On point-line geometry and displacement

A framework and the relevant algebraic treatment concerning point-line positions and displacements are explored using dual quaternion algebra. A screw or a dual vector is used to represent a point-line and the pitch is used to measure the endpoint location along the point-line. A point-line operator is developed to express a point-line transformation. The transformation allows a point-line to be considered as an independent rigid element having a completely specified motion without invoking rigid body transformation.