Istanbul 2004 
3D SPATIAL DATA MODEL BASED ON QUASI TRI-PRISM VOLUME 
AND ITS APPLICATION IN SUBSURFACE ENGINEERING 
x ac ; Lb . x . ~ . 7 
Penggen Cheng"*, Wenzhong Shi", Jianya Gong', Guoging Zhou? 
"Dept. of Surveying, East China Institute of Technology, Fuzhou, Jiangxi, China, 344000 - pgcheng(22 cn.com 
?Dept. of Land Surveying and Geo-Information, The Hong Kong Polytechnic University, Hong Kong; - 
Iswzshi@polyu.edu.hk 
‘State Key Lab for Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan, 
China, 430079 - geogjy@ 163.net 
‘Dept. of Civil Engineering and Technology, Old Dominion University, Norfolk, Virginia, USA - gzhou@odu.edu 
Commission IV, WG IV/1 
KEYWORDS: GIS, Modeling, Data Structures, Method, System, Visualization, Engineering, Application 
ABSTRACT: 
3D spatial data model and modelling are the core of 3D GIS theory and applications. For this reason, a data model based on Quasi 
Tri-Prism Volume (QTPV) has been presented in this paper. The QTPV definition and its special cases due to vertices of QTPV may 
be superposition have been considered. The proposed model is composed of five primitives and six objects. The primitives consist of 
vertex, segment (edge, triangle side), triangle, side quadrilateral, and QTPV, and the objects consist of point, line, face, solid, 
complex, and spatial object. Their data structures and topology describing stratigraphy are designed and implemented in detail. Some 
modelling methods are designed for the purposes of the QTPV modelling of stratigraphy and subsurface engineering according to the 
modelling data. The model manipulation for the QTPV cutting using an arbitrary plane is discussed. We implemented a system 
prototype, called 3DGeoMV, using VC++6.0 programming language integrated with SQL database and OpenGL graphic library 
under the windows environment. The real data from the boreholes, which located at a geological exploration area in China’s Inner 
Mongolia, is used to verify the developed model and the developed system prototype. The experiment result demonstrates that the 
QTPV model is feasible and efficient for applications in the subsurface engineering. With applications of the presented QTPV, 
irregular natural geological bodies and/or regular subsurface engineering can be represented efficiently. 
1. INTRODUCTION 
3D spatial data model and modeling are the core of 3D GIS 
theory and applications in different domains. Many 3D data 
models or data structures have been investigated in the past 
years. For instance, Molenaar proposed a 3D Format Data 
Structure (3D FDS) based on 2D topological data structure 
(Molenaar, 1992). Pilout (1993) and Chen (1995) have 
researched Tetrahedral Network (TEN) model. Li and Shi 
proposed hybrid data model known as Octree- TEN model (Li, 
1997) and TIN-Octree model (Shi, 1996), Gong (1997) 
proposed an object-oriented 3D data model integrated raster and 
vector data structure. In urban 3D model area, Zlatanova (2000) 
proposed a Simplified Spatial Model (SSM). and Sun (2000) 
proposed a 3D spatial data model based on surface triangular 
partition. From a geometric point of view, these 3D data models 
can be classified into the following three categories: surface- 
based (3D FDS, B-Rep), volume-based (CSG. TEN), and 
hybrids (Octree-TEN, TIN-Octree). These models have their 
own features and suitability. Some scholars have analyzed and 
compared these models in terms of application domain, 
: geometric. and technical validity, efficiency of geometric 
algorithm, accuracy, and need for storage (Houlding, 1994; 
Breuning, 1996; Fritsch, 1996; Cheng and Gong, 2001; Wu et 
al., 2003). 
In fact, many spatial objects could only be represented by 3D 
volume. The modeling method based on 3D volume has become 
widely and increasingly. The basic volumes in common use are 
hexahedron, four-prism cone, tetrahedron, and tri-prism. 
However, the geological bodies are complex. It is difficult to 
apply regular hexahedron as a basic volume element to 
represent boundary accurately. Tetrahedron is agility in 
representing complex geological bodies, but it will cause the 
huge data redundancy, and the algorithm of creating tetrahedron 
is more difficult and is under researching. In the recent years, 
some scholars have investigated 3D data modcl based on tri- 
prism volume. For examples, Zhang (2000) has made research 
about the normal tri-prism volume in 3D stratum modeling, and 
discussed the data structure and cutting algorithm. Gong (2002) 
and Qi (2002) introduced the irregular tri-prism volume and 
discussed its data structures and topological relationship, but the 
modeling method and spatial manipulation have not further 
been investigated. Quasi Tri-Prism Volume (QTPV) is a smart 
volume and has some advantages in representing complex 
geological bodies compared to hexahedron, four-prism cone and 
tetrahedron. 
This paper presents QTPV data model, its manipulation, and its 
application in subsurface engineering. In Section 2, the QTPV 
data model and its data structure are designed. In Section 3, 
some modelling methods are proposed for the purpose of QTPV 
modelling of stratigraphy and subsurface engineering according 
to the modelling data. In Section 4, an algorithm of model 
cutting is presented. Applications of the QTPV model in 
stratigraphy and laneway are given in Section 5. Finally, 
conclusions are given in Section 6. 
2. QUASI TRI-PRISM VOLUME DATA MODEL 
2.] Quasi-Tri-Prism Volume 
Normal Tri-Prism Volume (NTPV) is a volumetric element 
constructed by a triangle extending a distance along the vertical 
direction, shown in Figure la. Obviously, in the view of the