Michael Mossey wrote:
Read this version.
A composition consists of several voices or instruments, each indicated by its own *staff*. Visually, a staff is a layout of items such as notes, clef signs, and accidentals arranged horizontally from left to right, representing increasing time.
A *system* is a set of staves stacked vertically that represent instruments playing at the same time.
Here is a simple representation of a system, in which the pipe character represents items. Note that some of the items are aligned vertically meaning they will play at the same time. At other times, only one staff contains a note.
staff 1: | | | | staff 2: | | | |
Next we elaborate this model to show that items have visual width. Here they are represented by clusters of x's with a pipe in the middle. The pipe represents the part of the item that needs to be aligned with items on other staves. For example, in the visual representation of a chord, the part of the chord called the notehead needs to be aligned with noteheads on other staves. (A chord includes other symbols, like accidentals and flags, which get drawn to the right or left of the notehead and don't need to be aligned vertically with anything else.)
staff 1: x|x xx|xx x|x
staff 2: x|x x|x xxxxx|xxxxx
a b c d
Here you can see that there is an additional constraint on layout, which is that items need to have horizontal space around them so they don't collide. For instance, the very wide item at 'd' (on staff 2) means that the item on staff 1 at 'd' has to be positioned far to the right of its previous item.
A nice problem with an elegant solution. Let me demonstrate. First, let's solve the simpler problem of aligning just a single staff on unlimited paper. In other words, we are given a list of items that extend to the left and right, and we want to calculate a position for each one. In fact, let's dispense with items entirely and just work with a list of extents directly. type Pos = Integer type Width = Pos align :: [(Width,Width)] -> [Pos] For instance, the item (3,4) corresponds to xxx|xxxx Implementing this functions is straightforward align xs = scanl (+) a gaps where (a:as,bs) = unzip xs gaps = zipWith (+) bs as This is a very tight layout without any whitespace, but we can add some after the fact addWhitespace :: Width -> [Pos] -> [Pos] addWhitespace margin = zipWith (+) [0,margin..] With this, we can now align a list of events (from my previous message) given a function that tells us their visual extents. alignStaff :: (a -> (Width,Width)) -> Events a -> [Pos] alignStaff f = align . map f Now, what about the problem of aligning several staves on unlimited paper? It turns out that we've already solved it! After all, we can interpret a vertical group of items as a compound item whose total width is just the maximum width of its components. alignStaves :: (a -> (Width,Width)) -> [Events a] -> [Pos] alignStaves f = alignStaff f' . merge where f' = (maximum *** maximum) . unzip . map f In other words, we can lay out a group of staves by first merging them in time order (as done in my previous post) and then treating the result as a "compound" staff.
Note that data exists in two domains: there is data that describes notes; that is, pitches and timbres and volumes and times and duration. We'll call this the 'score'. It's the fundamental data. Then there is the visual *representation* of the score. Here we are concerned only with creating a visual representation. However, we need to refer to data in the score.
Thanks to polymorphism, keeping this data around is no problem. The alignStaves function simply doesn't care what items it is going to align, it only wants to know their widths. In fact, making alignStave polymorphic is key to reusing it for groups of staves. In other words, polymorphism is key to separating concerns. You should structure your layout engine as some kind of library that can align anything, caring only about widths and heights. For instance, dealing with finite paper size can be packed neatly into the align function. Regards, apfelmus -- http://apfelmus.nfshost.com