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The stack represents the state of the PDF graphics stack. We are only
interested in the current transformation matrix (CTM) so we only track
this object; a full implementation would need to track many other items.
The CTM is initialized to the mapping from user space to device space.
PDF units are 1/72". In a PDF viewer or printer this matrix is initialized
to the transformation to device space. For example if set to
(1/72, 0, 0, 1/72, 0, 0) then all units would be calculated in inches.
Images are always considered to be (0, 0) -> (1, 1). Before drawing an
image there should be a 'cm' that sets up an image coordinate system
where drawing from (0, 0) -> (1, 1) will draw on the desired area of the
page.
PDF units suit our needs so we initialize ctm to the identity matrix.
According to the PDF specification, the maximum stack depth is 32. Other
viewers tolerate some amount beyond this. We issue a warning if the
stack depth exceeds the spec limit and set a hard limit beyond this to
bound our memory requirements. If the stack underflows behavior is
undefined in the spec, but we just pretend nothing happened and leave the
CTM unchanged.
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PDFs do not include image resolution information within image data.
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image will be rasterized, and the effective resolution is the ratio of the
pixel size to raster target size.
Normally a scanned PDF has the paper size set appropriately but this is
not guaranteed. The most common case is a cropped image will change the
page size (/CropBox) without altering the page content stream. That means
it is not sufficient to assume that the image fills the page, even though
that is the most common case.
A PDF image may be scaled (always), cropped, translated, rotated in place
to an arbitrary angle (rarely) and skewed. Only equal area mappings can
be expressed, that is, it is not necessary to consider distortions where
the effective DPI varies with position.
To determine the image scale, transform an offset axis vector v0 (0, 0),
width-axis vector v0 (1, 0), height-axis vector vh (0, 1) with the matrix,
which gives the dimensions of the image in PDF units. From there we can
compare to actual image dimensions. PDF uses
row vector * matrix_tranposed unlike the traditional
matrix * column vector.
The offset, width and height vectors can be combined in a matrix and
multiplied by the transform matrix. Then we want to calculated
magnitude(width_vector - offset_vector)
and
magnitude(height_vector - offset_vector)
When the above is worked out algebraically, the effect of translation
cancels out, and the vector magnitudes become functions of the nonzero
transformation matrix indices. The results of the derivation are used
in this code.
pdfimages -list does calculate the DPI in some way that is not completely
naive, but it does not get the DPI of rotated images right, so cannot be
used anymore to validate this. Photoshop works, or using Acrobat to
rotate the image back to normal.
It does not matter if the image is partially cropped, or even out of the
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