A translation, or translation operator, is an affine transformation of Euclidean space which moves every point by a fixed distance in the same direction. It can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In other words, if v is a fixed vector, then the translation Tv will work as Tv(p) = p + v.
Let us have a clear visualization of this. In day to day life we use computers in all fields. Let us consider this window. This window if maximized to full dimensions of the screen is the reference plane. Imagine one of the corners as the reference point or origin (0, 0).
Consider a point P(x, y) in the corresponding plane. Now the axes are shifted from the original axes to a distance (h, k) and this is the corresponding reference axes. Now the origin (previous axes) is (x, y) and the point P is (X, Y) and therefore the equations are:
X = x − h or x = X + h or h = x − X and Y = y − k or y = Y + k or k = y − Y.
Replacing these values or using these equations in the respective equation we obtain the transformed equation or new reference axes, old reference axes, point lying on the plane.
Read more about this topic: Transformation (function)
Famous quotes containing the word translation:
“Whilst Marx turned the Hegelian dialectic outwards, making it an instrument with which he could interpret the facts of history and so arrive at an objective science which insists on the translation of theory into action, Kierkegaard, on the other hand, turned the same instruments inwards, for the examination of his own soul or psychology, arriving at a subjective philosophy which involved him in the deepest pessimism and despair of action.”
—Sir Herbert Read (1893–1968)
“Well meant are the wounds a friend inflicts, but profuse are the kisses of an enemy.”
—Bible: Hebrew, Proverbs 27:6.
KJ translation reads: Faithful are the wounds of a friend.
“To translate, one must have a style of his own, for otherwise the translation will have no rhythm or nuance, which come from the process of artistically thinking through and molding the sentences; they cannot be reconstituted by piecemeal imitation. The problem of translation is to retreat to a simpler tenor of one’s own style and creatively adjust this to one’s author.”
—Paul Goodman (1911–1972)