This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# RescalingTransform

 RescalingTransform gives a TransformationFunction that rescales the region with coordinate ranges to , etc. to the region with coordinate ranges to , etc. RescalingTransformgives a TransformationFunction that rescales to the unit square, cube, etc.
• RescalingTransform works in any number of dimensions. In 2D, it transforms rectangles to rectangles, and in 3D cuboids to cuboids.
Rescaling the rectangle to :
This now maps to :
Rescaling the cube to :
This maps to :
Rescaling the rectangle to :
 Out[1]=
This now maps to :
 Out[2]=

Rescaling the cube to :
 Out[1]=
This maps to :
 Out[2]=
 Scope   (3)
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:
 Applications   (5)
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 is given by RescalingTransform:
This shows that and are inverses:
Rescaling transformation is a composition of scaling and translation:
Rescale provides a scalar version of RescalingTransform:
A collection of randomly rescaled cuboids:
New in 6