Bilinear interpolation - Wikipedia
https://en.wikipedia.org/wiki/Bilinear_interpolationSuppose that we want to find the value of the unknown function f at the point (x, y). It is assumed that we know the value of f at the four points Q11 = (x1, y1), Q12 = (x1, y2), Q21 = (x2, y1), and Q22 = (x2, y2). We first do linear interpolation in the x-direction. This yields We proceed by interpolating in the y-direction to obtain the desired estimate: