Hi,

tl;dr: the `preview-get-dpi' function compares the wrong values for
horizontal monitors (i.e., ones that are flipped by 90/270 degrees).

When previewing LaTeX fragments via AUCTeX's `preview.el' library,
things get quite messed up when one or more monitors are set up in
"portrait mode".  I have attached three images that show this; bug1.png
shows a rendered equation for two vertical monitors, bug2.png for a
single one, and horiz.png displays that same equation being rendered on
a horizontal monitor (i.e., this is the expected result).

Looking into `preview.el', it seems like that `preview-get-dpi' (called
by `preview-get-geometry', which is in turn called by
`preview-generate-preview') calculates the wrong "resolution".  The
relevant implementation is

    (defun preview-get-dpi ()
      (let* ((monitor-attrs (frame-monitor-attributes))
             (mm-dims (cdr (assoc 'mm-size monitor-attrs)))
             (mm-width (nth 0 mm-dims))
             (mm-height (nth 1 mm-dims))
             (pixel-dims (cl-cdddr (assoc 'geometry monitor-attrs)))
             (pixel-width (nth 0 pixel-dims))
             (pixel-height (nth 1 pixel-dims)))
        (cons (/ (* 25.4 pixel-width) mm-width)
              (/ (* 25.4 pixel-height) mm-height))))

An example output of `frame-monitor-attributes' for a horizontal
monitor:

    '((name . "DP1")
      (geometry 0 0 1920 1080)
      (workarea 0 0 1920 1080)
      (mm-size 530 300)
      (frames <<omitted>>)
      (source . "XRandR 1.5"))

The same monitor in "vertical-mode" returns:

    '((name . "DP1")
      (geometry 0 0 1080 1920)
      (workarea 0 0 1080 1920)
      (mm-size 530 300)
      (frames <<omitted>>)
      (source . "XRandR 1.5"))

Crucially, the returned physical width and height of the monitor don't
change, but the geometry—what will be the pixel width and height—does.
However, turning the monitor by 90 degrees obviously switches the
physical width an height around as well, although that perhaps can't be
reported property.  In such a situation, we actually compare the pixel
_width_ of the monitor with its physical _height_, as well as its pixel
height with its width.  Naturally, and depending on the specific setup,
this produces too narrow or too wide previews.

I have fixed this locally by only comparing comparable values; i.e.,
instead of

    (cons (/ (* 25.4 pixel-width) mm-width)
          (/ (* 25.4 pixel-height) mm-height))

I wrote something like

    (cons (/ (* 25.4 (max pixel-width pixel-height)) (max mm-width mm-height))
          (/ (* 25.4 (min pixel-width pixel-height)) (min mm-width mm-height)))

This fixed the problem for me, but I don't know if there is some
situation (or strange resolution) in which it would be correct to
compare some other combination of values.

Hopefully this was comprehensible.  If not, feel free to ask for more
information.

Best,
  Tony

In GNU Emacs 29.0.50 (build 1, x86_64-pc-linux-musl, cairo version
 1.16.0) of 2022-10-29 built on pbox
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