Built-in Mathematica Symbol

RescalingTransform

RescalingTransform[{{x_min, x_max}, {y_min, y_max}, ...}, {{xp_min, xp_max}, ...}]
gives a TransformationFunction that rescales the region with coordinate ranges x_min to x_max, etc. to the region with coordinate ranges xp_min to xp_max, etc.

RescalingTransform[{{x_min, x_max}, {y_min, y_max}, ...}]
gives a TransformationFunction that rescales to the unit square, cube, etc.

MORE INFORMATION

RescalingTransform gives a TransformationFunction which can be applied to vectors.

RescalingTransform works in any number of dimensions. In 2D, it transforms rectangles to rectangles, and in 3D cuboids to cuboids.

EXAMPLES

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Basic Examples (2)

Rescaling the rectangle [xmin, xmax]×[ymin, ymax] to [0, 1]×[0, 1]:

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

Rescaling the cube [xmin, xmax]×[ymin, ymax]×[zmin, zmax] to [0, 1]×[0, 1]×[0, 1]:

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

Rescaling the rectangle [xmin, xmax]×[ymin, ymax] to [0, 1]×[0, 1]:

In[1]:=

Out[1]=

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

In[2]:=

Out[2]=

Rescaling the cube [xmin, xmax]×[ymin, ymax]×[zmin, zmax] to [0, 1]×[0, 1]×[0, 1]:

In[1]:=

Out[1]=

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

In[2]:=

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 z 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: