Three-Dimensional Data Models

Three-dimensional (3D) data models focus on portraying the third dimension of physical objects and phenomena through the integration of semantic, geometric, and spatial data relationships. Fundamentally, this is a perspective different from the static, 2D or bird's-eye perspective on the world in traditional spatial data modeling. There are two approaches to modeling the third dimension in geographic information systems (GIS): (1) quasi-3D data modeling and (2) true 3D data modeling.

In the first approach of quasi-3D data modeling, a geographic phenomenon can be constructed as a surface in which a given geographic location is defined by a set of x and y coordinates, and a single value z can be assigned to this location. The value z can be elevation above sea level or any other abstract value associated with the represented phenomenon, for example, population density. In the elevation example, the displayed land surface in a model would be close to what we actually see in the real world (Figure 1). In the population density example, the height of the displayed surface would be the population density at a location at a particular time. This type of approach can efficiently handle 3D visualization through a number of ways, such as generating the surface from value z, draping raster images onto [Page 2823]the surface (e.g., aerial photos), visualizing terrain from one point to another, and animation (e.g., the function of creating fly-through video). As this type of approach is insufficient to represent data with multiple z values, it cannot be regarded as true 3D data modeling. In addition, this approach is not capable of representing the space above, beneath, and between surfaces in data structure. It is therefore known as quasi-3D data modeling or 2.5D data modeling. Quasi-3D or 2.5D data models are not suitable for 3D solid objects that are continuously distributed in the 3D space, such as ore bodies. From another point of view, quasi-3D or 2.5D data models are mainly used for visualization purposes and cannot support full-3D data querying and analysis, which require geometric and topological relationships.

Figure 1 Three-dimensional display of digital elevation model for the county of Greene, Missouri

Source: Author.

Given the limitations of conventional 2D and quasi-3D (or 2.5D) data models, a different approach is needed for true 3D data modeling. In true 3D data models, a geographic phenomenon can be constructed as a 3D object, such as a solid cube. Any point in space is specified by three locational values of an x coordinate, a y coordinate, and a z coordinate (e.g., height or depth) and one or multiple values related to the phenomenon, for example, different geological layers (Figure 2). It should be noted that in true 3D data models every pair of x and y coordinates with multiple z coordinates allows the presentation and manipulation of full information relevant to 3D solid objects.

For 3D data model design, topology is considered the most important concept. Topology can be specified as a set of rules that model how adjacent or neighboring spatial features connect and link to each other in spatial data models. These spatial features can be points, lines, polygons, surfaces, or bodies (volumes). Past studies have reported several 3D data models. For example, Carlson (1987) developed the simplicial complex, including 0-simplex, 1-simplex, and 3-simplex, to describe point, line, surface, and volume. Molenaar (1990) proposed a model of 3D Formal Data Structure, which contains nodes, arcs, edges, and faces to denote points, lines, surfaces, and bodies. Pilouk (1996) introduced the Tetrahedral Network (TEN) to model 3D objects with vague boundaries based on the 2D Triangular Irregular Network (TIN). Coors (2003) designed the Urban [Page 2824]Data Model, using planar convex faces to represent bodies and surfaces. Lee (2007) proposed the 3D Navigable Data Model, which is a network representation of building factoring pedestrian movements based on a 3D Geometric Network Data Model (GNM) that he developed. In the 3D GNM, a set of nodes denote 3D objects in primal space, and a set of edges denote the spatial relationships between 3D entities in primal space. These models adopted different ways to define topological relationships, that is, spatial relationships between spatial objects, such as intersection, connectivity, direction, containment, and adjacency. The clearly defined spatial relationships enable researchers to describe spatial objects with either heterogeneous or homogeneous properties, using different basic elements in their specific models. Moreover, the clearly defined spatial relationships provide a basis for data manipulation, data analysis, and other functionalities, such as computation-based queries, editing and examining specific objects, geometric calculation of volume, overlay, and buffering.

...