Re: skyline vertical spacing

[Erik Sandberg]

On Wednesday 15 November 2006 21:01, Joe Neeman wrote:
> Bah, my attachments were to big. Trying again...
>
> On 11/15/06, Joe Neeman <address@hidden> wrote:
> > The jneeman git branch now has 2 new features: max-sloped skylines
> > (currently hard-coded at slope 2) and skyline debugging. I've attached a
> > couple screenshots with the debugging turned on.
> >
> > If anyone wants to have a look at this branch, just keep in mind that I
> > haven't done a lot of testing yet.

Hi,

I just got another idea of how to improve max-slope skylines. The motivation 
is mathematical rather than scientific, so there's no guarantee it's a good 
idea. But anyways:

The problem that max-slope tries to solve, is to separate objects from each 
other in X direction as well. My new idea is that what we really want is to 
separate objects by some minimum Euclidean distance (i.e. x^2+y^2); this can 
be achieved with skylines if the skyline is formed as circles around each 
object, and the spacing between skylines is set to 0, as in:

========================
________     ____________
        |   |    ___
        | | |   /   \
        | | |   | o |
  ___   | o |   | | |
 /   \  \___/   | | |
_| o |__/   \___|   |___
   |      o          
===|======|=============

The minimum Euclidean distance between objects is then twice the radius. It 
would probably be sufficient to approximate circles with regular octagons (as 
in the ascii art :) ), this should also be performance-friendly. It may also 
be useful to use ellipses rather than circles, if we want more padding along 
one axis.

I guess the main problem with this approach is that we need to calculate 
different skylines for different radii. E.g., if you first want to use 
skyline spacing to add text scripts above a staff, you can't recycle that 
skyline for spacing the resulting staff against the staff above, because the 
radii must be smaller when spacing the text.

-- 
Erik