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Re: skyline vertical spacing
From: |
John Mandereau |
Subject: |
Re: skyline vertical spacing |
Date: |
Mon, 20 Nov 2006 22:51:58 +0100 |
Erik Sandberg 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:
>
> ========================
> ________ ____________
> | | ___
> | | | / \
> | | | | 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'm not a programmer, only a math student, but why not using a simpler
distance which is even more performance-friendly, like:
Distance: d_1((x,y),(x', y')) d_infinity((x,y),(x',y'))
= a|x' - x| + b|y' -y| = Max ( a|x' -x|, b|y' - y| )
/\ ________
resulting "circle" / \ | |
/ \ | |
(in fact, a square \ / | |
in both cases) \ / |________|
\/
where a and b are positive real numbers that can be adjusted.
I don't know if one of these distances would be optimal for skyline
spacing, though.
Cheers,
--
John Mandereau <address@hidden>
- Re: skyline vertical spacing, (continued)
- Message not available
- Re: skyline vertical spacing, Joe Neeman, 2006/11/15
- Re: skyline vertical spacing, Erik Sandberg, 2006/11/20
- Re: skyline vertical spacing,
John Mandereau <=
- Re: skyline vertical spacing, Joe Neeman, 2006/11/21
- Re: skyline vertical spacing, Erik Sandberg, 2006/11/21
- Re: skyline vertical spacing, Joe Neeman, 2006/11/21
- Re: skyline vertical spacing, Erik Sandberg, 2006/11/22
Message not available
- Re: skyline vertical spacing, Joe Neeman, 2006/11/21
- Re: skyline vertical spacing, Joe Neeman, 2006/11/26
- Re: skyline vertical spacing, Han-Wen Nienhuys, 2006/11/26
- Re: skyline vertical spacing, Han-Wen Nienhuys, 2006/11/26
- Re: skyline vertical spacing, Han-Wen Nienhuys, 2006/11/26
- Re: skyline vertical spacing, Joe Neeman, 2006/11/26