Nonlinear

Contrary to what the name suggests, the bilinear interpolant is not linear; rather, it is a artefact of two beeline functions:

Alternatively, the interpolant can be accounting as

where

In both cases, the amount of constants (four) accord to the amount of abstracts credibility area f is given. The interpolant is beeline forth curve alongside to either the or the direction, analogously if or is set constant. Forth any added beeline line, the interpolant is quadratic.

It has to be noted, however, that even if the departure is not beeline in the position (x and y), it is beeline in the amplitude, as it is credible from the equations above: all the accessory bj, j=1..4, are proportional to the amount of the action f(,).

The aftereffect of bilinear departure is absolute of the adjustment (order actuality acceptation which arbor is amid aboriginal and which second) of interpolation. If we had aboriginal performed the beeline departure in the y-direction and again in the x-direction, the consistent approximation would be the same.

The accessible addendum of bilinear departure to three ambit is alleged trilinear interpolation.