Editing Bilinear interpolation (section)

== Properties ==
{{comparison_of_1D_and_2D_interpolation.svg}}
As the name suggests, the bilinear interpolant is ''not'' linear; but it is linear (i.e. affine) along lines [[Parallel (geometry)|parallel]] to either the ''x'' or the ''y'' direction, equivalently if ''x'' or ''y'' is held constant. Along any other straight line, the interpolant is [[Quadratic function|quadratic]]. Even though the interpolation is ''not'' linear in the position (''x'' and ''y''), at a fixed point it ''is'' linear in the interpolation values, as can be seen in the (matrix) equations above.

The result of bilinear interpolation is independent of which axis is interpolated first and which second. If we had first performed the linear interpolation in the ''y'' direction and then in the ''x'' direction, the resulting approximation would be the same.

The interpolant is a [[multilinear polynomial|bilinear polynomial]], which is also a [[harmonic function]] satisfying [[Laplace's equation]]. Its [[Graph of a function|graph]] is a bilinear [[Bézier surface]] patch.