Interpolation

Interpolation (and extrapolation) are mathematical procedures to estimate values of a function for certain desired inputs, given values for known inputs. If the desired input is within the range of the known values, it is referred to as interpolation. If it is outside the range, then it is called extrapolation.

Description
The simplest form of interpolation is where a function,, is estimated by drawing a straight line ("linear interpolation") between the nearest given points on either side of the required input value:

The method can also work by fitting a "curve" (i.e. a function) to two or more given points and then applying this function to the required input. Example uses are calculating from tables and audio waveform synthesis. There are variations using more than two points or higher degree functions. The technique can also be extended to functions of more than one input.