Calculate a double (bilinear) interpolated value from four table corner values plus x and y, or solve back for the x or y that hits a target value.
Double Interpolation Formula
The following equation can be used to calculate a value using bilinear (double) interpolation.
Bilinear value = (1 − tx)(1 − ty)Q11 + tx(1 − ty)Q21 + (1 − tx)ty Q12 + tx ty Q22, where tx = (x − x1)/(x2 − x1) and ty = (y − y1)/(y2 − y1). The two x grid lines must differ, as must the two y grid lines.
What is double interpolation?
Double interpolation is a mathematical technique used to estimate values in a two-dimensional grid by interpolating between known values. It is particularly useful when the available data points are insufficient to determine a desired value directly.
Imagine a scenario where you have a grid of data points with values given at specific coordinates. However, you need to determine the value at a location within this grid that does not have a known value. This is where double interpolation comes into play.
The process is typically done in two linear interpolation steps. First, interpolate along x on each of the two y grid lines, obtaining two intermediate values. Interpolate those two values along y to estimate the target. Solving for x or y holds the other coordinate fixed; a flat slice may have no unique solution.
Double interpolation is important because it allows us to fill in missing values and make estimates within a grid of data points.
