3.2.2 Local polynomial
While global polynomial interpolation fits a polynomial to the whole surface, local polynomial interpolation fits many polynomials, each within specific neighbourhoods. We can define the search neighbourhood using the size and shape, number of neighbours and configuration of the sector. A single plane is fitted through the points for the first order global polynomial interpolation, for the second order the surface is fitted along with a bend in it. Similarly, third order polynomial has two bends in it. But when there is a surface with sloping terrain or an irregular slope, a single polynomial surface does not fit well. More than one polynomial surface is required to represent the surface more precisely. LPI fits a polynomial of specified order with the help of input data for a defined neighbourhood. The neighbourhoods overlap and the value obtained at the centre of the neighbourhood is the predicted value.