This network of triangular faces is referred to as a Triangular Irregular Network (TIN) as shown in the next figure. Triangulation involves a process whereby all the original data points are connected in space by a network of triangular faces, drawn as equilaterally as possible.
However, peaks and valleys will extend beyond the local maximum and minimum values. Using the triangulation technique, the interpolated surface passes through the original data points. In modeling a topographic surface from scattered elevation readings, it is not reasonable to assume that data points were collected at the absolute top or bottom of each local rise or depression in the land surface. Elevation is an example of point values that are best “surfaced” with a technique that predicts some degree of over- and under- estimation. The surface created by triangulation passes through (honours) all of the original data points while generating some degree of “overshoot” above local high values and “undershoot” below local low values. Triangulation is a process of grid generation that is usually applied to data that requires no regional averaging, such as elevation readings. Chapter 3: Creating Grids Using Interpolation
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