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diff --git a/Documentation/algorithms b/Documentation/algorithms new file mode 100644 index 0000000000..f422332e41 --- /dev/null +++ b/Documentation/algorithms @@ -0,0 +1,98 @@ +Date: Tue, 5 Nov 1996 00:01:32 +0100 +From: Werner Icking <Werner.Icking@gmd.de> +To: hanwen@stack.urc.tue.nl +Cc: dsimons@logicon.com +Subject: Re: font sizes. + +> Date: Mon, 4 Nov 1996 22:37:54 +0100 (MET) +> From: Han-Wen Nienhuys <hanwen@stack.urc.tue.nl> +> > +> >There were different schemes when music was typeset by hand. If I remember +> >right Harder uses another scheme that Gomberg. Both scheme may be used +> +> Who are Harder and Gomberg? Do you have references? + +Both are mentioned in the master thesis by Steinbach & Schofer who +invented M(u)TeX, the grandmother of all M...TeXs. The Musiclibrary +in Bonn has the harder (printed in 1948?) and there are not many books +I liked more to own. + +The master thesis should be available at the CTAN archives under MuTeX +or MTEX maybe subdirectory DIPL (for Diplom). I have the TEX-source +and I may pack it to ftp.gmd.de if you are interested and can't find it +on CTAN. +================================================================ + +[breaking lines] +> +>Incidentally, I use a different approach in PMX, starting with the +>total number of systems for the piece instead of assuming a starting +>physical value for \elemskip. That's equivalent to setting the +>physical length of the whole piece if laid out in one long line. +>Knowing the total amount of scalable and fixed space I compute a +>starting physical value for \elemskip. I use that to get how many +>bars go in the first line. Then I force a line break there, remove +>those bars and their scalable and fixed space from the accounting, and +>start over with the second line, etc. + + +Since you are getting into technical details, I will show mine too: I +think my way is the most elegant algorithm i've seen so far. Some +terminology: I call a vertical group of symbols (notes) which start at +the same time a "column". Each line of a score has notes in it, +grouped in columns. The difference in starting time between those +columns makes it possible to determine ideal distances between those +columns. + +Example: + + time -----> + + col1 col2 col3 col4 + + +voice1 1 1 + +voice2 2 2 2 2 + + +(1 is a whole note, 2 a half note.) + +time_difference (col1 , col2) = 0.5 wholes, +time_difference (col1 , col3) = 1 wholes, +time_difference (col2 , col3) = 0.5 wholes, +etc. + +these differences are translated into ideal distances (these translations +have been the subject of discussion in this thread). + + distance (col1,col2) = 10 pt + distance (col1,col3) = 14.1 pt + distance (col2,col3) = 10 pt + etc. + +as you can see, these distance are conflicting. So instead of +satisfying all those ideals simultaneously, a compromise is sought. + +This is Columbus' egg: LilyPond attaches "springs" to each +column-pair. each spring has an equilibrium-position which is equal to +the above mentioned distance, so + + spring (col1, col2) and spring(col2,col3) try to push column 1 +and 3 away (to a distance of 20pt) from each other, whereas the spring +between col 1 and col 3 tries to pull those two together (to a +distance of 14.1 pt). The net result of this pushing and pulling is an +equilibrium situation (the pushing cancels the pulling), which can be +calculated as the solution of Quadratic program: it is the solution +with minimum potential energy, for you physicists out there. + +This algorithm for doing one line, gives a "badness" parameter for +each line (the potential energy). Now one can use TeX's algorithm for +making paragraphs (using this new version of "badness"): one should +try to minimise the overall badness of a paragraph. LilyPond also uses the +concept of pre- and post-breaks. + +(actually, it is a bit more complicated: each column also has a +minimum distance to other columns, to prevent symbols from running +into symbols of other columns.) + |