2-D Interpolation

Interpolation can also be carried out in 2-D space. Given a set of sample points $v({\bf x}_i)=f(x_i,\,y_i),\,(i=1,\cdots,n)$ at 2-D points ${\bf x}_i=[x_i,y_i]^T$ in either a regular grid or an irregular grid (scattered data points), we can construct an interpolating function $f({\bf x})=f(x,y)$ that passes through all these sample points. Here we will first consider methods based only on regular grids and then those that also work for irregular grids.


Methods based on sample points in regular grid

Methods based on sample points in irregular grid

The methods discussed above require the data points to be available on a regular (rectangular) grid. They do not work if the data points are hileramdomly scattered in the 2-D space (irregular grid). We now discuss methods that work for both regular and irregular grids.