Textbook: Slocum,
T. A. 1999. Thematic Cartography
and Visualization.
Prentice Hall: New Jesey.
URL :
https://www.angelfire.com/mo/yagoub
Chapter 8: Interpolation
Methods for Smooth Continuous Phenomena
See Page: 136-151
The basic objective of the chapter
is to identify the methods that used for interpolating data between irregular
spaced control points of known values. For example, drawing of contour lines
(Isometric and Isopleth maps) through few metrological stations (temperature,
rainfall, etc.).
List the main
interpolation methods that used for true point data, illustrate by
figures?
1. Triangulation
Fits a set of triangles to control
point locations and then interpolates along the edges of these triangles (see
Figure 8.1, page 137).
2. Inverse distance
The inverse distance methods lay an
equally spaced grid of points on top of the control points, estimate values at
each grid point as a function of their distance from control points, and then
interpolate between grid points (see Figure 8.3, page 139).
3. Kriging
Kriging is similar to inverse
distance method in that a grid is overlaid on top of the control points, and
values are estimated at each grid point as a function of distance from control
points. Rather than considering distances to control points independently of
one another, however, kriging considers the spatial autocorrelation in the
data, both between the grid points and the surrounding control points, and
among the control points themselves.
For better understanding of the
above methods, it is recommended to have some practice with ArcView 3D Analyst
in the GIS Lab or Vertical Mapper in MapInfo.
List the criteria for
selecting an interpolation method
for true point data?
1. Correctness of estimated data at
control points (honor of raw data).
2. Correctness of estimated data at
other points (prediction of unknown points).
3. Ability to handle discontinuities
(e.g. geological faults).
4. Execution time of the method
(faster or slow).
5. Time spent selecting
interpolation parameters.
6. Ease of understanding the method.
List two problems
associated with computer interpolation for true point data as compared with
traditional manual procedures?
1. Jagged lines (Fitting spline -
Figure 8.5, page 141 and Figure 8.11, page 148).
2. Spurious details (Figure 8.11,
page 148).
List the main
interpolation method that used for conceptual point data, illustrate by
figures?
Pycnophylatic (volume preserving)
method:
It begins by assuming that each
enumeration unit is raised to a height proportional to
the value of its associated control
point. This three-dimensional surface is then
gradually smoothed, keeping the
volume within each enumeration unit constant. This is accomplished using
cell-based smoothing process analogous to generalizing procedures used in image processing
(see Figure 8.12, page 149).
Exercise
Using the equation for inverse
distance on page 139 and Figure 8.3 calculate the estimated value at the grid
point in the Figure.
