[pstricks] 3-d general Conic Sections illustration. (Also a note on \psaxes[showorigin=false])

[Dougherty, Michael]

Dear all,

I am working on a second-semester calculus textbook, and have managed to get some nice volumes of revolution illustrations with non-3d PSTricks with a bit of effort (for my first-semester book), and some nice graphics for series, improper integrals, and the like.  I'm not a power-user by any measure.

I would like to include a PSTricks-generated illustration for conic sections if possible, showing how a plane intersecting a conic gets you such a curve.  Basically, the first illustration in the wikipedia article on conic sections is what I would like to reproduce.
https://en.wikipedia.org/wiki/Conic_section
[https://upload.wikimedia.org/wikipedia/commons/thumb/c/cc/TypesOfConicSections.jpg/1200px-TypesOfConicSections.jpg]<https://en.wikipedia.org/wiki/Conic_section>
Conic section - Wikipedia<https://en.wikipedia.org/wiki/Conic_section>
In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 ...
en.wikipedia.org


I can just include that graphic, according to the publisher, but the book is not in color, and finding shades that work to show everything in grayscale seems to be a problem.

So I'm just wondering if those who have played with such things can point me in the right direction to accomplish this.  I have Herbert's 2011 book on PSTricks.  (I tried the 3-d packages a long time ago, and am getting back to this problem now, and hope not to go down too many dead ends if I can avoid them.)  Thanks in advance.

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Also, I noticed that my current  pdfTeX (Version 3.14159265-2.6-1.40.20 (TeX Live 2019/Debian) on Linux Mint 20.2) has [showorigin=true] being default with \psaxes, and I'm pretty sure that wasn't the case before.  I may be misremembering, but I found myself changing a lot of graphs in my 750-page first-semester calculus book to include [showorigin=false] in those commands, because the two zeros did not fit well with those axes.  I apologize if this has been addressed before.  (Now when I look at prevoius PDF files I do see that the origins weren't shown, by default.)  Maybe there's a global tweak I can make?

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That said, PSTricks was a godsend when I wanted to make these books, and when I discovered it in the 1990s as a lowly assistant professor of mathematics.  My colleagues appreciated seeing it as well, and they found "tricks" within it I was unaware of, as they learned it.

Kind regards,
Mike Dougherty
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