A keyframe animation specifies an object's state at selected times and reconstructs intermediate states by interpolation.

For scalar or vector values $a$ and $b$, linear interpolation at $0\le t\le1$ is

$$\operatorname{lerp}(a,b,t)=(1-t)a+tb.$$

Positions and scales can often be interpolated this way. Piecewise polynomial curves can provide smoother velocity when abrupt changes at keyframes are undesirable.

Rotations require interpolation methods that respect the structure of rotations rather than simply blending arbitrary matrix entries, which need not produce another valid rotation.

Animation systems usually evaluate several channels—translation, rotation, scale or material parameters—at the current time and combine them into the object's transformation or appearance.

Keyframes describe what states occur when; the interpolation rule determines the motion between them and therefore affects speed, smoothness and path shape.