Interpolation is the procedure of estimating the value of properties at unsampled points or areas using a limited number of sampled observations.
Figure 2.1 and Figure 2.2 show the principle of curve fitting and surface fitting respectively to interpolate the value at an unsampled point using surrounding sampled points.
In case a single function of the curve or surface fitting is determined, the interpolation is called global interpolation, and in case different functions are adopted locally and repeatedly in a small portion of the total area, it is called local interpolation.
When curve or surface fitting is executed with all the sampled observations, the interpolation is called exact interpolation, where as in case the fitted curve or surface does not pass through all the sampled observations because of some expected errors, it is called approximate interpolation.
Approximate interpolation is sometimes used in spatial prediction of trend or representation of grid cells or unit areas.
Figure 2.3 shows prediction of trend with an approximate curve interpolation and the variation from the trend. Figure 2.4 shows an example of representation at a grid cell based on majority rule.