Bilinear Interpolation Calculator

Bilinear interpolation estimates a value inside a rectangle from its four corner values.

How the Math Works

Bilinear interpolation calculates a value at a point within a 2D grid by first performing linear interpolation along the x-axis between the two nearest points in the horizontal direction, then repeating the process along the y-axis using the interpolated x-values. The formula combines these two weighted averages, where weights are derived from the relative distances to the grid corners, ensuring smooth transitions between known data points. This method effectively estimates intermediate values by considering the influence of all four surrounding grid points.

Practical Applications

This calculation is widely used in image processing to resize or smooth digital images, where pixel intensities at new coordinates are estimated from neighboring pixels. Engineers also apply it to model physical phenomena across a grid, such as temperature distribution or stress analysis, by interpolating between measured values at grid corners. In computer graphics, bilinear interpolation helps render textures onto 3D surfaces by predicting color or depth values between predefined points.

Day-to-Day Use

You encounter bilinear interpolation daily when zooming into digital photos on your phone or computer, where it prevents pixelation by estimating new pixel values from surrounding ones. It also appears in weather apps that generate smooth temperature or precipitation maps by interpolating between data from distant weather stations. Additionally, it improves the quality of video game graphics and maps by creating seamless transitions between textures or elevation data.

Worked example

Corners 10/20/30/40 at the centre (0.5, 0.5) → 25.

FAQ