# Talk:Transformations and Matrices

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The content on this page was written by Steve Cunningham. I have formatted it for the website and made the main image and image description.

Nordhr 16:36 1 July 2011

## Checklist

### Message to the Future

• There was an applet on a previous version of this page that I could not get to work on this page. It would be nice if at some point it was put onto this page. I would put this in a future messages section, but I don't still have the tag. I know that if I edit the page with the form, other things will get deleted.
• I don't have any further messages to the future for this page.

### References and Footnotes

• All images have in their discussion section that they are from Steve Cunningham (except for the main image, which I create).
• There aren't any direct quotes.
• Steve Cunningham wrote this page from his knowledge, so I put this in the references section.

### Good Writing

#### Context

• I think that transformation matrices have a very clear reason why they are interesting (stated on the page in prose).

#### Quality of prose and structuring

• I think that the prose was written very well and that Steve Cunningham's discussion is clear and fluid.
• Each section is a different type of transformation or something new to do with a matrix.
• The matrix page is a helper page because it will be useful in other places.
• The math is introduced when necessary to show how to do a specific transformation with a matrix.
• There was some discussion about changing the order to put the transformations in the basic description section, but I like the way the page is now.
• I do think that the majority of the content should be moved down to the "more mathematical" section. We want to avoid matrices in a "basic description"
I moved the sections with matrices into the more mathematical explanation. --Nordhr
• I encourage breaking up the following chunk of text a bit and adding a bit more explaination "Here a positive-angle is from the X-axis towards the Z-axis, but $X \times Z = -Z \times X = -Y$, so the rotation axis dimension is pointing in the opposite direction from the Y-axis. Thus a the angle for the rotation is the negative of the angle we would see in the axes above, and since cos is an even function but sin is odd, we have the rotation matrix"
I reworded that section to make it more understandable. Is that what you had intended? -- Nordhr

#### Integration of Images and Text

• Images are referred to and text points out why they are there and what should be gotten from them.

#### Connections to other mathimatical topics

This page is said to be in the field of geometry, but it is at least as much in algebra. I suggest that it be listed as both algebra and geometry. SteveC
Good thought! I added it to algebra as well. --Nordhr

• This page is connected to others though the graphics page.
• There is a link on this page to the matrix page.

In several places there is a mention of homogeneous ooordinates or of affine transformations. These should link to the page on [2D, 3D, 4D real spaces; affine spaces; homogeneous coordinates] when that page is ready. SteveC
I added that it should be linked in a 'messages to the future' section, that way someone will come back and link the pages once there is a page to link to. --Nordhr

#### Examples, Calculations, Applications, Proofs

• There are numerical examples for all transformations.
• Equations for transformations are also provided.

The rotation inverse would probably be better if the matrices for the original rotation and the inverse rotation were given; probably it is enough to give it for a 2D example. SteveC
I added in an example. --Nordhr

The pseudocode for the rabbit head has errors that come from the source, not Nordhr. After each pop there should be a statement push so that each set of actions has its own transformation that is removed when it is finished. My apology for the error. SteveC
Good catch-all fixed :). --Nordhr

• In your first example of composing the two matrices, I'd encourage explaining what type of rotation the second matrix does all on its own. Perhaps adding pictures with what matrix would do individually would help the reader see what's going on
I added images to explain what the different matrices did apart and together. --Nordhr

#### Mathematical Accuracy and precision of language

• The page has been proofread by me and others, so hopefully we have ironed out all of the mathematical kinks.
• I feel that Steve Cunningham did a good job in making the page easy to read while still very informative.
• Somewhere on the page, can you make some note about what you mean by homogenous coordinates?
I was looking through the other graphics pages, and the 2D, 3D, 4D real spaces page is going to have a section dedicaded to homogeneous coordinates. I added to the 'future work' section that this page should link to that section of that page once it has been created. --Nordhr

#### Layout

• Short paragraphs with images and symbols breaking the page up nicely.
• Each section is hidden so one type of transformation can be viewed on its own. I think it looks very organized.
• There is a little whitespace around images and matrices, but after trying different layouts, this is my favorite.
• Images are centered or right aligned to avoid margin changes.
• Images are entirely in the correct section.
• I can't get the main hide/show on the page to look nice. I got the rest of them working, but I can't get this one to stop displaying the html tag. I wanted to fix it with using NumChars = 8, because I think that would be the best way to fix it. I would appreciate help with it. :)
• If one shrinks the page excessively, formulas stick over into the blue on the right side, but they stay aligned with each other. The scroll bar works to view the entire image. I found no other window size issues.
• There are a couple of formatting issues in the rotation section: a theta that doesn't appear correctly and a br that lost a bracket
I found those two places and fixed them. --Nordhr