Scaling (/m/02_pxd)

In Euclidean geometry, uniform scaling is a linear transformation that enlarges or shrinks objects by a scale factor that is the same in all directions. The result of uniform scaling is similar 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 is obtained when at least one of the scaling factors is different from the others; a special case is directional scaling or stretching. 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. It occurs, for example, when a faraway billboard is viewed from an oblique angle, or when the shadow of a flat object falls on a surface that is not parallel to it.
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