Translation (Geometry)
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In Euclidean geometry, a translation is moving every point a constant distance in a specified direction. It is one of the rigid motions (other rigid motions include rotation and reflection). A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. A translation operator is an operator T_mathbf{delta} such that T_mathbf{delta} f(mathbf{v}) = f(mathbf{v}+mathbf{delta}). If v is a fixed...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In Euclidean geometry, a translation is moving every point a constant distance in a specified direction. It is one of the rigid motions (other rigid motions include rotation and reflection). A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. A translation operator is an operator T_mathbf{delta} such that T_mathbf{delta} f(mathbf{v}) = f(mathbf{v}+mathbf{delta}). If v is a fixed vector, then the translation Tv will work as Tv(p) = p + v. If T is a translation, then the image of a subset A under the function T is the translate of A by T. The translate of A by Tv is often written A + v.
