A method of estimating unknown values between known data points.Interpolation is a mathematical technique for estimating values that lie between known data points. When you have a set of measurements or observations, interpolation lets you fill in the gaps by assuming a smooth or predictable relationship between the points. It is distinct from extrapolation, which tries to guess values outside the observed range — interpolation stays within the known boundaries, making it a safer and more reliable operation.
The concept dates back to ancient astronomers and mathematicians, but a formal treatment emerged with Newton's forward difference formula in the 17th century and later with Lagrange's polynomial method in the 18th century.
The simplest form is linear interpolation, which draws a straight line between two adjacent points and reads off the value at any position along that line. More sophisticated methods, such as polynomial or spline interpolation, fit higher-order curves through multiple points to capture curvature and produce smoother results. The choice of method depends on the nature of the data and the required accuracy.
Interpolation is used everywhere from image resizing in digital photography to reconstructing continuous signals from discrete samples in audio processing, and in scientific computing to approximate functions that are expensive to evaluate directly.
The term comes from the Latin 'interpolare', meaning 'to refurbish' or 'to alter', which originally referred to touching up old manuscripts.
