Re: Page and line penalties

[Han-Wen Nienhuys]

Joe Neeman wrote:
> Suppose we add penalties. Let G(B) be the penalty function for a partition 
> into lines. G(B) has no nice structure at all. It will probably be zero most 
> of the time, with a few very large spikes. And we want to minimize F(B) + 
> G(B). Suppose the user makes a small change:

I believe most of what you say; however, there are some questions:

* IIRC, line breaking is not that stable as you suggest. It tends to 
have the same problem. Due to uniform density scoring, two consecutive 
line breaks may also have global effects.

* Did you look at penalties for page-breaking at rests, or did you also 
put penalties for line-breaking?

* Isn't it possible to devise a G(B) which has a more regular structure? 
  What kind of G(B)'s did you try?  I can imagine it might be 
difficult, but have we thought about all the alternatives?

The problem that you sketch is not caused by F(B) being nice and G(B) 
not, but rather because their magnitudes are very similar.

For example, what if you adjust the penalty of a page-breaks by using 
the max distance to the next/previous rest? Then an isolated rest in a 
fully filled score will get a huge bonus, but for scores with more 
rests, the penalties will be small, relative to the spacing penalties.

* is there any value in removing page-break penalties? Shouldn't we 
rather add a forbid/allow property, and otherwise just use normal 
penalties?  Then we use forbid/force for user tweaks, with automatic 
penalties (ie. restrict the domain of possible B). This doesn't change 
the shape of the graph, just the parts that we consider. Of course, this 
 may still cause jumps of the optimum, but they might be more predictable

LilyPond's algorithm BTW, indeed is very similar to TeX's for line breaking.

> PS: This also solves the problem that the penalties are arbitrary values. 
> Currently, Lilypond might conceivably ignore a user-forced \break if it 
> causes the forces to work out too badly.

I agree that we have to stop using penalties as a kludge for force/forbid.

--

Han-Wen Nienhuys - address@hidden - http://www.xs4all.nl/~hanwen

LilyPond Software Design
 -- Code for Music Notation
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