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.
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Chen Xiaoyong& lkeda,K:1994a. Raster algorithms for
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Chen Xiaoyong & Ikeda , K.: 1994a . Three- dimensional
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International Archives of Photogrammetry and Remote Sensing,
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