Bilinear interpolation is interpolation of values at the four vertices of a rectangle
by a polynomial that has polynomial
degree at most 1 in each of the two variables separately.
Let the rectangle be ![[x_0,x_1]×[y_0,y_1]](/images/equations/BilinearInterpolation/Inline1.svg)
, with 
and 
, and let 
denote the value at 
. With 
and 
, the interpolant
is
 |
The same result is obtained by interpolating along either coordinate direction first and then along the other.
In general, the interpolant has the form 
, so it need not be a linear
function of the pair 
. For example, corner values 0, 0, 0, and 1 at 
, 
, 
, and 
give 
. On a rectangular grid, the construction can be applied
to each cell and is used, for example, in image resampling.
