Pitney Bowes MapInfo Vertical Mapper - Manual (Page 32)

Triangulation with Smoothing
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Vertical Mapper 3.7
A smooth grid surface is then fitted to the TIN using a bivariate fifth-order polynomial expression in
the x- and y- direction for each triangle face. This method guarantees continuity and smoothness of
the surface along the sides of each triangle and smoothness of the surface within each triangle. The
slope blending algorithm is designed to calculate new slope values for each of the triangle vertices
(such as each point of the data) where the influence of adjacent slopes in the blending calculation is
weighted according to specified triangle properties.
Five properties of data point geometry and value greatly influence the ability of the slope blending
algorithm to control smoothing of the TIN surface. These include the triangle centroid location, the
triangle aspect ratio, the triangle area, the angle versus slope of the triangle, and the statistically-
derived slope of a triangle vertex. For example, triangles with centroids farther from the vertex being
solved have less influence on the slope calculation than triangles whose centroids are closer;
similarly, triangles with greater areas have greater influence in the slope calculation than triangles
with a smaller area. The end result is a smoothing process that significantly reduces the frequency
of angular artifacts, representing remnants of the original TIN facets in the final gridded surface.
Exploring TIN Interpolation: Create TRI Dialog Box
Once the data points have been analyzed by Vertical Mapper and exported to a temporary file, the
TIN Interpolation: Create TRI dialog box opens. Two features of the triangulation algorithm,
designed to build the Triangular Irregular Network (TIN) surface, are particularly critical and should
be carefully considered:
• Maximum Triangle Side Length
• Coincident Point Distance
The Maximum Triangle Side Length box enables you to limit the creation of triangles between
points you consider too far apart. Depending upon the geographic distribution of points in a file, this
distance setting will restrict the generation of unnecessarily large and/or sliver triangles and will limit
interpolation between points across distances that may be inappropriate. For example, a set of field
observations may contain large gaps in the coverage due to sampling problems. If the gaps are
quite large, it would be inappropriate in most cases to interpret new values lying within these areas.
Generally, you are expected to have an understanding of the distribution characteristics of your data
in order to enter an appropriate value. The default value is usually appropriate for most data sets.