transformscale21

Transformscale21 is a term used in software libraries and graphics pipelines to denote a scaling transformation with a fixed scale factor of 21. It may be implemented as a uniform scaling of coordinates in two- or three-dimensional space and is often used to resize geometry, images, or normalized coordinate data within a processing chain.

Mathematically, in 2D the transform maps a point (x, y) to (21x, 21y). In homogeneous coordinates a 3x3 matrix [ [21, 0, 0], [0, 21, 0], [0, 0, 1] ] can be used. In 3D the transform maps (x, y, z) to (21x, 21y, 21z) and is represented by a 4x4 matrix with diagonal entries 21, 21, 21, and 1.

It is commonly employed in graphics pipelines to scale models or textures, in procedural generation to adjust feature size, and in data preprocessing to normalize magnitudes for downstream algorithms. Depending on context, the term may appear as a function name, a method, or an element of a transformation stack.

Using a large factor such as 21 can affect precision, clipping, and interpretation of units. Inverse or rescaling operations are sometimes required to revert the transformation. The exact implementation details vary across libraries, and transformscale21 is not a universally defined standard.

See also: scaling transformation, affine transformation, homogeneous coordinates, 3D graphics, normalization.