Linepivot

Linepivot is a term used to describe a geometric operation in which a line is rotated about a fixed pivot point by a specified angle. It is a specific case of a planar rigid-motion applied to a single line, and can be formalized as the mapping that sends every point X on the original line L to a rotated point X' around the pivot P by angle theta. The image of L under this rotation is a new line L'. If the pivot P lies on L, the rotated line L' also passes through P; if P is not on L, L' remains a distinct line after the rotation.

The concept is commonly encountered in discussions of line-based transformations within computer graphics, CAD, and geometric modeling. It is often described informally to emphasize the rotation aspect of line manipulation, distinguishing linepivot from translations or scalings of a line. Linepivot is closely related to the general rotation about a point and to rigid-body transformations in the plane.

Key properties include that the rotation preserves distances from the pivot P and preserves the relative orientation of points on the line with respect to P. The angle between the original line L and the rotated line L' equals the chosen rotation angle theta. When theta is varied continuously from 0 to 2pi, L traces a family of lines that are all related by rotation about P.

See also: rotation, pivot point, rigid motion, line transformation.