ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
In surface 3D triangulation, one edge should not span two 
limbs of one fold, just as in 2D triangulation, points in two 
sides of a ridge line or valley line should not be connected. 
For this reason, the surface of rock should be divided to a 
serial of sub-surface by fault or hinge of the fold. But the 
question is that before forming a surface, the computer 
dose not know where are faults, where are hinges of fold. 
So, automatic triangulation has many difficulties, it needs 
geologist help. Obviously, for 3D triangulation of 
complicated geology surface, a lot of expert intervenes 
are needed. Expert arbitrating dose not depress 
practicability of the system, because the problem is too 
complicated indeed. 
3.3.3 3D TRIANGULATION OF SIMPLE SURFACE 
Simple surface is that the surface belongs to one limb of 
a fold, without fault cutting. In 3D triangulation of simple 
surface, 3D distance is used to replace 2D distance. In 
optimize of 2D Delauny triangulation, there are ‘shortest 
diagonal rule’ and ‘largest diagonal angle rule’. In 3D 
triangulation, ‘shortest diagonal rule' may be easy used. 
3.4 EXPRESS OF BODY INTERIOR 
Express of body boundary relies on boundary surface. 
What is the detail of inside? Inside of body are rarely 
uniform. In most case, inside of body can be treat as 
uniform, but in some case it is needed to detail express 
inside of a body. Two ways may be used. 
(1) Subdivede body: one way is subdividing the body into 
sub-body, let every sub-body relative uniform 
(2) Volume Function 
Another way is that basing on sampling points, form a 
volume function to interpolate values in the body. It needs 
dividing the volume to tetrahedrons by 3D sampling 
points, just as triangulation to setup TIN in 2D. 
Triangulation in 2D is an easy work, but in 3D, it is a 
difficulty work. 3D Voronoi polyhedron may be a good way 
for this task. 
3.4.1 3D LINEAR VOLUME FUNCTION 
The simplest volume interpolate is 3D linear function, 
such as: 
v = C 0 +Ci * X+C 2 * Y+C 3 * Z 1 
In the EQ 1, 
v : volume function value (such as densty) ; 
X, Y, Z : spatial interpolate point coordinate; 
C 0 , Ci, C 2l C 3 : coefficents of the linear volume function 
The 3D linear volume function can be used as simple 
volume Interpolation. Interpolation by 3D linear volume 
function, will form a density change ratio abrupt change 
surface between two adjacent sub-volumes 
Fig.10 In the position of circle 4, the densty is 
cntinuous, but the change ratio is not continuous 
3.4 3D CUBIC VOLUME FUNCTION: 
If a smooth change effect in inner body is wanted. 3D 
cubic volume interpolation function (as in EQ2) should be 
used. 
v=A„+A 1 *X+A 2 *X 2 +A 3 *X 3 +B 1 *Y+B 2 *Y 2 +B 3 *Y 3 +C 1 *Z+C 2 *Z 2 
+C 3 *Z 3 2 
In the EQ 2, 
v: volume function value (such as densty) 
X, Y, Z : spatial interpolate point coordinate; 
Ao, Ai, A 2 , A 3 Bi, B 2 , B 3 . Ci, C 2 , C 3 : coefficents of the 
cubic volume function 
Interpolation by cubic volume function will not form 
density and change ratio interface between two adjacent 
sub-volumes 
Fig.11 Not only Densty, but also change ratio is continuous 
4.CONCLUSIONS 
The authors would emphasize these views in the end of 
the paper: (1) 3D GIS will become base platform for mine 
GIS. (2) Mine data model is manifold and complexity, 
object - oriented vector model have particular advantage. 
(3) Integration of different data model will be correct 
direction. (4) 3D geology model is a base for 3D mine 
model. (5) Surface expressing takes up an important 
position in 3D model. (6) 3D surface triangulation is a 
good way to express nearly vertical or overturn surface. 
(7) For complicated geology surface, computer can't 
perform whole automatic 3D triangulation, it need to be 
assisted by human, geologist traditional method is 
deserved to reference. (8) Volume interpolating function 
can be used to express uneven of body interior. 
REFERENCES 
Chen Xiaoyong& lkeda,K:1994a. Raster algorithms for 
generating Delaunay tetraheadal tessellation. In : International 
Archives of Photogrammetry and Remote Sensing, Munich, 
Germany, Vol.XXX, Part 3/1,pp124-131. 
Chen Xiaoyong & Ikeda , K.: 1994a . Three- dimensional 
modelling of GIS based on Delunay tetraheadral tessellations In : 
International Archives of Photogrammetry and Remote Sensing, 
Munich, Germany, Vol.XXX , Part 3/1,pp132-139. 
Chen Yunhao& G.uo Dazhi: A 3D GIS topological structure , Acta 
geodatetica et cartography sinica , 1999,28(1): 41-44