# 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.

# 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:

Wolfram Research (2007), RescalingTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/RescalingTransform.html.

#### Text

Wolfram Research (2007), RescalingTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/RescalingTransform.html.

#### CMS

Wolfram Language. 2007. "RescalingTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RescalingTransform.html.

#### APA

Wolfram Language. (2007). RescalingTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RescalingTransform.html

#### BibTeX

@misc{reference.wolfram_2024_rescalingtransform, author="Wolfram Research", title="{RescalingTransform}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/RescalingTransform.html}", note=[Accessed: 16-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_rescalingtransform, organization={Wolfram Research}, title={RescalingTransform}, year={2007}, url={https://reference.wolfram.com/language/ref/RescalingTransform.html}, note=[Accessed: 16-June-2024 ]}