A NOTE ON RELATION BETWEEN POINT-LINE DISPLACEMENT AND EQUIFORM TRANSFORMATION

Abstract

− The present paper studies the relation between the point-line displacement and theequiform transformation in Euclidean 3-space R3. A point-line can be transformed into another pointline via an equiform transformation. Observing that a point-line is nothing but a line element whenits reference point is the origin of the coordinate system, we show that this transformation can also beperformed by using dual quaternions

Keywords

• − line geometry
• line element
• dual quaternion
• equiform kinematics