Difference between revisions of "184: Matrix Transform"

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{{comic
 
{{comic
 
| number    = 184
 
| number    = 184
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| date      =  
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| date      = November 15, 2006
 
| title    = Matrix Transformation
 
| title    = Matrix Transformation
 
| image    = matrix_transform.png
 
| image    = matrix_transform.png
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| titletext = In fact, draw all your rotational matrices sideways. Your professors will love it! And then they'll go home and shrink.
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| titletext = In fact, draw all your rotational matrices sideways. Your professors will love it! And then they'll go home and shrink.
 
}}
 
}}
  
 
==Explanation==
 
==Explanation==
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A rotational matrix transformation (i.e. the big brackets with a few "cos" and "sin" in them) is used in computer graphics to rotate an image. The product of the transform matrix and the argument vector (a1, a2) is a rotated version of the argument vector. Here, the joke is that the author turned the image of the vector rather than writing the correct answer.
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A rotational matrix transformation (i.e. the big brackets with a few "cos" and "sin" in them) is used in computer graphics to rotate an image. The product of the transform matrix and the argument vector (a1, a2) is a rotated version of the argument vector. Here, the joke is that the author turned the image of the vector rather than writing the correct answer. Rotational matrix transformations are a special case of the general linear matrix transform, which can do other things to images, including shrinking them. However, turning the rotational matrix sideways does not make it a shrinking matrix.
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Rotational matrix transformations are a special case of the general linear matrix transform, which can do other things to images, including shrinking them. However, turning the rotational matrix sideways does not make it a shrinking matrix.
 
  
 
==Transcript==
 
==Transcript==
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{{comic discussion}}
 
{{comic discussion}}
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[[Category:Math]]

Revision as of 00:54, 13 February 2013

Matrix Transformation
In fact, draw all your rotational matrices sideways. Your professors will love it! And then they'll go home and shrink.
Title text: In fact, draw all your rotational matrices sideways. Your professors will love it! And then they'll go home and shrink.

    Explanation

    A rotational matrix transformation (i.e. the big brackets with a few "cos" and "sin" in them) is used in computer graphics to rotate an image. The product of the transform matrix and the argument vector (a1, a2) is a rotated version of the argument vector. Here, the joke is that the author turned the image of the vector rather than writing the correct answer. Rotational matrix transformations are a special case of the general linear matrix transform, which can do other things to images, including shrinking them. However, turning the rotational matrix sideways does not make it a shrinking matrix.

    Transcript


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    Discussion

    This baby needs a bit more rigor. --Quicksilver (talk) 05:23, 24 August 2013 (UTC)

    I think this is also a reference to the movie "The Matrix", specifically the now famous scene where Neo does 90degree back bending to dodge bullets. 173.245.62.84 07:54, 7 April 2014 (UTC)

    Maybe another reference: They'll go home (translation matrix) and shrink (scale matrix). Translation, scale and rotate are probably the most popular linear transformations. 108.162.218.89 23:39, 14 May 2014 (UTC)

    I've been teach that the rotation was anticlockwise. Do computer turn the other way round that math teachers? by the way (left ( matrix{0 # 1 ## -1 # 0} right )*left ( binom 1 0 right)=left (binom 0 1 right) if you know what i mean. get fun. Yomismo (talk) 09:28, 18 March 2015 (UTC)

    IIIII'm pretty sure the "shrink" is a typo, and he meant "drink". My evidence is the xkcd book, where he just flat-out says it. 162.158.178.97 (talk) 12:57, 16 April 2019 (UTC) (please sign your comments with ~~~~)

    On clockwise/counterclockwise: I think Randall is using screen coordinates (where the top left is (0,0) and the point (1,4) is one below (1,3)), instead of standard Cartesian coordinates where the bottom left is (0,0) and going from (1,3) to (1,4) means going upwards. 162.158.155.170 13:07, 17 May 2019 (UTC)

    RE positive or negative rotation: The rotation of the vector is 90 degrees in the NEGATIVE direction, but also notice that the matrix has the off-diagonal minus sign in the opposite place from where it would be for a positive rotation in a right-handed coordinate system. The interpretation of this is that either a) RM is using a left-handed coordinate system, instead of the typical right-handed one, or b) he took the matrix for rotating by -90 degrees and simplified by moving in the minus out of the trig functions. Either way, the math is correct, but slightly confusing. (source: I teach CS 184) 136.144.42.175 (talk) 22:46, 22 February 2026 (UTC) (please sign your comments with ~~~~)
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