Great article, Leonard, although you should admit that it is written for your students in order to attract them to doing LF photography, and not for photographers in order to attract them to mathematics
Regarding the question of the limits of depth of field with slanted planes I recommend to use an approximation, the "venitian blind approch". Instead of finding the real ellipse of confusion, imagine that you check for the circle of confusion on a small venitian blind located at a given point of the slanted image plane but lifted up in order to stay parallel with the exit pupil.
Look at my article (the English version is still not up to date!! shame on me ! )
see figures 5, 6, 7
http://www.galerie-photo.com/profond...heimpflug.html
There, you have the advantage that the circle of confusion is invariant in the image and I'm sure that you can apply the elegant formalism of projections to demonstrate in one or two powerful projective formulae that the limits of acceptable sharpness are slanted planes according to the usual rules explained in other articles.
Another issue is that at a first mathematical glance, depth of field and depth of focus issues are different since depth of field ussues use the harmonic mean to place the planes of best focus in the middle of limit planes of acceptable sharpness ; whereas depth of focus uses the regular mid-plane.
We discussed this issue with Jeff Conrad by mail, but my conclusion is that in practice with reasonable view camera settings and a reasonable choice of the circle of confusion both means are very close to each other, hence you get another simplification that allows you to demonstrate the wedge shaped depth of field in a snap.
After that, if you wish, you could go through the general shape of elliptical projection of the exit pupil on film, but I think most of future readers would be delighted to see the proof for the "DOF slanted planes" in the elegant way you demonstrate the basic Scheimpflug rule (as explained in Tuan's hand-drawn diagram on his web site)
Right now I' trying to use xfig and inkscape.
What follows is for aficionados of free software using Linux.
I've been using xfig for 8 years under unix and linux and I have no reason to switch to any other software for vectorized graphics.
The only thing painful and limited in xfig comes when you want to insert mathematics inside the diagram. Even simple subscripts are a pain.
So as soon as I have some formulae to insert into a figure, I create them with LaTeX. Then I export the formula from LaTeX into a tiny .eps file using the command dvips with the -E option.
For example assume that my LateX formula is in the file sinomega.tex
% this file is sinomega.tex
\documentclass[12pt]{article}
\usepackage{amsmath} %% of course, Leonard !!
\begin{document}%
\pagestyle{empty}
\begin{Huge}
$\sin(\omega \, t+\phi)$
\end{Huge}
\end{document}%
% end fo file
Then I create a small eps file with a tight bounding box around the formula:
latex sinomega.tex ; dvips -E sinomega.divi -o sinomega.eps
Then, I can incorporate the .eps formula inside xfig easily like I can incorporate any picture.
In the final ps or pdf output the typesetting will be perfect since xfig is clever enough to keep the .eps file as is.
You can even re-incoporate this figure inside another LaTeX document.
I use the graphicx package and from xfig I export in .eps.
See the attached pdf page where figure 2 created with xfig incorporates good-solid LaTeX mathematics and where figure 3 has (almost) no latex mathematics.
For plotting curves I've bee using gnuplot and nothing else for 15 years.
In gnuplot you can either export as .eps or export as xfig code to be re-incorporated
into another xfig figure, eventually incorporated in the final latex document.
From this latex document with minimum changes in the latex code, I convert them into html with the French & Free software HeVeA developed by Luc Maranget at INRIA.
http://pauillac.inria.fr/hevea
This is how I create both a pdf and a html for my articles on galerie-photo.
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