Bilinear interpolation: definition

Beginner

Guessing a value that falls between four measured ones by blending them, trusting the closest ones most.

Novice

Interpolating in two directions at once: first along one axis between two pairs of table entries, then along the other axis between the two results. Timing tools use it to read NLDM tables between their grid points.

Expert

$f = (1-u)(1-v)\,y_{00} + u(1-v)\,y_{10} + uv\,y_{11} + (1-u)v\,y_{01}$ , with $u, v$ the fractional positions in the bracketing interval. Linear along each axis, quadratic along a diagonal. Outside the grid, the same formula with $u$ or $v$ beyond $[0, 1]$ extrapolates linearly.