linguistic:voice_change, information:extraction
In affine geometry, uniform scaling is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically). 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. When the scale factor is larger than 1, scaling is sometimes also called dilation or enlargement. When the scale factor is a positive number smaller than 1, scaling is sometimes also called contraction or reduction. In the most general sense, a scaling includes the case in which the directions of scaling are not perpendicular. It also includes the case in which one or more scale factors are equal to zero (projection), and the case of one or more negative scale factors. Scaling is a linear transformation, and a special case of homothetic transformation. In most cases, the homothetic transformations are non-linear transformations.