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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.
An environment texture mapped onto models of spoons, to give the illusion that they are reflecting the world around them. In computer graphics, reflection mapping or environment mapping [1] [2] [3] is an efficient image-based lighting technique for approximating the appearance of a reflective surface by means of a precomputed texture.
An xy-Cartesian coordinate system rotated through an angle to an x′y′-Cartesian coordinate system In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and ...
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.
Also, cube mapping provides a much larger capacity to support real-time rendering of reflections relative to sphere mapping because the combination of inefficiency and viewpoint dependency severely limits the ability of sphere mapping to be applied when there is a consistently changing viewpoint.
Transformations with reflection are represented by matrices with a determinant of −1. This allows the concept of rotation and reflection to be generalized to higher dimensions. In finite-dimensional spaces, the matrix representation (with respect to an orthonormal basis ) of an orthogonal transformation is an orthogonal matrix .
Reflection map may refer to: Reflection mapping in computer graphics; A reflection (mathematics), specifically an element of a reflection group; an element of a Weyl group; Reflection map (logic optimization), a conventional Gray code Karnaugh map in logic optimization
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