Re: Page and line penalties

[Joe Neeman]

On Fri, 7 Apr 2006 22:59, Han-Wen Nienhuys wrote:
> Joe Neeman wrote:
> > On Fri, 7 Apr 2006 20:02, Han-Wen Nienhuys wrote:
> >> ...we should rather
> >> introduce some convexity in the penalties, so one perfect plus two
> >> extremes is much worse than three so-so lines.
> >
> > In constrained-breaking, I use the square of the force rather than its
> > absolute value -- I made the change for precisely this reason.
>
> Hmm, doesn't that introduce scaling/dimension problems?
In what sense? Not within the constrained-breaker -- the demerits calculation 
is purely internal so the only possibility of a scaling problem is with 
externally introduced penalties.

There is the issue of scaling between the line and page breakers but that will 
exist anyway (and the page breaker also uses squares of forces).

> Or does 
> everything else also use square(force) as a dimension?
The page breaker does too. Is there anything else?

> It would be 
> better if we could figure out a scaling constant, and then introduce an
> arbitrary convex function, which may be set separately. I would guess
> that the scaling should depend on line-width and spacing-increment.
We are talking about the relative importance of page and line breaking, right? 
If so, which way would the effect work?
longer line-width => more important line spacing
or the other way around?

>
> FWIW, I used x^{1.1} for a similar problem with cross-staff knee beaming.

x^2 seemed natural to me because when I think of minimising something, I 
usually think of it in terms of least-squares. I suspect it wouldn't make a 
huge difference, though.