The Three Dimensional Visualization & Analysis of Geographic Databy:
The purpose of maps, geographers know, is to model reality. In the Nature of Maps Robinson & Petchenik (1976) defined a map as a "graphic representation of the milieu." The use of the term milieu is interesting because it suggests much more than the flat, static maps we are familiar with. It presents a challenge to step beyond the comfortable reach of two dimensional (2D) representations to higher dimensions of visualization. To model reality most clearly, it certainly makes sense that we strive to map what we actually experience. What follows is a brief look at the addition of a third dimension (3D) to geographic visualization and geographic information systems (GIS).
Van Driel (1989) recognized that the advantage of 3D lies in the way we see the information. It is estimated that 50 percent of the brain's neurons are involved in vision. What's more, it is believed that 3D displays stimulate more neurons: involving a larger portion of the brain in the problem solving process. With 2D contour maps, for example, the mind must first build a conceptual model of the relief before any analysis can be made. Considering the cartographic complexity of some terrain, this can be a arduous task for even the most dextrous mind. 3D display, however, simulates spatial reality, thus allowing the viewer to more quickly recognize and understand changes in elevation.
Geographic Visualization depends on psychological cues to create a natural 3D scene on a 2D computer monitor. In a sense, visualization models are not photographs, but pictures or renditions. Hence, the process of generating a scene is termed rendering. To render the most realistic scene, the geographer might rely on such visual cues as simple perspective rules or the subtle change of color or texture with distance. Depth may also come from feature obstruction and overlap, or from the addition of atmospheric attenuation such as fog or haze. Often the clever use of lighting sources and clouds can heighten the relative distance within a scene. Finally, the generation of trees or even seasonal characteristics such as snow can artificially enhance the sense of reality. There are physiological cues, as well, such as accomodation, convergence, or the retinal disparity of a stereoscopic image. Whatever the combination, geographers should be careful not to abstract reality too much, consequently misleading the audience.
Still, due to time and sampling constraints, terrain simulation has become common practice in visualization. Instead of wasting time laboring over every detail, geographers employ computer algorithms that reasonably synthesize a terrain surface. Most terrain algorithms are based in fractal geometry which argues the concept of self similarity. Self similarity implies the invariance of spatial structures or features under changes of scale; that is, what appears at one scale repeats itself at another. Landscape form can be described by the fractal dimension of the surface. A fractal dimension is measured as a real number ranging between 2 for a perfectly smooth surface and 3 for an infinitely variable surface. Although self similarity does not occur in nature, a fractal dimension between 2.2 and 2.3 will produce a very realistic looking landscape.
Most GIS software is capable of handling topographic data, usually as a digital elevation model (DEM), and of generating isometric views and contour maps. Many products also integrate scene generation systems for the 3D visualization of data. Yet, although Z coordinate data is now easily recorded or readily available for surface features, this third dimensional aspect of a GIS dataset is generally disregarded. This makes little sense considering, for example, that in geological analysis, instead of struggling with different layers to identify the relationship between lithology and landforms, a geologic map can simply be draped over the topography. This 2.5D capability, as it is referred to, does not qualify a GIS as a 3D GIS, however. To be considered a 3D GIS, the system must be capable of handling data as more than a surface; it must handle data as an object.
In comparison to the advancements in 3D visualization, relatively little has been accomplished in the realization of a practical 3D GIS. The obvious reason remains: the transition to 3D means an even greater diversity of object types and spatial relationships as well as very large data volumes. In a 2D GIS, a feature or phenomenon is represented as an area of grid cells or as an area within a polygon boundary. A 3D GIS, on the other hand, deals with volumes. Consider a cube. Instead of looking at just its faces, there must also be information about what lies inside the cube. To work, a 3D GIS requires this information to be complete and continuous. Clearly, the data management task has increased by another power. More problematic, however, is the initial task of acquiring 3D data. In medical imaging this is not particularly difficult. But for geographers working at much greater scales, this can be an exercise in interpolation and spatial adjacency. The data acquisition problem is particularly acute for geologists who must overcome the limited availability of subsurface information.
Once the data is collected, a raster or vector 3D data structure must be chosen to describe geo-objects. Besides points and arcs, features can also be indexed as surfaces and bodies. Take the cube again, a simple example of a body, and drill an imaginary hole through it. Now, how do you describe this instantly more complex object?
Geographers have come up with a number of approaches to representing 3D geo-objects as volumes. Hopefully, this overhead will make some sense of what I'm about to say. Raster solutions subdivide the 3D universe into volume elements or voxels. This contrasts with the vector approach in which volume is determined by a feature's bounding surface. Whatever the structure, true 3D GIS analysis demands that feature points, arcs, surfaces, and bodies be manipulated and analyzed as discrete entities.
In the raster approach, voxels serve as the building blocks for geo-objects. There are three methods to store voxels. The simplest form of storage is as a Binary raster, where voxels are indexed as on or off depending on whether they make up a particular geo-object. Understandably, this approach often requires large amounts of available storage. Another alternative is indexing by octree, the 3D equivalent of the quadtree. In this technique, a volume of space is recursively divided into 8 parts until each part of the subdivision is homogeneous. The octree structure allows for efficient Boolean operations on geo-objects, but it is time-consuming to build. Lastly, constructive solid geometry (CSG), a common CAD/CAM solid modelling technique, combines the occurrences of 3D primitives--objects such as cubes, spheres, and cylinders--using geometrical transformations and regularized set operations into a binary tree.
Vector data models are more complex and, some would argue, more concrete. Mathematicians, with their theory of knots, have tried to understand the complexities of embedding an arc in 3D space. What geographers should garner from their study is that this is no trivial task. In a topological approach, 3D boundary representations or iso-surfaces are defined for the indexing of geometrical data. Boundary representations (B-reps) describe the surface of a volume by the relationships between the faces, edges, and nodes which compose that volume. An appropriate geo-relational system then links these B-reps to attribute data. The topolical data structure, which makes 2D systems like Arc/INFO so good at analyzing spatial relationships, imposes a query model that inhibits interactivity.
The alternative, then, is object-oriented structuring. What this approach sacrifices in terms of spatial analysis, it makes up for in its ability to allow direct and continual access to attribute data. This is accomplished by linking feature attributes to structures designed for 3D graphical representation; hence, allowing the geographer to perform continuous mapping and querying in an interactive environment. The dynamic GIS, an effective tool in the analysis of spatiotemporal problems, is an interesting application of this. By forsaking volumetric data and integrating the dimension of time with 2.5D visualization structures, a dynamic GIS makes it possible to observe change.
The true power of a 3D GIS, then, is the ability to communicate complex geographic phenomena. Besides showing change, the added dimensionality of a 3D GIS allows geographers to themselves in fence diagrams, isometric surfaces, multiple surfaces, stereo block diagrams, and geo-object cut-aways.
The introduction of 3D graphics into architecture, engineering, and molecular biology has fostered new expectations in those fields. There certainly appears a need for visualization in nearly every subfield of geography as well. For example, it could prove a very persuasive tool in the hands of city planners, urban designers, and traffic engineers. Possibly even, they could use it to bring abstract project variables like visual impact analysis into the cost-benefit equation. The potential is definitely there to do a lot more than interesting perspective views of remotely sensed data. Of course, there are some problems in the transition from 2D to 3D that must still be addressed. Cartographically, for example, how do you label a feature that is to be looked at from many different of angles?
In contrast, a 3D GIS seems limited to geology, geophysics, meteorology, climatology, and hydrology. Volumetric analysis has proven to be well suited to hydrogeological applications such as petroleum reservoir characterization or groundwater contamination modeling. Still, perpetual improvements in hardware and software technology will ensure that a 3D GIS becomes easier to implement and finds some unique uses elsewhere in the discipline.
For my visualization exercise, I chose a square mile section in the Ponca Hills region of Omaha. A quarter of a mile north of Interstate 680 and the Mormon Bridge, just south of Hummel Park, and lying west of the Missouri river and Dodge Park, this site showed the most significant elevation change for the area. The site ranges in elevation from 980 ft. at river level to about 1200 ft. More than this, the site serves as a good example of a bluff headland, the region's most distinguishing feature.
To create a visualization of this square mile, an 85x85 grid was transposed onto an enlarged USGS quadrangle map. The elevations for 195 random points were recorded in an X-Y-Z data file. This file was imported into Surface III+ as a data grid. The grid was then extrapolated to 256x256 and exported as a Z data matrix. The matrix was inputted into a DOS utility, Z2DEM, the data was vertically exaggerated by a factor of 2, and a usable DEM was outputted.
Through testing, an exaggeration of 2 was found to be optimal for improving the visual impact of the rendered scene without sacrificing the character of the terrain. The DEM was then successfully opened in Vistapro and compared closely with the USGS quadrangle map and a test contour map done in Surface III+. Finally, a number of different camera angles, lighting sources, surface conditions, and color palettes were experimented with to produce the most realistic scene for the area.
A. Mile section chosen in the Ponca Hills
from USGS Quad map.
B. DEM created for use in VistaPro.
Recent development tool releases from Apple, QuickDraw 3D Rave, and Microsoft, Direct3D, will enable 3D software like the above to benefit from a host of soon to be released 3D accelerator boards. For less than $300, this hardware brings the same power to your PC that cost a staggering sum to install in a Silicon Graphics workstation only 5 years ago. The days of the wireframe model may be limited, as real-time Gouraud shading, texture mapping, antialiasing, Z-buffering, and double-buffering become standard. According to Multimedia World (May, 1996) experts anticipate that, by year's end, PC makers will have shipped some 8 million 3D enabled computers. And those numbers are expected to rise more than twofold in 1997. Truly, now is an exciting time for geographers to look again at the milieu.