Pointwise interpolation is used in case the sampled points are not densely located with a limited influence or continuity in surrounding observations, for example climate observations such as rainfall and temperature, or ground water level measurements at wells.
Following two methods are commonly used for pointwise interpolations.
Thiessen Polygons
Thiessen polygons can be generated using distance operator as shown in Figure 2.5 (a) which creates the polygon boundaries as the intersections of radial expansions from the observation points. This method is also known as Voronoi tessellation.
Pointwise interpolation within a Thiessen polygon is based on nearest neighbor, which estimates the value as the same value with that of the sampled observations in the area.
Weighted Average
A window of circular shape with the radius of dmax is drawn at a point to be interpolated, so as to involve six to eight surrounding observed points as shown in Figure 2.6 (a).
Then the value of a point is calculated from the summation of the product of the observed value zi and weight wi, divided by the summation of the weights.