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The translations here arise from the glide reflections, so this group is generated by a glide reflection and either a rotation or a vertical reflection. p11m [∞ +,2] C ∞h Z ∞ ×Dih 1 ∞* jump (THG) Translations, Horizontal reflections, Glide reflections: This group is generated by a translation and the reflection in the horizontal axis.
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. The line L is called the reflection axis or the associated mirror.
A blazed grating – also called echelette grating (from French échelle = ladder) – is a special type of diffraction grating. It is optimized to achieve maximum grating efficiency in a given diffraction order. For this purpose, maximum optical power is concentrated in the desired diffraction order while the residual power in the other orders ...
Glide reflection. 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 ...
A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L1. Then reflect P′ to its image P′′ on the other side of line L2. If lines L1 and L2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...
Reflections, or mirror isometries, denoted by F L, where L is a line in R 2. (F is for "flip"). This has the effect of reflecting the plane in the line L, called the reflection axis or the associated mirror. Glide reflections, denoted by G L,d, where L is a line in R 2 and d is a distance.
A reflection against an axis followed by a reflection against a second axis not parallel to the first one results in a total motion that is a rotation around the point of intersection of the axes. In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by ...
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D there is a line/axis of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable ...