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)]地点：
- 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.
常用术语及换算表
| 按揭年数 | 定义 |
|---|---|
| 插值 | The process of estimating unknown values between known data points |
| 双线性插值 | A method of interpolation in two dimensions using linear interpolations along both axes |
| 网格点 | The known data points that surround the target point |
| 加权平均 | A method of computing an intermediate value by assigning different weights to different values |
| Known Points | 估计的价值 |
| （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.
最常见的常见问题解答
Double interpolation is commonly used in numerical analysis, physics, engineering, and meteorology to estimate values in datasets where direct 测量 不可用。
Bilinear interpolation provides a good approximation but is less accurate than higher-order interpolation methods like bicubic interpolation. The accuracy depends on the 密度 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.