Xerox/WH PDF Part 20 Affine Transforms

Since Hermitian appears to be a bit confused, I have added the vectors. I thought it was self evident, but apparently I was mistaken

Hermitian asked for some help in obtaining the formulas. Let me show how a rotation, scaling and translation operation can be rewritten as a single matrix.The math is not too hard but I will walk through it in small steps for those who are interested in following where the data lead us.

The operation is as follows, the a b c d e cm can be represented as

|x'|   | a   c   e| |x|
|y'| = | b   d   f| |y|
|1 |   | 0   0   1| |1|

Two observations:

1. Although the affine transforms are two dimensional, the only way to add translation is to extend it with a ‘fake’ third dimension.

2. You can map this transformation to the PDF transformation which is row based by observing the trivial transformation:

X’ = A X

X’T=(A X)T
X’T=XT AT

this is basic Matrix 101

Or, alternatively written

                        | a  b  0 |
[ x'  y'  1]  = [x y 1] | c  d  0 |
                        | e  f  1 |

Just as the manual shows:

Now how hard is that… Of course, anyone with a bit of time (10 minutes) could have written them out in the PDF notation and found the same results…

affinematrix
rotate, scale, translate

| 1  0  tx| |sx    0    0 | | cos a  -sin a   0| 
| 0  1  ty| |0     sy   0 | | sin a   cos a   0| 
| 0  0  1 | |0     0    1 | |  0       0      1|

| 1  0  tx| | sx  cos a   -sx sin a  0 |
| 0  1  ty| | sy sin a     sy cos a  0 |
| 0  0  1 | | 0            0        1 |

| sx cos a   -sx sin a  tx |
| sy sin a    sy cos a  ty |
| 0           0         1  |

x'=sx cos a x  - sx sin a y + tx
y'=sy sin a x  + sy cos a y + ty

a**2+c**2 =sx**2
b**2+d**2 =sy**2
e=tx
f=ty

Scale, rotate, translate

| 1  0  tx| | cos a  -sin a   0| |sx    0    0 | 
| 0  1  ty| | sin a   cos a   0| |0     sy   0 | 
| 0  0  1 | |  0       0      1| |0     0    1 | 

| 1  0  tx| | sx cos a  -sy sin a  0 |
| 0  1  ty| | sx sin a   sy cos a  0 |
| 0  0  0 | | 0             0      1 |

| sx cos a  -sy sin a  tx |
| sx sin a   sy cos a  ty |
| 0          0          1 |

x'=sx cos a x  - sy sin a y + tx
y'=sx sin a x  + sy cos a y + ty

a**2 + b**2 = sx**2
c**2 + d**2 = sy**2
e=tx
f=ty

For the cm transform we are looking at the same results, whether we rotate before we scale or scale before we rotate because of the fact that we rotate 0/90 degrees.

798.72 0.00 0.00 614.40 -3.36 -1.20 cm /XIPLAYER0 Do Q

sx= 798.72
sy= 614.40
a = 0
sin a = 0 
cos a = 1

0 798.72 -614.4 0 613.2 -3.36 cm /Im1 DO Q

rotate, scale, translate

a = 90
sx= 614.4
sy= 798.72

x' = -614.4 y + tx
y' = 798.72 x + ty

scale, rotate, translate

sx= 798.72
sy= 614.4
a = 90 degrees

x'= -614.4 y + tx
y'= 798.72 x + ty

30 thoughts on “Xerox/WH PDF Part 20 Affine Transforms

  1. NBC and MATRIX MATH

    My first comment is that you did not include your coordinate column vectors [x y z] and [x’ y’ z’] in carrying out the matrix multiplications. Therefore you haven’t shown that your equations

    x ‘= sx cos a x – sy sin a y + tx

    y ‘= sx sin a x + sy cos a y + ty

    are the product of your calculations.

    My second comment is that your first case concatenated (x’,y’) coordinate system is non-orthogonal. Consequently, you cannot apply the Pythagorean Theorem to calculate the distance between points.

    The family of Affine Transformations includes nonorthogonal systems as well as orthogonal systems

    The nonorthogonal Affine Coordinate Transformations in two dimensions are often referred to as “Oblique Coordinates”. I am very familiar with oblique coordinates. One cannot grasp the Special Theory of Relativity without a working knowledge of oblique coordinates.

    Now the bottom line conclusion in your post was that the order in which the three simple transformations are applied doesn’t matter. In other words the calculation is commutative.

    See: https://en.wikipedia.org/wiki/Commutative_property

    Now the PDFReference14.pdf page 143 requires that these simple transformations MUST be applied in the order specified. The PDF specification would not lay down this rule if it didn’t matter.

    From PDFReference14.pdf starting on page 143 and continuing on page 144.


    If several transformations are combined, the order in which they are applied is
    significant. For example, first scaling and then translating the x axis is not the
    same as first translating and then scaling it. In general, to obtain the expected
    results, transformations should be done in the following order:

    1. Translate
    2. Rotate
    3. Scale or skew

    Figure 4.6 shows the effect of the order in which transformations are applied. The
    figure shows two sequences of transformations applied to a coordinate system.

    After each successive transformation, an outline of the letter n is drawn. Graphics CHAPTER 4
    144

    FIGURE 4.6 Effect of transformation order

    The transformations shown in the figure are as follows:

    • A translation of 10 units in the x direction and 20 units in the y direction
    • A rotation of 30 degrees
    • A scaling by a factor of 3 in the x direction

    In the figure, the axes are shown with a dash pattern having a 2-unit dash and a
    2-unit gap. In addition, the original (untransformed) axes are shown in a lighter
    color for reference. Notice that the scale-rotate-translate ordering results in a
    distortion of the coordinate system, leaving the x and y axes no longer perpendic-
    ular, while the recommended translate-rotate-scale ordering does not.

    NBC you know just enough to be dangerous.

  2. Several times NBC has posted that Adobe Illustrator is confused.

    Now, more than once, I have stated the fact that the WH LFCOLB PDF file opens correctly in two Adobe Illustrator 16 (CS6) and Adobe Illustrator 17 (CC). Additionally the same PDF file opens in the correct orientation in Adobe Acrobat XI Pro, Adobe Reader XI, PDF XChange Viewer Pro, PDF XChange Editor Pro and Inkscape. It also opens in the correct orientation in PDF Transformer 3.0 Pro and the OCR finds all of the printed form text and typed text.

    Thus Adobe Illustrator is not “confused” when it opens the WH LFCOLB. I had previously stated that the LFCOLB PDF image “opens” in the correct portrait orientation in Adobe Illustrator 16 (CS6) and Adobe Illustrator 17 (CC). Thus we can safely assume that the WH LFCOLB PDF file is device independent for Adobe Illustrator and all the other named graphics programs.

    But we know even more! We know that the WH PDF opens in Illustrator without any warnings or error messages. Moreover we know that it opens as a layered PDF file in Illustrator.

    Now the reader may not appreciate the importance of these facts in light of the ongoing debate that is raging on this blog.

    These facts are real evidence that the WH LFCOLB PDF file was created by Adobe Illustrator. Adobe only guarantees PDF file compatibility with Illustrator if the PDF file was created by Illustrator. Just any old PDF file will not do. Typically Illustrator will not even open PDF files created by some other programs. It is not unusual for Illustrator to to open a PDF file but give the message “This document contains PDF objects that have been reinterpreted.” Most PDF files which are mostly text will open with font substitution warnings.

    Based on the many posts of NBC’s dealing with the interaction between the Xerox Workstation 7535 and MAC OS Preview we must conclude that PDF files created on the Xerox Workcenter 7535 are not device independent with respect to preview.

    Thus it is reasonable that PDF files created by the scan to PDF option on the Xerox Workcenter 7535 and then printed to PDF from Preview would not always be device independent for Adobe Illustrator.

    And we already know that the Xerox scan to PDF file of the WH LFCOLB opens in landscape mode in Illustrator rather than portrait mode.

  3. “Thus Adobe Illustrator is not “confused” when it opens the WH LFCOLB. I had previously stated that the LFCOLB PDF image “opens” in the correct portrait orientation in Adobe Illustrator 16 (CS6) and Adobe Illustrator 17 (CC). Thus we can safely assume that the WH LFCOLB PDF file is device independent for Adobe Illustrator and all the other named graphics programs.”

    The WH LFBC was saved in Preview. We don’t know how it would have loaded had it not been saved in Preview.

    Open the 7535 pdf in illustrator, it will be in landscape mode while opening in portrait mode in other Adobe products. Now save it as a PDF in Preview. It will now open in Portrait mode in Illustrator.

    Now open the President’s 2010 tax return pdf in Illustrator it will open in landscape mode but in portrait mode in all other Adobe products. Now save it as a pdf in Preview , it will now open in Illustrator in Portrait mode.

    Also none of these programs generated a warning message in Illustrator and they open as layered PDF files.

  4. My first comment is that you did not include your coordinate column vectors [x y z] and [x’ y’ z’] in carrying out the matrix multiplications. Therefore you haven’t shown that your equations

    ROTFL… Really?… Wow, I must have really overestimated your familiarity with matrix multiplications…

    My second comment is that your first case concatenated (x’,y’) coordinate system is non-orthogonal. Consequently, you cannot apply the Pythagorean Theorem to calculate the distance between points.

    ROTFL… I am not using the Pythagorean Theorem to calculate distances I use the simple fact that cos**2 + sin**2 = 1. My goodness, this is getting quite entertaining…

    Now the bottom line conclusion in your post was that the order in which the three simple transformations are applied doesn’t matter. In other words the calculation is commutative.

    That is incorrect. What I showed is that for the rotations in question, the order does not matter. In general the matrix multiplications are not commutate, that’s matrix 101…

    Sigh… I need to perhaps take even smaller steps to accommodate Hermitian’s new found math skills…

    Somehow I had expected him to at least understand the basics..

    Boy was I wrong… And of course, he still has not shown that my findings were wrong, he has only shown that he has come to realize that matrix multiplications are not commutative… Wow…

  5. These facts are real evidence that the WH LFCOLB PDF file was created by Adobe Illustrator.

    ROTFL.. Even though the PDF was created by Preview… You’re hilarious.

    You are reaching conclusions that are not supported by the data.

    I have shown how a Xerox captured file when saved in preview, renders correctly in Illustrator but Illustrator does not render the original Xerox one correctly as it opens rotated.

    I have shown how this can be understood and I have shown how all data points strongly to a workflow that starts with a Xerox scanner and ends with a Preview saved PDF.

    It explains the rotated objects, the similarity in letters, the embedded jpeg comment, the quantization matrices being the same, and so on and so on..

    You can lead a horse to water, but you cannot make it drink.

    Logic is just not Hermetian’s strongest point and the fact that he considers to ignore all the evidence that points towards the workflow I have outlined is somewhat fascinating.
    But amongst birthers the confirmation bias tends to be quite strong relieving birthers of any requirements to have to support their analysis based on factual evidence and a competing hypothesis.

    Even if the document were created with Adobe tools, and there is no evidence of this, this would still not mean a necessary forgery.

    I am sure that the reader understands these simple facts.

    The fact that illustrator cannot properly handle some files, which are properly opened by other Adobe tools, should have been a fair warning to our friend.

    He still has failed to notice how based on the workflow I outlined, he can make predictions about the monochrome layers in the Xerox document.

    I will give him another day to think about it. It’s a powerful hypothesis that can be tested…

  6. Open the 7535 pdf in illustrator, it will be in landscape mode while opening in portrait mode in other Adobe products. Now save it as a PDF in Preview. It will now open in Portrait mode in Illustrator.

    Now open the President’s 2010 tax return pdf in Illustrator it will open in landscape mode but in portrait mode in all other Adobe products. Now save it as a pdf in Preview , it will now open in Illustrator in Portrait mode.

    Also none of these programs generated a warning message in Illustrator and they open as layered PDF files.

    I predict that Hermitian will ignore your observations and continue to claim forgery… Even though he has failed so far to show any evidence of such… He has allowed his ignorance of how the document was ‘created’ to conclude “therefore forged” without testing a real hypothesis. When I presented him with an actual workflow which creates all the artifacts, he still insists on a forgery…

    That is just hilarious… I had never thought to capture a live example of ‘confirmation bias’.

    He has totally ignored how all the evidence, and now even more (quantization matrices) all point to a single workflow which includes a Xerox scanner and a Mac OS.

  7. Thank the White House for providing a scanned document on a Xerox WorkCentre 7655🙂

    I believe that I can now explain all the artifacts in the PDF through this workflow, including artifacts that had remain hidden from ‘researchers’ who failed to use low level tools to look at the raw data streams.

    I am of course still interested in any competing hypothesis that goes beyond our ignorance or merely states that a forger could have followed all the same steps in ‘creating’ its document. I am particularly interested as to why such a ‘forger’ would include rotated bitmaps and jpeg images and then rotates them into place. Or why a forger would align two of the sides of all the bitmaps at 8 bit boundaries or why a forger would have two of the sides of all the bitmaps end touching the internal object. These are all artifacts that are created by the Xerox scanner, as I have shown quite conclusively.

    I believe that, unless Hermetian comes up with a real issue, not the realization that matrix multiplications are in general not commutative, we can finally lay this all to rest.

    I will be preparing my posting announcing all these findings soon. I will coordinate with Dr Conspiracy to see if he is interested in hosting the findings as well.

    This has been a fantastic journey where Hermitian’s comments have helped further strengthen the xerox workflow hypothesis. And for that I want to thank him.

    If he needs any help decoding the raw data streams or with matrix multiplications, then I am here for him. However, I have shown him several examples now, and I hope he can do the rest himself. It’s a very educational way of familiarizing oneself with affine transformation matrices.
    And no, it does not include the Pythagorean Theorem, just simple trigonometry.

  8. “Thank the White House for providing a scanned document on a Xerox WorkCentre 7655🙂 ”

    The 2010 tax return was created on April 15th, 2011. Twelve days before the WH LFBC PDF was created.

    It’s too bad the individual scanners don’t leave a comment identifying them.

  9. It’s too bad the individual scanners don’t leave a comment identifying them.

    Not when scanning but they are rumored to leave behind a printing ‘bar code’ which is visually hard to detect.

    Somehow I am sure that also the scans can be tracked… Time to research…

    Of course, I believe that we have now tracked down our ‘forger’ with 99% certainty.

    Thanks to Hermetian.

  10. Gorefan

    “”Thus Adobe Illustrator is not “confused” when it opens the WH LFCOLB. I had previously stated that the LFCOLB PDF image “opens” in the correct portrait orientation in Adobe Illustrator 16 (CS6) and Adobe Illustrator 17 (CC). Thus we can safely assume that the WH LFCOLB PDF file is device independent for Adobe Illustrator and all the other named graphics programs.””

    “The WH LFBC was saved in Preview. We don’t know how it would have loaded had it not been saved in Preview.

    “Open the 7535 pdf in illustrator, it will be in landscape mode while opening in portrait mode in other Adobe products. Now save it as a PDF in Preview. It will now open in Portrait mode in Illustrator.

    “Now open the President’s 2010 tax return pdf in Illustrator it will open in landscape mode but in portrait mode in all other Adobe products. Now save it as a pdf in Preview , it will now open in Illustrator in Portrait mode.

    “Also none of these programs generated a warning message in Illustrator and they open as layered PDF files.”

    Which all adds up to the fact that you and NBC are both comfortable with the Xerox Workcenter 7535 NOT being device independent with respect to MAC OS Preview.

    And both of you are absolutely sure that Preview makes no other changes to the Xerox scan to PDF file except a 90 degree rotation. Of course we don’t need to worry about that because you haven’t checked to see.

    So I’ll volunteer to check that for you. NBC just needs to post a link to the Preview PDF file and I’ll let you know within 10 minutes.

    Gee I wonder why the Xerox Workcenter creates scan to PDF files which are not device independent on a MAC OS with Preview? You would expect that Xerox would make sure that their PDFs are device independent for both MAC OS and Windows.

  11. NBC

    “Not when scanning but they are rumored to leave behind a printing ‘bar code’ which is visually hard to detect.”

    Is that the “Friends of the Fogbow” Bar Code ???

  12. Hermitian:
    Which all adds up to the fact that you and NBC are both comfortable with the Xerox Workcenter 7535 NOT being device independent with respect to MAC OS Preview.

    It’s not what we are comfortable with, it’s what the data show.

    Hermitian: And both of you are absolutely sure that Preview makes no other changes to the Xerox scan to PDF file except a 90 degree rotation. Of course we don’t need to worry about that because you haven’t checked to see.

    We have in fact checked… You may be a little behind here. I have carefully outline the changes made by preview when saving a document. It does not rotate the internal images but selects a portrait orientation for the mediabox and rotates the images into the portrait layout. The Xerox PDF shows how it uses a landscape format (as this is how the document was captured) and does not rotate the images into the canvas but then does a 270 degree rotation at the page level. Most PDF readers are not confused by this but for some reason Illustrator renders the document in landscape.

    Hermitian: So I’ll volunteer to check that for you. NBC just needs to post a link to the Preview PDF file and I’ll let you know within 10 minutes.

    You make a lot of claims and are unable to support them? How ironic…. I have shown you in full detail what Preview does and you still doubt me🙂 Well, since you are an ‘expert’ on PDF’s created with Preview, you should at least have checked yourself before you submitted your affidavit…

    Hermitian:Gee I wonder why the Xerox Workcenter creates scan to PDF files which are not device independent on a MAC OS with Preview? You would expect that Xerox would make sure that their PDFs are device independent for both MAC OS and Windows.

    They are quite device independent on a Mac as they render correctly, however they confuse Illustrator. The facts speak for themselves… It’s perhaps time to come to terms with them?

  13. s that the “Friends of the Fogbow” Bar Code ???

    ROTFL. No, it is a ‘barcode’ in yellow which has been secretively added to print outs. They are/were hard to observe but contained a lot of identifying information.

    Do a google search.

  14. “Which all adds up to the fact that you and NBC are both comfortable with the Xerox Workcenter 7535 NOT being device independent with respect to MAC OS Preview. ”

    The President’s 2010 tax return were not done on a 7535, they were created on 7655.

    What do you mean by ” NOT being device independent with respect to MAC OS Preview”.

    “And both of you are absolutely sure that Preview makes no other changes to the Xerox scan to PDF file except a 90 degree rotation. Of course we don’t need to worry about that because you haven’t checked to see.”

    Never said that.

    We know that Preview uses PDF Version 1.3, the Xerox (both the 7655 and 7535)
    uses Version 1.5 . So, yes there are changes just from that alone.

  15. BTW, I’m not comfortable with it and intend to send a scathing letter to Xerox demanding they make their scanners create PDFs that load in Portrait mode when opened in Adobe Illustrator.

  16. Never said that.

    We know that Preview uses PDF Version 1.3, the Xerox (both the 7655 and 7535)
    uses Version 1.5 . So, yes there are changes just from that alone.

    Funny how unfamiliar Hermitian appears to be with the 1.3 and 1.5 standards. For example 1.3 does not support the following

    1. ObjStm
    2. JBIG2

    Which means that Preview, when outputting the document will have to save the data differently. It should not come as much of a surprise that it indeed does do so. JBIG2 data are now stored in a stream using FlateDecode, which of course increases the size of the PDF. And ObjSTM are stored as individual Xobjects.

    I have some pending experiments to report on however let’s focus first on Hermitian’s confusions.

    We have tax forms from the White House which were created on a 7655 WorkCentre and which open up landscape in Illustrator… Just like the 7355 created ‘birth certificate’. This makes sense because the document is scanned as a landscape document (think about it) but presented as a portrait document (Xerox software compensates for this, retaining the original image objects and just doing the right rotation into the mediabox)

    Once you realize this, you can make some interesting predictions… I am still waiting for Hermitian to catch on to that one… It has to do with the monochrome objects…

    In the WH PDF they are rotated counter clockwise, n the 7355 PDF clockwise…. You can now make additional predictions about the bitmaps…

    And test them…

    How many hints do I have to give before Hermitian understands how and why the prediction can be made…
    And then one can test the prediction…

    This is how science works…

  17. BTW, I’m not comfortable with it and intend to send a scathing letter to Xerox demanding they make their scanners create PDFs that load in Portrait mode when opened in Adobe Illustrator.

    ROTFL but the ‘injured’ party is poor Hermetian who relied on these high level tools and failed to look at the raw data.

  18. Oh and a simple google search shows that this is a problem in illustrator…

    here for instance

    The email>FAX provider says that it must be a problem on the copier because there is inconsistency as to how the PDF displays. In Acrobat it is portrait and looks fine. In Illustrator it is landscape. So, it’s the copier. My explanation there is that Acrobat will probably obey the rotation because it’s designed primarily for ‘print views’ – Illustrator isn’t and therefore may display as it sees the page definition. Further, in Illustrator if you goto print preview it does rotate to portrait.

    Time to get a refund from Adobe I guess🙂

  19. NBC

    On which device did you first show that all the Xerox scanned to PDF images were rotated clockwise by 90 degrees?

    Also the same 17 images showed that the 1 Bit layers were white text on black.

    Did you produce these images on a MAC OS or on a Windows platform?

    Also what Graphics program did you display the images with? Gimp ? IrfanView ? Photoshop ? Preview ?

    I’m still waiting for you to post a link to the Preview PDF !!

  20. I opened the 7535 pdf in Adobe Photoshop and “saved as” a pdf. It now opens in Illustrator in portrait mode.

  21. I opened the 7535 pdf in Adobe Photoshop and “saved as” a pdf. It now opens in Illustrator in portrait mode

    Oh the shock and surprise… Does Hermitian really believe we would not have checked? This is basic forensics and logic.

  22. “Oh the shock and surprise”

    It also flattened the layers into a single one layer document.

  23. ’m still waiting for you to post a link to the Preview PDF !!

    Are you really telling me that you wrote an affidavit on a preview created PDF and you do not have a way to even generate one?

    Sloppy sloppy…

    Let’s see how resourceful you can be…

  24. On which device did you first show that all the Xerox scanned to PDF images were rotated clockwise by 90 degrees?

    Through multiple ways:

    1. Look at the cm matrices in the raw data file. Yes I know, they still confuse you.
    2. Look at the width/height
    3. Look at them rendered by GIMP

    White indicates that a bit was set. The bitmaps are imagemasks, if you had not figured that out…

  25. Just in case you fail to understand.. I will let you support your own musings for once. Do not expect others to do all your homework…

    Show initiative my friend, it’s part of the inquisitive mind of a scientist.

  26. It also flattened the layers into a single one layer document.

    I exported as pdf no special filters and I printed to PDF both show layers.

    The images remain rotated (use preview or GIMP)

  27. Updated to accomodate Hermetian’s struggles with Matrix calculations as well as proof how my column based approach matches the Adobe PDF row based approach. Basic algebra 101 really.

    Hope this will allow Hermitian to move beyond these obstacles and look at what the cm matrices tell us.

Comments are closed.