International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV. Part B4. Istanbul 2004
graphic theory, a NTPV is an aggregate consisting of vertices V.
edges E, triangles T and side-quadrilateral Q, i.e,
NTPV - (V. E, T. QI
7 ={V; Va Vi, Va, Vs, Ve }
5» ru à
j3; E25; Eoi, E45, Eso; Ea, E14s E25, Ee]
where
and the constrained conditions
(1) Vi, ve Va, y» Vaux, ue Vx, vb Vix v Vix. y)
(2) Ei4 // E55 // Eas
(3) Quzs4s Qz365 and Q3145 are plane quadrilateral
NTPV is a perfect volume and exists when the vertices located
in regular situation. For a subsurface engineering, although the
borehole is designed with a vertical direction or with a special
azimuth and inclination, the borehole central line does not
always obey the designed location because of the influence of
rock pressure. That means that the vertices, which borchole
cutting stratigraphy interfaces, are not in a vertical line and their
horizontal coordinates of the vertices are different. With
application of these vertices to construct Tri-Prism Volume, we
cannot obtain the NTPV, rather than Quasi-Tri-Prism Volume
(QTPV) (Figure 1b). QTPV has the same structure and topology
with NTPV, but QTPV does not comply with the constrained
conditions of NTPV. Obviously, being similar to tetrahedron,
QTPV can be used as a basic volumetric element to design a 3D
spatial data model.
{b)
Figure 1. Tri-prism volume
[n practical application, vertices may be superposition and
QTPV may be one of the four special cases. As illustrated in
Figure 2, (a) and (d) are tetrahedrons, (b) is four-prism cone. It
is obvious that no matter how complex a geological body, the
body can be described using QTPVs with different sizes and
shapes. The extrusive advantage of QTPV is that only one data
structure, but not the hybrid data structure, such as Octree-TEN,
can be used to represent a geological body.
{d)
Figure 2. The special cases of QTPV
Vertex data structure
| VertexID X y Z
Attribute|IsBelong| Type | CutFlag
"IsBelong" refers to the geological objects the vertex belongs to;
interpolation point.
2.2 Data model based on QTPV
Object-oriented technology is widely used in computer society.
The characteristic of Object-Oriented Modeling (OOM) is that
no matter how complex a spatial entity, it can be described by
an object. Using object identities the relationship among objects
can be created. A QTPV has five primitives: Vertex, segment
(edge. triangle side). triangle, side quadrilateral, and QTPV.
They are basic elements to construct primary objects, which are
point, line, surface and body. There are many types of spatial
objects in subsurface engineering domain. For example,
borehole is a line object composed of segments; an interface or
fault is a surface object composed of triangles or side
quadrilateral (triangled); the inner of a geological body is a
body object and composed of QPTVs; gas rallying point or
sample point of ore deposit is point object and represented by a
vertex. According to the principle of the object-oriented data
model, the above primitives and objects are the foundations of
designing a data model based on QTPV. Based on the above
idea, a conceptual data model based on QTPV is depicted in
Figure 3.
Spatial-obi
|» oint-ob i | | Line
]
— Composition
Segment
—— > Inhentance
— 4 Azgregation
——> Association
Figure 3. Conceptual model based on QTPV
2.3 Data Structure Design
In order to construct a 3D geological model with spatial location,
topological relationship and attribute information, and of saving
storage memory, more detailed data structures of the primitives
and elementary objects should be considered. The data
structures include vertex, side of a triangle. edge, triangle, side-
quadrilateral and QTPV. On the other hand, in order to
represent 3D stratigraphy bodies and their topological
relationship, several data structures on TIN, interface
(composed of TINs), geological body and image or texture
should be designed. Here the definitions of six data structures
composed of a QTPV and three other data structures composed
of geological objects are provided as the follows:
"Type" refers to the vertex of either an original sample point or
40
International A
Triangle side d.
TriaSideID
Edge data struc
EdgelD | St
If the value of
Triangle data st
TrialD | Ve
Side quadrilate:
SQuadID | V
QTPV data stru
QTPVID | V«
TIN data struct
TINID | T
Stratigraphy or |
uno]
Geological obje:
BN EA
GeoObjID | €
3. MODI
3.1 Stratigraph
With the differc
method can be
points of startis
borehole's captu
3.1.1 Modeling
modeling metho
three steps. First
different layers a
stratigraphy intei
and thus, regula
have coincident
of later modeling
be regular and
corresponding f
interfaces. If the
special processes
triangulation an
referred to Figure
