Rotation via Double Reflection

Reflect a vector across one line, then reflect the result across a second line, and what is left is a rotation. This page lets you drag the pieces and watch it happen: a vector s reflected at u and then at v ends up rotated inside the plane the two span. The pair of reflectors is called a rotor, where the two point does not matter and only the angle between them counts, and since the rotation comes out at twice that angle, building one of a given size means opening the reflectors half as far. Laszlo Korte wrote it as a small browser demo with the reasoning set beside the diagram.