Bilinear Interpolation Calculator

What is bilinear interpolation?

Bilinear interpolation is a common technique for two-dimensional interpolation on a rectangle. Values are estimated between known values using Bilinear interpolation. It is a method for figuring out where one point on a curve is in relation to the locations of the other two points.

Bilinear Interpolation Formula

The following actions must be taken to find point P(x, y) using bilinear interpolation:

One linear interpolation along the y-axis, finding point P, and two linear interpolations along the x-axis, discovering intermediate points \(R_1\) and \(R_2\).

You can see that bilinear interpolation consists of one linear interpolation along the y-axis and two linear interpolations along the x-axis.

The definition of Point \( R_1(x, y) \) is

\( R_1(x, y) = \dfrac{Q_{11} (x_2 – x)}{(x_2 – x_1)} + \dfrac{Q_{21} (x – x_1)}{(x_2 – x_1)} \)

Point \( R_2(x, y) \) is given as follows:

\( R_2(x, y) = \dfrac{Q_{12} (x_2 – x)}{(x_2 – x_1)} + \dfrac{Q_{22} (x – x_1)}{(x_2 – x_1)} \)

We define the interpolated point P(x, y) as follows:

\( P(x, y) = \dfrac{R_1 (y_2 – y)}{(y_2 – y_1)} + \dfrac{R_2 (y – y_1)}{(y_2 – y_1)} \)

Why Do We Use Bilinear Interpolation?

The most often utilized applications of bilinear interpolation in engineering and science are as follows:

• Basic image processing and resampling methods are part of computer vision
• As a method to extract values from a specified set of data, embedded control systems

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