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In Euclidean geometry, uniform scaling (or isotropic scaling [1] ) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions. The result of uniform scaling is similar (in the geometric sense) to the original. A scale factor of 1 is normally allowed, so that congruent shapes are also classed as similar. Uniform scaling happens, for example, when enlarging or reducing a photograph, or when creating a scale model of a building, car, airplane, etc. More general is scaling with a separate scale factor for each axis direction. Non-uniform scaling ( anisotropic scaling ) is obtained when at least one of the scaling factors is different from the others; a special case is directional scaling or stretching (in one direction). Non-uniform scaling changes the shape of the object; e.g. a square may change into a rectangle, or into a parallelogram if the sides of the square are not parallel to the scaling axes (the ...

A translation moves every point of a figure or a space by the same amount in a given direction. A reflection against an axis followed by a reflection against a second axis parallel to the first one results in a total motion which is a translation. In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction. In Euclidean geometry a transformation is a one-to-one correspondence between two sets of points or a mapping from one plane to another. [1] A translation can be described as a rigid motion: the other rigid motions are rotations, reflections and glide reflections. 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 Tδ {displaystyle T_{mathbf {delta } }} such that Tδ f(v)=f(v+δ ).{displaystyle T_{mathbf {delta } }f(mathbf {v} )=f(mathbf {v} +mathbf {delta } )....