the details of arc drawing (was: drawing commands in groff(7))

[G. Branden Robinson]

At 2023-06-07T09:54:29-0400, Douglas McIlroy wrote:
> 3. It isn't said that arcs run counterclockwise.
> 
> 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. This
> would allay sticklers' anxiety about overconstraint  and sometimes
> allow one to make a reasonable guess rather than calculating it.

I'm still figuring out a way to demonstrate this (for my own edification
and comprehension, not to encumber our manuals with an example of it,
since it seems pretty deep into the weeds).

But today I _did_ learn that the arc's end point (h, v) is relative to
the (adjusted) center, _not_ to the initial drawing position, which I
had assumed, and once I started playing, I got a surprise.  If I squint,
I can see the reasoning.  As the successive vertices of a polygon \D'p'
are drawn from their predecessors, the center of an arc can be thought
of as a vertex with no line plotted to (or from) it.  Nevertheless I
mean to make this explicit.

A little play also reveals the significance of counterclockwise
circumscription.

Here's a small exhibit if others would like to experiment.

.sp 2i
\h'1i'\Z'.C'\v'0.5i'\D'a 0 -0.5i 0 -0.5i'\v'0.5i'\
\h'2i'\Z'.C'\v'-0.5i'\D'a 0 0.5i 0 0.5i'X
.sp 2i
\h'1i'\Z'.C'\h'-0.5i'\D'c 1i'

Regards,
Branden

signature.asc
Description: PGP signature