Interpolation

What is it?

Formulas

$$\operatorname{lerp}(a, b, t) = (1 - t)\,a + t\,b, \quad t \in [0, 1]$$

$$p(x) = \sum_{i=0}^{n} y_i \prod_{j \ne i}\frac{x - x_j}{x_i - x_j}$$

Lagrange form

Where it shows up in computing

• Image processing and computer vision★★★★★fundamentalSignals, media and vision

  Resizing and rotating images samples between pixels with bilinear or bicubic interpolation.

• Lighting and shading★★★★★frequentComputer graphics

  GPUs interpolate colours, normals and texture coordinates across each triangle (barycentric interpolation).

• Bézier curves and splines★★★★★frequentComputer graphics

  De Casteljau's algorithm evaluates a Bézier curve by repeated linear interpolation.

• Signal processing★★★★★frequentSignals, media and vision

  Resampling audio between rates interpolates between samples (ideally with a sinc kernel).

Where is it used?

Computing topics reachable from here, through the chain of ideas that leads to them: