On 11/20/06, Erik Sandberg <[EMAIL PROTECTED]> wrote:
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:
I'm not sure that we actually want a Euclidean distance. Consider the case (I won't try to draw it) where you have a very low object on the top staff and a very high object on the bottom staff. The horizontal space between them is just over the minimum distance. Then the object on the top staff will end up close to the bottom staff and the object from the bottom staff will end up close to the top staff. The fact that their horizontal distance is relatively small might introduce confusion as to which staff the objects belong. The nice thing about the max-slope idea is that it sort of captures the hand-waving notion that the 2 staves are different objects that need to be placed vertically in such a way that they don't interleave "too much." That is, the amount that they interleave doesn't introduce any confusion as to which objects belong to which staff.
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