Geometric transformation combining reflection and translation
A glide reflection is the composition of a reflection across a line and a translation parallel to the line.This footprint trail has glide-reflection symmetry. Applying the glide reflection maps each left footprint into a right footprint and vice versa.
In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide") in a direction parallel to that hyperplane, combined into a single transformation. Because the distances between points are not changed under glide reflection, it is a motion or isometry. When the context is the two-dimensional Euclidean plane, the hyperplane of reflection is a straight line called the glide line or glide axis. When the context is three-dimensional space, the hyperplane of reflection is a plane called the glide plane. The displacement vector of the translation is called the glide vector.
When some geometrical object or configuration appears unchanged by a transformation, it is said to have symmetry, and the transformation is called a symmetry operation. Glide-reflection symmetry is seen in frieze groups (patterns which repeat in one dimension, often used in decorative borders), wallpaper groups (regular tessellations of the plane), and space groups (which describe e.g. crystal symmetries). Objects with glide-reflection symmetry are in general not symmetrical under reflection alone, but two applications of the same glide reflection result in a double translation, so objects with glide-reflection symmetry always also have a simple translational symmetry.
When a reflection is composed with a translation in a direction perpendicular to the hyperplane of reflection, the composition of the two transformations is a reflection in a parallel hyperplane. 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. A glide reflection can be seen as a limiting rotoreflection, where the rotation becomes a translation. It can also be given a Schoenflies notation as S2∞, Coxeter notation as [∞+,2+], and orbifold notation as ∞×.
geometry, a glidereflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide") in...
symmetry. Reflection in a line and glidereflection are preserved on expansion/contraction along, or perpendicular to, the axis of reflection and glide reflection...
as length. There are four types: translations, rotations, reflections, and glidereflections (see below § Classification). The set of Euclidean plane isometries...
2\theta \,),(x\sin 2\theta -y\cos 2\theta \,)).} A glidereflection is the composition of a reflection across a line followed by a translation in the direction...
Look up glide in Wiktionary, the free dictionary. Glide may refer to: Gliding flight, to fly without thrust Glide API, a 3D graphics interface Glide OS, a...
contains translations and may contain glidereflections, reflections along the long axis of the strip, reflections along the narrow axis of the strip, and...
to the plane, or a reflection with respect to a perpendicular plane glidereflection with respect to a plane, and a translation in that plane inversion...
from a simple motif like a line segment by repeated application of a glidereflection. Although the origin of the word is unclear, its first printed appearances...
lack of known segmented legs or limbs, coupled with the presence of glidereflection instead of symmetric segments, suggests that an arthropod classification...
reflection through a line (or plane) translation by a vector rotation of finite order around a point infinite rotation around a line in 3-space glide-reflection...
In crystals, screw rotations and/or glidereflections are additionally possible. These are rotations or reflections together with partial translation....
operations. That is, by turning screw rotations into rotations, glidereflections into reflections and moving all symmetry elements into the origin. Each crystallographic...
to the right and left from a zig-zag medial suture (thus exhibiting glidereflection, or opposite isometry). The genus Charnia was named for Charnwood Forest...
translation or a rotation. Any opposite isometry is either a reflection or a glidereflection. Coxeter 1969, p. 29 Coxeter 1969, p. 39 Beckman, F.S.; Quarles...
disputed whether the segments are offset from each other following glidereflection, and are thus isomers, or whether the segments are symmetric across...
(projection) or negative; the latter includes reflection, and combined with translation it includes glidereflection, rotation combined with a homothety and...
more, if the rings are indeed annual in nature. Some sea pens exhibit glidereflection symmetry, rare among extant animals. Sea pens are sometimes sold in...
The Lebesgue measure is a complete translation-invariant measure. Glidereflection Displacement Periodic function Lattice (group) Translation operator...
emphasize that it includes orientation-reversing isometries (reflections, glidereflections and improper rotations), as long as those isometries map this...
(ILS) was installed at the runway along with the installation of a glidereflection mirror. The security area at the runway was also expanded. Phase II...
contrast, a translation moves every point, a reflection exchanges left- and right-handed ordering, a glidereflection does both, and an improper rotation combines...
include glidereflection symmetry (a reflection followed by a translation) and rotoreflection symmetry (a combination of a rotation and a reflection). A dyadic...
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