Linear Transformations and GraphicsComplex

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Linear Transformations and GraphicsComplex

Postby Jose_Luis_Gomez » Wed Feb 17, 2010 10:52 pm

Hello dear group

I have created two tutorials for students that are learning about linear transformations, with emphasis in the geometrical representation.

These students first have a traditional class where they calculate and draw by hand the effect of 2D linear transformations on a unitary square.

A second class in the laboratory they reproduce the examples and solve the exercises of this Mathematica tutorial for 2D transformations and GraphicsComplex: http://homepage.cem.itesm.mx/lgomez/data/LAD02.pdf

In a third class in the laboratory they do the same with a 3D tutorial:
http://homepage.cem.itesm.mx/lgomez/data/LAD03.pdf

I hope you find them useful
best regards
Jose
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I have a question

Postby Jose_Luis_Gomez » Mon Feb 22, 2010 4:45 pm

Dear group, I have a question: I have used the standard command GeometricTransformation to let my students explore the geometrical effect of a linear transformation, please see the second half of this computer-lab work: http://homepage.cem.itesm.mx/lgomez/data/LAD02.pdf . As you can see, I try using only standard Mathematica commands, without the "advanced" notation shortcuts like @ &, etc. My students did some similar work by hand before going to the lab.

Now, for our next lab session, I want my students to take an image of "The Ambassadors", by Holbein http://en.wikipedia.org/wiki/File:Holbe ... sadors.jpg and then apply to the position of each pixel a linear transformation to generate an image similar to this one: http://commons.wikimedia.org/wiki/File: ... phosis.jpg so that the hidden skull is clearly revealed. My problem is that I want them to do it with simple standard Mathematica commands (they are NOT students of engineering nor Math, their career is more Art-oriented), I would like to have something similar to the command GeometricTransformation, where they only enter the Image, the Matrix, and they get the result, if possible I do Not want them to use Mathematica commands to actually mutliply the matrix times each pixel position (they already have done that by hand in very very simple "images")

Do you have any suggestions?

Best regards
Jose
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Re: Linear Transformations and GraphicsComplex

Postby Michael_Morrison » Tue Mar 16, 2010 4:13 am

Hi, Jose,

I'm not sure how to use GeometricTransformation here since your file isn't a Graphics object. The folks at MathGroup (http://forums.wolfram.com/mathgroup/) may be able to help.

However, I did find a Demonstration that involves image warping:
http://demonstrations.wolfram.com/ImageWarping/

You could download the source code and simply replace the image of the bear with an image of the painting, and then manually manipulate the image to the desired shape/proportions...

Regards,
Michael
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Re: Linear Transformations and GraphicsComplex

Postby Jose_Luis_Gomez » Wed Mar 17, 2010 4:22 pm

Thanks Michael,

That is an interesting demonstration, and useful for my course indeed.

José
México
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