Data can often be collected in varying densities and spatial patterns.
It can then be used as a point database, a TIN, or converted to a grid.
The following mechanisms can be used for the creation of the grid:
- Drop in the bucket. The figure above shows a grid in the
solid lines, and we want the value at each line intersection. The
dotted lines divide the region into blocks, and each block is closest to a
single intersection of the grid. For example, the red box outlines the
region that is closest to the green grid point. In the simplest drop
in the bucket algorithm, each collected point is assigned to the nearest
grid intersection. There is no attempt to assign weights by where in
the box the point occurs. If there are more than one point in the box, either
the first or the last can be selected. To select the first, a check
must be made that the point is not missing, and the new value is only
assigned if the point is missing. To select the last, points are
processed and later points can simply overwrite previous ones. With
additional care in designing the algorithm, drop in the bucket can
pick the median or mean. There is no consideration of where the data
points occur with respect to the intersection location.
- Highest point: create a DSM,
or the ceiling
- Lowest point: create a DTM,
or the floor
||In some cases with a rectangle, there can be two ways to draw the
contours, as in the case on the left. On the left, a ridge
connects the two points with elevation of 80, and on the right, a valley
connects the two points with elevation 70. The number of such
boxes will generally be small, and with a large DEM, the effect will
also be very small.
- TIN: since three points determine a
plane, this provides unambiguous placement for contour lines (in some cases
with a rectangle, there can be two ways to draw the contours, as in the
example above). Computer graphics also likes triangles: it is easy to
computer the normal to the surface, and hence the lighting; high end
graphics cards measure their speed in triangles per second.
Additional algorithms not used in MICRODEM for grid creation.
- Distance or inverse distance weighting. This algorithm
finds the nearest neighbors. Variants require a specific number of
points, or points in various directions, say one in each of the four
principle directions or eight directions. The values are weighted by
distance, and can use a linear, squared, or other weighting to apply greater
weights to points close to the grid intersection.
- Trend surface: in this
algorithm, a number of points surrounding the grid intersection are
selected. A surface is fit to the points, and the value of the trend
surface at the grid intersection is taken as the value for the grid.
- Kriging or geostatistics: this was designed by the mining
industry, and rests on the assumption that you can find a relationship about
how values of the surface change with distance. More complex versions
can account for anisotropy, that values change faster in some directions
than others. You must first create a variogram, which will have a
nugget and a range out to which you can infer relationships.
Last revision 2/15/2017