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Extending Geographic Information System from two-dimensional to three-dimensional approaches
The data model is at the core of 3D GIS and the most common approach of 3D storage is the use of a planar polygon with a height value as this is, of course, the easiest solution. However, once the goal is to store 3D spatial objects in their real, multi-facet structures, the data model becomes more complex. There are many data models have been proposed such as the DTT, the Simplified Spatial Model (SSM) (Zlatanova and Tempfli, 2000), or the 3D topology model (Pilouk, 1996). The next issue with 3D GIS is the volume of data that is usually very large in size and being updated continuously. The volume of data may incur significant disk Input/Output (I/O) overhead during query and updating operations. In order to reduce the I/O access overhead, some researchers have suggested using specific compression algorithms to remove, wherever possible, the redundant data in a dataset without information loss during the process of compression or decompression. Related discussions on the compression techniques, particularly for tetrahedral meshes, can be referred to Yang et al. (2002) and Gumhold et al. (1999).
Data indexing is another mechanism that is usually applied to accelerate the process of queries in the database by keeping some extra information. There are many types of indexing methods have been cited such as the R-tree (Guttman, 1984), the K-D-B-tree (Robinson, 1981) or the Z-ordering (Orenstein, 1986). For en extensive review of multidimensional indexing structures see Castelli (2001) and Gaede (1998). In order to further improve the performance of queries, some researchers combined mechanisms common in computer graphics with multidimensional indexing structures such as the LOD-R-tree (Kofler et. al., 2000), Reactive Data Structures (Oosterom, 1990) or V-Reactive Tree (Li et. al., 2001). In this paper the Hybrid Tree will be used as the primary search index. This mechanism was chosen because it facilitates feature similarity search in high dimensionality feature space and the index structure can be fine-tuned to handle spatial search. 3. Storing Three Dimensions Object In the existing database structure of GeoMedia, 2D geometry data is stored as Binary Long Object (BLOB) along with the non-spatial data in one single row (Figure 1). This structure can be extended to store 3D geometry data by simply adding in another new BLOB column. Although both data and indexes are stored inside the database, the procedures for creating and updating to the relevant component are done externally using specific tools that are held up together in the procedure library for the sake of versions management. This simple extension of the existing structure is used here as it extends the capabilities of GeoMedia, without fundamentally changing its underlying data storage. While the underlying database structure was modified slightly to accommodate 3D data, the data model required specific development. In the next section, we provide a description of the data model. 4. Data Model Although 2D data is a subset of 3D data, the content of 3D data model is far more complicated than the existing 2D model as shown in Figure 2. In the context of GIS, geometry is the most essential property of a data model and 2D system usually stores planar geometry of each feature, while attributes are stored separate fields but within the same record (Figure 3a). However, it is not enough to just extrude the planar geometry using a height value as 3D data model requires the ability to store solid geometry as well as attributes that are associated to each face of the geometry such as the texture entity (Figure 3b). Apart from the geometry property, this paper considers adding in the colour description as the second property under the data model. Following the required properties, the data model which is used here is based on the four basic elements of geographic data: point, line, shape and volumetric object. It starts with point defines a single position on the space and two points define a line, then three adjoining lines define the simplest shape, which is a triangle. Finally four enclosing triangular surfaces define the simplest volumetric object, a tetrahedron. Theoretically any kind of shape can be formed using a combination of triangles; meanwhile, any kind of volumetric object can be formed using a combination of tetrahedrons. The term tetrahedral mesh is used to describe a complex structure that contains the four basic elements.  Figure 2: (a) 2D data model with planar geometry and single colour description (b) 3D data model with solid geometry and multiple colour description. 2D is a subset of 3D For the creation of tetrahedral mesh, we have used an existing 3D tetrahedral mesh generator named TetGen (2002). If the data is either a point, line or surface, it can be paired up with the related texture value in one-to-one relationship. The only exceptional is tetrahedron, which is actually defined by four adjoining triangles where each triangle can have a different value of texture property. Thus, texture entity is attached to each face of the geometry and this kind of relationship has been considered when attempting to define the structure of data model. More explanations regarding to data model structure are given in section 5. Finally, we need to consider the properties of existing 2D data model that cannot be simply left out, such as map projection and co-ordinate transformations. Theoretically, 3D geometry shares at least one face with the 2D geometry (Figure 3); the sharing face provides an opportunity for both sides to supply each other with particular information that might be lacking at either side.  Figure 3: The relationship between 2D and 3D data model, courtesy of Medit (2003). To place a 3D model on the Cartesian coordinate system, it can be referred to the existing 2D model wherever the related information is found |