The past decade has seen an explosion of observations from airborne and satellite-based multiand hyperspectral sensors, as well as from synthetic-aperture radar and LiDAR. Distilling useful information from this wealth of raw data is the domain of geospatial analysis, the collection of analytical, statistical, and heuristic methods for extracting information from georeferenced data. This information is important in serving the needs of a diverse set of industries including environmental conservation, oil and gas exploration, defense and intelligence, agriculture, coastal monitoring, forestry, and mining.

3D visualization techniques play an important role in geospatial analysis. The ability to represent the 3D nature of a geospatial data product on a 2D computer screen — including the ability to manipulate the data product in a 3D coordinate system — is essential; it enhances a user’s ability to explore the data, aiding in discovery and insight into features of the data that may not be apparent from a 2D view.

#### Representing 3D in Computer Graphics

In computer graphics, a typical convention is to specify a right-handed 3D coordinate system such that when a viewer is facing the display, +x is directed to the right, +y is directed up, and +z is directed out of the display, toward the viewer. Points — and 3D objects, which are treated as groups of points — within this 3D coordinate system are represented by homogeneous coordinates, which are formed by adding a fourth coordinate to each point. Instead of being represented by a triple (x,y,z), each point is instead represented by a quadruple (x,y,z,w). Homogeneous coordinates simplify coordinate transformations (i.e., translation, rotation, and scaling) by allowing them to be treated as matrix multiplications.

To view an object from a 3D coordinate system on a 2D display, a view volume, a projection plane, and a viewport are needed. The view volume is a subset of the 3D coordinate system; for simplicity it is often a unit cube centered at the origin. This is where the action takes place: Any object within the view volume is visualized; any object that falls outside the view volume is not. Objects can be scaled, rotated, and translated to fit within the view volume.

Objects within the 3D view volume are mapped into a 2D projection using a planar geometric projection, usually some form of perspective or parallel projection. The projection is defined by rays that emanate from a point, the center of projection, and pass through every point of the object to intersect with the projection plane. The contents of the projection plane are then mapped onto the viewport, a 2D window defined in the device coordinates of the display.

In computer graphics, complex 3D objects are constructed from a small number of primitive graphical items: points, line segments, and convex polygons. 3D curved surfaces are approximated by large numbers of small, flat polygons, typically triangles or quadrilaterals. Increasing the density of the polygons makes a smoother-looking surface.

Surfaces can be rendered using filled polygonal primitives drawn with a single color. This is known as flat shading. Surfaces can also be rendered using smooth or Gouraud shading, where the colors of the polygonal primitives are instead interpolated between the vertices. See Figure 1 for a comparison of the two techniques.

#### Applications of 3D in Geospatial Analysis

Digital elevation models (DEM), which give a 3D representation of the Earth’s surface, are used frequently in geospatial analysis. A DEM can be visualized in 3D as a polygonal mesh or a filled surface, with shading to heighten the 3D appearance of the model, or with colors proportional to height.

The data density of the visualization can be heightened by overlaying, as an image, additional georeferenced data onto the 3D DEM surface through texture mapping. The additional image data could be sourced from, for example, meteorology (surface temperatures, ozone concentration), geology (mineral types identified by multi- or hyperspectral imaging), or urban planning (zoning or land use), as well as many others. As an example, Figure 2 shows a visualization of USGS GTOPO30, a U.S. Geological Survey global digital elevation model, over the Front Range of northeast Colorado. The image features an overlay, through texture mapping, of land use with the USGS National Land Cover Dataset 1992 product, a 21-class land cover classification scheme. Colors are keyed to land cover types; urban and residential areas, for example, are red and pink. A vertical exaggeration of 0.2 is used in the visualization.