About Double Interpolation Calculator (Formula)
A Double Interpolation Calculator, also known as a Bilinear Interpolation Calculator, is a tool used to estimate an intermediate value within a two-dimensional grid or data set when given the values at the grid’s four corner points. This type of interpolation is particularly useful when you need to estimate values within a table or grid where the data points are not evenly spaced.
Here’s an explanation of how the Double Interpolation Calculator works, along with the formula used for bilinear interpolation:
Bilinear Interpolation Formula:
Bilinear interpolation is used to estimate a value (Z) at a point (X, Y) within a rectangular grid defined by four corner points (X1, Y1), (X1, Y2), (X2, Y1), and (X2, Y2), where:
- (X1, Y1) corresponds to the lower-left corner of the grid.
- (X1, Y2) corresponds to the upper-left corner of the grid.
- (X2, Y1) corresponds to the lower-right corner of the grid.
- (X2, Y2) corresponds to the upper-right corner of the grid.
The formula for bilinear interpolation is as follows:
Z = (1 / ((X2 – X1) * (Y2 – Y1))) * (Q11 * (X2 – X) * (Y2 – Y) + Q21 * (X – X1) * (Y2 – Y) + Q12 * (X2 – X) * (Y – Y1) + Q22 * (X – X1) * (Y – Y1))
Where:
- Z is the interpolated value at point (X, Y).
- X and Y are the coordinates where you want to estimate the value.
- X1 and Y1 are the coordinates of the lower-left corner.
- X2 and Y2 are the coordinates of the upper-right corner.
- Q11 is the value at the lower-left corner.
- Q21 is the value at the lower-right corner.
- Q12 is the value at the upper-left corner.
- Q22 is the value at the upper-right corner.
The formula calculates a weighted average of the values at the four corner points, with the weights determined by the distances between the point of interest (X, Y) and the four corner points. This process provides a reasonably accurate estimation of the value at the specified location within the grid.
Double Interpolation Calculators make it easy to apply this formula and quickly obtain interpolated values from non-uniformly spaced data points in a grid or table, which is valuable in various fields such as scientific research, engineering, and data analysis.