9860

Decomposing Rotations into Shear Mappings

Decomposing rotation matrices into three shear matrices, one can rotate an image an arbitrary number of degrees by simply performing shear operations. This allows rotations to be performed in basic image-editing software without free rotate, such as Paint.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The specific choices for and are explained in [1]. Using these, I manually computed the height and width of the resulting cropped image and used these values for the cropping functions. Similar calculations can be performed for counterclockwise rotations, but I restricted the values for here to the range 0 to 90 in order to program one case.
Try out your own image in the "myimage" variable. The coin image provided is from Wikimedia Commons.
Reference
[1] DataGenetics. "Rotating Images" (blog). (Oct 8, 2013) datagenetics.com/blog/august32013/index.html.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+