest". 
Another key term is the “multi-dimensional“. The first question 
arising is "what's is a dimension?" In Euclidean geometry, one 
is familiar with the 3-dimensional coordinate system, X, Y and 
H. This system is also a mathematical basis of current GIS. In 
fact, it is a commonplace that traditional GIS are dealing with 
2-D geometry and associated attributes. There are also some 
2.5-D solutions such as perspectives, fire frame 
representation, etc. However, the volumetric 3 dimensional 
GIS is still under development. In this sense volumetric 3-D 
GIS is a “multi-dimensional“ GIS already. 
There are also arguments on “dimension" in spatial information 
science. Davis and Williams (1989) suggested to consider 
attributes as the 4 th dimension and to consider time as a fifth 
dimension. Li (1994) consider scale and time as another two 
dimensions. Instead of 5 dimensions, he suggests a new 3-D 
coordinate system with space (Z), time (T) and scale (S) as the 
three axes. In GIS, spatial analysis is then performed along 
these three axes (X, T and S) or on the three planes (ZT, ZS, 
TS). De Cola (1997) suggests that “all data may be 
considered as existing in a space of four conceptual 
dimensions, each with its unique characteristics: 
• space -- continuous and unbounded; 
• time - continuous and bounded in one direction 
(the future); 
• feature - discontinuous and unbounded; 
• scale - continuous and bounded in one direction 
(the finest available resolution).“ 
One may also find that theme has also been considered as a 
basic dimension in some literature. In fact, the terms 
“attribute", "feature" and “theme" have similar meaning in this 
sense, the word "theme" is used in this paper. To raise scale 
to a level as a basic dimension is a recent event although 
scale has been considered as an important issue in many 
sciences (Li, 1997, 1999). It was highly advocated by Li 
(1994, 1996, 1997 and 1999). Li's arguments have been 
indirectly supported by many researchers (e.g. De Cola, 1997). 
Indeed, Quattrochi and Goodchild (1997) in the Epilogue of 
their book also re-irritated a similar view: “Scale is a 
fundamental and inescapable dimension of geographic data”. 
Indeed, Lee and Molenaar (2000) have made a general 
statement on the context of dynamic and multi-dimensional: 
“By dynamic, we imply the ability of the system 
to capture the ever-changing world, and by 
multi-dimensional, we mean the liberation of 
spatial data from the confines of the two- 
dimensional space of traditional map. When