A surface is a mathematical entity—in particular, it is a function of two variables. That is, if you consider the Cartesian plane, with variables x and y, for every coordinate pair, there is one, and only one, third value z. Visually, you can imagine the flat plane with a cloth billowed above it. The distance, measured perpendicularly from the plane to the cloth is the z value. (Actually, some values of z might be negative, which would indicate that part of the cloth was below the z = zero surface.)

An obvious example of such a surface is elevation14 above sea level. Another is the daily pollution level of a particular contaminant. A third might be wind speed at a given moment at a given altitude. For every geographic point, there is a z value for these themes. Since there exists an infinite number of points on a plane, there exists an infinite number of z values. Obviously, we could not store an infinite number of values, even if we knew what they were, in a finite computer store. We, therefore, apply the usual GIS techniques, which by this time you are used to, of storing some data and inferring information as we need it. The triangulated irregular network (TIN) is such a device. TINs, which you met in Chapter 1, are described in more detail in Chapter 9, which deals in part with 3-D GIS and is entitled the Third Spatial Dimension. The goal just here is to describe the data model that lets the computer tell you about the surface that the TIN represents.

The idea of a TIN ...

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