Our Inverse Bilinear Interpolation Calculator helps you determine the unknown X and Y coordinates that correspond to a given interpolated Z value within a 2D grid. Easily solve for the source coordinates when you have the interpolated result. Perfect for engineers, scientists, and data analysts.
Formula:
Inverse bilinear interpolation involves finding the original X and Y coordinates given a bilinearly interpolated Z value. The standard bilinear interpolation formula is:
Z(x', y') = Z00(1-x')(1-y') + Z10x'(1-y') + Z01(1-x')y' + Z11x'y'
Where x' = (X - X0)/(X1 - X0) and y' = (Y - Y0)/(Y1 - Y0) are normalized coordinates between 0 and 1.
To solve the inverse problem, we rearrange this equation to find the x' and y' that yield the target Z value. This often requires numerical methods, as there isn't always a simple closed-form solution for both x' and y' directly.
- Ztarget: The known interpolated Z value.
- X0, Y0: Coordinates of the bottom-left corner of the grid.
- X1, Y1: Coordinates of the top-right corner of the grid.
- Z00: Z value at (X0, Y0).
- Z10: Z value at (X1, Y0).
- Z01: Z value at (X0, Y1).
- Z11: Z value at (X1, Y1).