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RescalingTransform

RescalingTransform
gives a TransformationFunction that rescales the region with coordinate ranges to , etc. to the region with coordinate ranges to , etc.
RescalingTransform
gives 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 :
In[1]:=
Click for copyable input
Out[1]=
This now maps to :
In[2]:=
Click for copyable input
Out[2]=
 
Rescaling the cube to :
In[1]:=
Click for copyable input
Out[1]=
This maps to :
In[2]:=
Click for copyable input
Out[2]=
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 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:
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