Книга: Scaling Geometry: Scaling Geometry, Euclidean Geometry, Isotropy, Linear Map, Scale Factor, Homothetic Transformation, Similarity Geometry, Anisotropy, Scale Ratio, Scale Map

High Quality Content by WIKIPEDIA articles! In Euclidean geometry, uniform scaling or isotropic scaling is a linear transformation that enlarges or increases or diminishes objects the scale factor is the same in all directions it is also called a homothety. 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, but some school text books specifically exclude this possibility. More general is scaling with a separate scale factor for each axis direction. Non-uniform or anisotropic scaling is obtained when at least one of the scaling factors is different from the others a special case is directional scaling, in one direction. Non-uniform scaling changes the shape of the object a rectangle may change into a rectangle of a different shape, but also in a parallelogram, the angles between lines parallel to the axes are preserved, but not all angles.