RescalingTransform

RescalingTransform[{{xmin,xmax},{ymin,ymax},},{{xpmin,xpmax},}]

gives a TransformationFunction that rescales the region with coordinate ranges xmin to xmax, etc. to the region with coordinate ranges xpmin to xpmax, etc.

RescalingTransform[{{xmin,xmax},{ymin,ymax},}]

gives a TransformationFunction that rescales to the unit square, cube, etc.

Details

Examples

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Basic Examples  (2)

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}:

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:

Properties & Relations  (3)

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:

Neat Examples  (1)

A collection of randomly rescaled cuboids:

Introduced in 2007
 (6.0)