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(A reflection would not preserve handedness; for instance, it would transform a left hand into a right hand.) To avoid ambiguity, a transformation that preserves handedness is known as a rigid motion, a Euclidean motion, or a proper rigid transformation. In dimension two, a rigid motion is either a translation or a rotation.
Reflection. Reflections, or mirror isometries, denoted by F c,v, where c is a point in the plane and v is a unit vector in R 2.(F is for "flip".) have the effect of reflecting the point p in the line L that is perpendicular to v and that passes through c.
A reflection in a line is an opposite isometry, like R 1 or R 2 on the image. Translation T is a direct isometry: a rigid motion. [1] In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.
reflection with respect to a plane, and a translation in that plane, a rotation about an axis perpendicular to the plane, or a reflection with respect to a perpendicular plane; glide reflection with respect to a plane, and a translation in that plane; inversion in a point and any isometry keeping the point fixed
A reflection through an axis. In mathematics, a reflection (also spelled reflexion) [1] is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.
Application of any rigid transformation (dual quaternion) or reflection to any object, including points, lines, planes and indeed other rigid transformations, is ~, where is object to be transformed. This is known as group conjugation or colloquially as the "sandwich product".
Its elements are called rigid motions or displacements. Rigid motions include the identity, translations, rotations (the rigid motions that fix at least a point), and also screw motions. Typical examples of rigid transformations that are not rigid motions are reflections, which are rigid transformations that fix a hyperplane and are not the ...
However, when a reflection is composed with a translation in any other direction, the composition of the two transformations is a glide reflection, which can be uniquely described as a reflection in a parallel hyperplane composed with a translation in a direction parallel to the hyperplane. A single glide is represented as frieze group p11g.