Rescaling the rectangle to :

This now maps {xmax,ymax} to {1,1}:

Rescaling the cube to :

This maps {xmax,ymax,zmax} to {1,1,1}:

Transforming the rectangle to the rectangle :

This transforms the midpoint in the source rectangle to the midpoint in the target rectangle:

Transformation applied to a 2D shape:

Transformation applied to a 3D shape:

Transforming graphics primitives:

Compute the transform from user coordinates to Scaled coordinates in 2D:

Transform some particular coordinates:

Compute the transform from Scaled to user coordinates:

Transform some particular coordinates:

Compute the transform from user coordinates to Scaled coordinates in 3D:

Transform some particular coordinates:

Compute the transform from Scaled to user coordinates:

Transform some particular coordinates:

Transform from user coordinates to Scaled coordinates with a particular PlotRange:

Specify the disk in user coordinates and the circle in Scaled coordinates:

Compute the model view transform for OpenGL, using the axis pointing out from the screen:

Transform user coordinates to the standard model coordinates:

The inverse of RescalingTransform[{{l₁,u₁},…},{{L₁,U₁},…}] is given by RescalingTransform[{{L₁,U₁},…},{{l₁,u₁},…}]:

This shows that t1 and t2 are inverses:

Rescaling transformation is a composition of scaling and translation:

Rescale provides a scalar version of RescalingTransform:

A collection of randomly rescaled cuboids: