Pitney Bowes MapInfo Vertical Mapper - Manual (Page 40)

Natural Neighbour Interpolation
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Vertical Mapper 3.7
Put simply, natural neighbour interpolation makes use of an area-weighting technique to determine a
new value for every grid node. As shown in the next figure, a natural neighbour region is first
generated for each data point. Then, a new natural neighbour region is generated at every node in
the new grid which effectively overlies various portions of the surrounding natural neighbour regions
defining each point. The new grid value is calculated as the average of the surrounding point values
proportionally weighted according to the intersecting area of each point.
A display of the natural neighbour regions around the point file as well as those
created around a grid node.
You can choose one of three variations on the natural neighbour technique. The next figure
illustrates the behaviour of each variation.
• A Constant Value Solution in which each grid node takes on the value of the underlying natural
neighbour region.
• A Linear Solution where the grid value is determined by averaging the point values associated
with surrounding natural neighbour regions and weighted according to the area that is
encompassed by a temporary natural neighbour region generated around the grid cell (see the
next figure).
• A Slope-Based Solution where the grid value is determined by averaging the extrapolated slope
of each surrounding natural neighbour region and area weighted as in the linear solution. By
examining the adjacent points, a determination is made as to whether that point represents a
local maximum or minimum value. If it does, a slope value of zero is assigned to that value and
the surface will honour that point by neither overshooting nor undershooting it.
A graph showing the three variations of NN interpolation.