z-Values

Cartesian Coordinates in 3D

Cartesian coordinates specify how a geographic location, such as a road intersection or a town, can be uniquely identified by its x-, y-, and z-coordinates. Generally, as implemented in most current GIS, x- and y-coordinates provide the locational reference on the plane surface, while the z-value provides the measure of an attribute, such as elevation of the terrain (or depth of the sea floor). These together provide the values for the three physical dimensions of space: width, length, and height. x- and y-coordinates are measured on horizontally directed lines perpendicular to each other, while the z-value axis points upward.

2.5 Dimensions

Many people are familiar with points, lines, and areas as being of zero, one, and two dimensions, respectively. The third dimension provides the height or depth information at any location. When a set of z-values is associated with a set of (nonredundant) (x, y) coordinate locations, it is possible to project all three axes as a surface. This projection transforms the map such that each z attribute defines a position on the z-axis for each (x, y) coordinate pair, thereby creating a surface with no thickness, which can be visualized within 3D space, thus simulating the view of the landscape seen by a human observer from a point within the 3D space.

However, these surface mappings are not true representations of 3D space; there are no data above or below the surface. Thus, these representations are often referred to as being 2.5-dimensional. Digital terrain models are a good example of 2.5D representation. To achieve full 3D representation, it must be possible to have more than one z-value for every (x, y) location. However, in current standard 2D GIS software, which relies on attribute tables containing one row of data associated with each (x, y) location, full 3D representation is not possible, as it would mean that a single point would have two rows in the attribute table.

Visualizing other Attributes

Sometimes it is useful to use the concept of 3D coordinates to visualize attributes other than elevation, [Page 516]such as average household income or volume of traffic on a road. Assigning these values to the third dimension, the z-value, allows these attributes to be depicted as a surface and rendered in perspective views for easier interpretation.