Search results
Results from the WOW.Com Content Network
(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.
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.
one of these groups in an m-dimensional subspace combined with another one in the orthogonal (n−m)-dimensional space; Examples in 3D of combinations: all rotations about one fixed axis; ditto combined with reflection in planes through the axis and/or a plane perpendicular to the axis
As the special Euclidean group is a subgroup of index two of the Euclidean group, given a reflection r, every rigid transformation that is not a rigid motion is the product of r and a rigid motion. A glide reflection is an example of a rigid transformation that is not a rigid motion or a 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".
The set of all reflections in lines through the origin and rotations about the origin, together with the operation of composition of reflections and rotations, forms a group. The group has an identity: Rot(0). Every rotation Rot(φ) has an inverse Rot(−φ). Every reflection Ref(θ) is its own inverse. Composition has closure and is ...