Surface fitting is widely used for interpolation of points on continuous surfaces such as digital elevation model (DEM), geoid, climate model (rainfall, temperature, pressure etc.) and so on.
Surface fitting is classified into two categories: surface fitting for regular grid and for random points.
Surface Fitting for Regular Grid
Following two methods are commonly used.
Bilinear Interpolation
Bilinear function is used to interpolate z using the following formula with respect to normalized coordinates (u, v) of the original coordinates (x, y) as shown in Figure 2.13.
z is calculated using the following formula.