International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Parr B4. Istanbul 2004
triangle of a QTPV, and the vertices of this triangle
correspond to three boreholes.
(2) Expand a new triangle (down-triangle) down along the three
boreholes according to the adjacent attribute codes of the
up-triangle points. As shown in Figure 5, if their codes are
the same, the new triangle points are the next points along
the boreholes (see Figure 5a). If their codes are different, in
the borehole with a smaller code (for example a in Figure 5),
the new triangle points are the next points along the
boreholes. In the borehole with a large code (for example b
or c in Figure 5), the new triangle points will not change, as
illustrated in Figure 5b-5d.
—
(3) Construct a QTPV according to the up-triangle and down-
triangle, and then change the down-triangle into the up-
triangle.
(4) Repeat steps (2) and (3) until all the up-triangle points are at
the bottom of the three boreholes.
(5) Expand the triangle along the triangle's side on the earth's
surface by using the methods of constructing a Delaunay
TIN. Repeat steps (2)-(4) and construct all of the QTPVs.
(6) If all of the points are constructed into the triangle, stop the
modeling process; otherwise, go back to step (5).
Figure 5. The down-expansion of QTPV
3.2 Deposit Local Modelling
Suppose that a stratigraphy model has been constructed. There
is a deposit B located in stratigraphy A (Figure 6). In order to
maintenance the constructed topological relationship of QTPVs
model, we should adopt local modelling method. How do we
insert the deposit B into the stratigraphy A? Firstly, vertical
lines are created to pass tine points (a, b, c, d), and the lines are
crossed with adjacent stratigraphy interfaces into some
intersection points (a, a", b', b^,...) (Figure 6a). Secondly, local
model should be conducted in the stratigraphy A performing the
two steps of triangulation (Figure 6b) and construction of
QTPVs. After the local modelling finished, the topological
relationship between the local model and the adjacent QTPVs
should be handled. This process is divided into two aspects:
flank relationship maintenance and fluctuate relationship
maintenance.
3.3 Subsurface Engineering Modelling
Subsurface engineering, such as silo, laneway, mine, etc. always
are regular. In these cases, some crossed sections are captured in
different distance according to the changes of section shape
along the engineering main axis, so as to the section shape
change be in permitted range between adjacent sections (Figure
7a), thus a lot of columnsare obtained, then partition the column
into QTPVs. Different partition methods should be adopted
according to the section shapes. For example, Figure 6b
illustrates a circle laneway, adjacent sections have the same
shape, in the circle section, the center of a circle is taken as
center point, a series of triangles is constructed for every other
definite central angle, and then QTPVs is constructed by
connecting corresponding triangles in adjacent sections. Figure
7c, 7d and 7e show the different cases of constructing QTPVs
on laneways.
(b) Plan Projection
Figure 6. Subsurface Engineering construct QTPV
; sels -
fe
(d) te)
Figure 7. Subsurface Engineering construct QTPV
4. QTPV MODEL CUTTING PROCESS
Geological fence sections are a conventional method for
geologists to understand the geological information. To extract
data of a section from the geological model, one always cuts the
model along an arbitrary plane. If a Section Plane (SP) is
employed to cut a QTPV, many different results will be leaded.
The QTPV vertices can be classed into three kinds: black, white
and triangle vertex. Black vertex locates at the positive side of
the SP, write vertex locates at the negative side and triangle
vertex is on the SP exactly. Theoretically, there are 64 — 2
different configurations of black and white vertices
considerably within a QTPV. Considering the fluctuation and
rotation around vertically axial symmetric characteristics of
QTPV vertices and the fact that SP is a plane rather than an
isosurface, there are eight kinds of cutting cases according to
the number of black vertices. shown in Figure 8. Among these
cases, a special case, in which the side-quadrilateral of QTPV
may be convex or concave, has been taken into account, i.e. two
black vertices lied on the diagonal of convex or concave
quadrilateral are treated separately, in Figure 8e and 8f. Because
the side quadrilateral may not be a plane, the shade polygon
vertices are points of SP intersect the sides (prism edge, triangle
side) of a QTPV. In practice application, the points of SP
intersect the diagonal of side-quadrilateral should be calculated
if we pay attention to a single QTPV.
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