Bézier curve
A smooth curve defined by a handful of control points, where the curve passes through its endpoints and is pulled toward the inner ones.
Pierre Bézier formalised them at Renault in the 1960s to describe car bodywork for CAD; Paul de Casteljau had derived the same math slightly earlier at Citroën, but it stayed a trade secret. A cubic Bézier — two endpoints and two handles — is the workhorse: it is what a pen tool draws, what TrueType and PostScript fonts are built from, and what an animation-curve editor exposes as draggable tangents.
Evaluation is cheap and numerically stable via de Casteljau's algorithm, repeated linear interpolation between points. Chain many short curves and you get a Bézier spline; for a smooth path through fixed waypoints a Catmull-Rom spline is often easier, since it runs straight through every point.