A Double Interpolation Calculator helps estimate unknown values within a two-dimensional grid using bilinear interpolation. This method applies a weighted average of the four closest known data points to determine an intermediate value. It is widely used in engineering, meteorology, and computer graphics for approximating values between tabulated data points.
Formula of Double Interpolation Calculator
f(x,y) = f(x₁,y₁) × (x₂-x)(y₂-y)/[(x₂-x₁)(y₂-y₁)] +
f(x₂,y₁) × (x-x₁)(y₂-y)/[(x₂-x₁)(y₂-y₁)] +
f(x₁,y₂) × (x₂-x)(y-y₁)/[(x₂-x₁)(y₂-y₁)] +
f(x₂,y₂) × (x-x₁)(y-y₁)/[(x₂-x₁)(y₂-y₁)]Where:
- f(x,y) is the interpolated value at point (x,y).
- (x₁,y₁), (x₂,y₁), (x₁,y₂), (x₂,y₂) are the four corners of the rectangular grid containing (x,y).
- f(x₁,y₁), f(x₂,y₁), f(x₁,y₂), f(x₂,y₂) are the known function values at these points.
This formula provides an accurate approximation for missing values by considering the influence of adjacent data points.
Common Terms and Conversion Table
| Term | Definition |
|---|---|
| Interpolation | The process of estimating unknown values between known data points |
| Bilinear Interpolation | A method of interpolation in two dimensions using linear interpolations along both axes |
| Grid Points | The known data points that surround the target point |
| Weighted Average | A method of computing an intermediate value by assigning different weights to different values |
| Known Points | Estimated Value |
| (2,3), (5,3), (2,7), (5,7) | Interpolated Value |
| (10,15), (20,15), (10,25), (20,25) | Interpolated Value |
Example of Double Interpolation Calculator
Suppose you have four known values at the corners of a rectangular grid:
- f(2,3) = 10, f(5,3) = 14
- f(2,7) = 18, f(5,7) = 22
You want to determine the value at (3,5).
Using the bilinear interpolation formula:
f(3,5) = 10 × (5-3)(7-5)/[(5-2)(7-3)] +
14 × (3-2)(7-5)/[(5-2)(7-3)] +
18 × (5-3)(5-3)/[(5-2)(7-3)] +
22 × (3-2)(5-3)/[(5-2)(7-3)]After solving, the interpolated value at (3,5) is 16.
Most Common FAQs
Double interpolation is commonly used in numerical analysis, physics, engineering, and meteorology to estimate values in datasets where direct measurements are unavailable.
Bilinear interpolation provides a good approximation but is less accurate than higher-order interpolation methods like bicubic interpolation. The accuracy depends on the density of the data points and their distribution.
Yes, double interpolation is frequently used to estimate temperature, pressure, and other environmental parameters in weather forecasting and engineering applications.