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

[Douglas McIlroy]

Deri,

Thanks for concentrating our attention on detail.

Now I see that Branden hid some easter eggs for us to find.

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.

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. On
the other hand it may be TMI for many readers. (At least it doesn't
flaunt Lagrange multipliers.)

Doug

On Tue, Jun 6, 2023 at 6:14 PM Deri <deri@chuzzlewit.myzen.co.uk> wrote:
>
> On Tuesday, 6 June 2023 21:07:07 BST G. Branden Robinson wrote:
>
> >     \D'a hc hv h v'
>
> >         Draw circular arc centered at (hc, vc) from the drawing position
>
> >         to (h, v).
>
>
> Hi Branden,
>
>
> I'm not sure if this is relevent but have you seen the comment in the routine 
> adjust_arc_center (geometry.cpp) which has this comment:-
>
>
>   // We move the center along a line parallel to the line between
>
>   // the specified start point and end point so that the center
>
>   // is equidistant between the start and end point.
>
>   // It can be proved (using Lagrange multipliers) that this will
>
>   // give the point nearest to the specified center that is equidistant
>
>   // between the start and end point.
>
>
> This gave me a big headache when trying to make gropdf produce the same arcs 
> as grops, until I found this comment, since I was using the given centre 
> rather than the adjusted centre to draw the arc! I don't know how relevant 
> this is to the documentation, I am definitely not a maths savant, the special 
> school I went to saw little point in giving us an academic education.
>
>
> Cheers
>
>
> Deri
>
>
>