Pitney Bowes MapInfo Vertical Mapper - Manual (Page 31)

Chapter 3: Creating Grids Using Interpolation
User Guide
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Triangulation with Smoothing
Triangulation is a process of grid generation that is usually applied to data that requires no regional
averaging, such as elevation readings. 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. Elevation is an example of point values that
are best “surfaced” with a technique that predicts some degree of over- and under- estimation. 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.
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Using the triangulation technique, the interpolated surface passes through the original
data points. However, peaks and valleys will extend beyond the local maximum and
minimum values.
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. This network of triangular faces is
referred to as a Triangular Irregular Network (TIN) as shown in the next figure. Points are connected
based on the nearest neighbour relationship (the Delaunay criterion) which states that a circumcircle
drawn around any triangle will not enclose the vertices of any other triangle.
A three dimensional view of a Triangular Irregular Network (TIN).