Re: drawing commands in groff(7) (was: undiagnosed pic error)

[G. Branden Robinson]

At 2023-06-07T09:54:29-0400, Douglas McIlroy wrote:
> Thanks for concentrating our attention on detail.
> 
> Now I see that Branden hid some easter eggs for us to find.

They hid from me, too!  :-O

> 1. An ellipse is said to have "diameter d". Actually it has principal
> axes of lengths h and v.
> 
> 2. There's a typo hv for the relative vertical position of arc center
> vc.

I found and caught these while preparing take two.

> 3. It isn't said that arcs run counterclockwise.

Didn't even think of this one.  I guess this affects where the drawing
position is left afterward; I'll test this.  In comments I annotated
another twist to arc drawing: it's one of the few cases where using
out-of-range coordinates makes sense--one could reasonably place the
center of an arc off the page, and yet still draw only on the page.

> 4. It could be said that the center of an arc is adjusted to the
> nearest point on the perpendicular bisector of the arc's chord.

I like this.

I'll address points 3 and 4 and post an updated revision of the drawing
commands material.  As often happens, my edits sent out creepers and
I've ended up revising the relevant parts of groff_diff(7) and our
Texinfo manual as well (which really needed it in this area).

> This would allay sticklers' anxiety about overconstraint and sometimes
> allow one to make a reasonable guess rather than calculating it. On
> the other hand it may be TMI for many readers. (At least it doesn't
> flaunt Lagrange multipliers.)

Let me attempt to reassure Deri.  Even if his school never taught him
Lagrange multipliers, my university did--but failed (as far as I can
recall) to motivate them with any applications, so I forgot about them
for a long time.

Later in life I decided I wanted to learn variational mechanics, which
involve a quantity known as the Lagrangian, which I managed to convince
myself _was_ related, but not really used all that often in
problem-solving exercises(?).  The foundational insight of the calculus
of variations is a neat trick[1].  I also discovered that economists
apparently use Lagrange multipliers all the time in optimization
problems.  Variational calculus applies to physics because nature never
does any more work than it has to to achieve an equilibrium state.

But in the end I never did manage to acquire variational mechanics,
or reacquaint myself with Lagrange multipliers, so even with some
preparation, that source comment leaves me just as much at sea.

Personally, I have an antipathy for statements like "it can be proven
that" without even so much as a footnote pointing you to a reference.
That sort of glibness reminds me of someone.

"I have many, many friends who are saying that any three-dimensional
topological manifold which is closed and simply-connected must be
homeomorphic to the 3-sphere.  And it's true, folks!  I must tell you,
it's true.  I have the best people working on it.  Believe me, I'm gonna
have the best proof you've ever seen.  Everybody's talking about it."

Regards,
Branden

[1] It probably depends on functions that are everywhere continuous
    and/or differentiable.  Weierstrass threatens to haunt us again.

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