If is a fixed vector, known as the translation vector, and is the initial position of some object, then the translation function will … See more

The translation operator turns a function of the original position, , into a function of the final position, . In other words, is defined such that This operator is more abstract than a function, since defines a relationship between tw… See more

The set of all translations forms the translation group , which is isomorphic to the space itself, and a normal subgroup of Euclidean group . The quotient group of by is isomorphic to the group of rigid motions which fix a … See more

A translation is an affine transformation with no fixed points. Matrix multiplications always have the origin as a fixed point. Nevertheless, there is a common workaround using homogeneous coordinates to … See more

While geometric translation is often viewed as an active process that changes the position of a geometric object, a similar result can be achieved by a passive transformation that moves the coordinate system itse… See more

An object that looks the same before and after translation is said to have translational symmetry. A common example is a periodic function, which is an eigenfunction of a translation operator. See more

The graph of a real function f, the set of points , is often pictured in the real coordinate plane with x as the horizontal coordinate and as the vertical coordinate.
Starting from the graph of f, a horizontal translation … See more