Re: Vertical spacing regression !?

[Boris Shingarov]

On 06/30/2010 01:04 AM, David Kastrup wrote:
> > until after line-breaking. Also, the vertical collision avoidance means
> > that in { c1^"long long markup" c1^"long long markup" }, we cannot
> > calculate the height of the second bar without considering the first bar
> > too (and the answer will change if they are on different lines).
> >      
> Maybe I am dull, but we need the line heights (or skyline) for a given
> line breakpoint sequence, and a given line breakpoint sequence has a
> given skyline for each line.
>    
Correct.  And there is O(2^N) breakpoint sequences for N possible 
breakpoint places (roughly, for N bars); so we need O(2^N) 
heights/skylines and page breakings.  The dynamic programming algorithm 
deals with this complexity, but even though there are less than O(2^N) 
actual configurations to calculate a demerit score for, it is still 
prohibitively expensive to perform a full layout every time we need a 
demerit score.

> Maybe the problem can be alleviated by not associating a fixed line
> height/skyline with each bar, but something that is dependent on the
> current breakpoint sequence being considered.
>    
Not sure what you mean.  We do not and can not have a fixed line height 
/ skyline for each bar -- as Joe just explained.  For example, consider 
music in the G clef; if a particular bar comes after a line break, it 
will have a clef, making the bar much taller.  So I am not sure what you 
have in mind here... something else that I do not see?

Originally, the skyline was approximated by its bounding rectangle.  In 
other words, there was only one measurement: the "line height".  About a 
year ago, to address the problem with G clefs, Joe added the distinction 
between "begin-" and "rest-of-line", for inter-staff, intra-system 
space.  (So instead of one point we have two).  This worked reasonably 
well for music with many staves per system; but for music on one staff 
(e.g. instrument parts, or monody) this does no good, because all the 
space is inter-system.  So about two months ago I introduced the 
"begin/rest" distinction for inter-system space (i.e. for computing 
pure-height of a whole system).  This still left some unaddressed things 
like 1062, which is what today's discussion is about.

Boris