2-4 Surface Fitting

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.

Bicubic Interpolation
Third order polynomial is used to fit a continuous surface using 4 x 4 = 16 adjacent points as shown in Figure 2.14.

z is calculated using the following formula.

Surface Fitting for random Points
Triangular network called as Triangulated Irregular Network (TIN) is applied as shown in Figure 2.15. A triangle forms a plane with straight contour lines. The detail of TIN is described in Chapter 3.