ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001 
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summery of GIS functionalities (existing and potential) versus the 
level of applications is given in Figure 9. 
With increase in the application level, the function required 
aggregates from simple analysis function to multiple functions, 
then ‘close-couple’ model integration and ‘loops-couple’ 
integration. 
Fig. 4. Aquatic Reserves Map. 
Currently, the majority of GIS applications in coastal zone has 
reached Level 1 and Level 2. There growing needs for Level 3 
development and more and more applications will continues to 
grow, when new models of particular scientifical fields become 
available from different user groups and improvement of user 
interface is available from commercial vendors. 
Some suggested functions 
A. True 3D buffer 
Current GIS application in coastal and marine environment is still 
limited by adopting the methods that are commonly used in land- 
based (2D) application, attributed to being lack of analysis 
functions in 3D GIS. Coastal GIS is one of challenge frontier in 
the development of GIS (Bartlett, 1999). Based on CSG 
(Construction Solid Geometry) data model, the author proposed 
a method of object-oriented representation of geographical 
objects in raster-based 3D space and basic 3D GIS functions (3D 
buffer and 3D overlay). 
In this method, an object is defined as a subset of the elements 
(voxel) of object-space and embedded in an object-space, which 
is represented as a matrix or flat-file data structure. Three types 
of 3D buffer are defined, namely ‘universal buffer’, ‘impediment 
buffer’ (plan-based and directed buffer). 
GIS function is realised by manipulating the matrix. This 
innovated method provides a conceptual framework for 
developing a true 3D GIS, potentially applied for coastal/marine 
modeling, such as marine habitats, pollution and coastal change, 
as well as ground water modeling. It can be further expanded to 
multi-dimensional GIS application and also can be used in 2D- 
GIS with respect of temporal change. 
a) Definition of geographical object 
Object Orientation in GIS has been articulated (Ye, 1996; Fisher, 
1993; Coad and Yourdon, 1991). Based on the traditional set 
theory and Donald, M., 1982 Geometric modeling using Octree 
encoding (Donald 1982), a 3D space is represented as: 
m y n y o 
s«?)=XK/ t ) 
/=1 
y=1 
k= 1 
where ay is an element in a grided horizonal plan which has m 
colume and n row, and d k is a vertical position or ‘disc’, which can 
be viewed as a layer or slice or a snap-shot of a given time. 
In the 3D space S(0), a point object is defined as: 
Object(P) = { au/U} or [a M d k ] 
where symbol ‘ A ’ means the intersection position in the matrix of 
3D space, S (O). 
For a line object or a 3D object (or body), as follows: 
Object (A) = {a,d*.* a,, l 'Yj k , or 
[Si-xj-ydk-z, ay.dk., 3i+x,i+ydk+z,] 
A point object can be viewed as subset of line or 3D object, while 
the later is a subset of S (O), e. a.: 
Object (P) c Object (A) c S (O) 
The object space and the objects as such can be represented as 
a matrix (see below flat-file), which is used for mathematical 
operations to build GIS functions, such as 3D buffer and 3D 
overlay (union and intersect). 
Based on this definition, some 3D GIS functions can be realised. 
The next section discuses two basic GIS functions: Buffer and 
Overlay 
b) Three dimension (3D) GIS functions 
3D buffer function 
The object space, S (O), and objects are stored as a matrix in a 
database. This makes it easy to perform a mathematical 
computation to build 3D GIS functions. 3D buffer function is quit 
different from 2D buffer. Three types of basic buffer functions are 
identified, here named as: 
• Universal buffer - buffer in all direction (Fig. 11), 
• Plan-based buffer - buffer perpendicular to a plan, e.g. x-y 
plan (z direction), and 
• Directed buffer - buffer with angle or angles from an object. 
Multi-objects buffer or a class of objects 3D buffer 
For three object: / r (y\ ; ) ä ,F(B l j ) d ,F{C t j ) d 
BUFFER_(ABC)=£ {min[buf _ F(A (J ) d .buf _ F(B Lj ),,buf _ F(C,, )„ ]I 
4=1 
Where: F(A,j ) d , F[B U ) d , and F(Cy ) d are the projected value, 
calculated with F function of Object A, B, C at disc d, 
respectively, and i,j refers to a cell location.