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From: Philippe O. Pouliquen (philippe AT alpha DOT ece.jhu.edu)
Date: Fri Oct 27 2000 - 18:37:16 EDT

  • Next message: Jeff W. Sondeen: "Re: Non-manhattan geometry in magic" 

    Jeff W. Sondeen wrote:
>
>Rajit Manohar writes:
> > 
> > If I understand this correctly, Tim's suggestion is to support
> > diagonal tiles of the form
> > 
> >        ------
> >       |`.    | 
> >       |  `.  |
> >       |    `.|
> >        ------
> >
>
> but imagine that this is a 1000 by 1000 lambda tile, and we're
> checking 2 other tiles, one is 750,750 to 751,751 and the other is
> 753,753 to 754,754.  they way tiling works, this check would have to
> consider tiles far away from it (namely the big one at 0,0) so you
> essentially lose the 1-d sorting that the corner stitching had been
> giving you.
> 

You must be talking about something that I don't quite follow.  How
can there be a tile at ((750,750),(751,751)) and ((753,753),(754,754))
if the big tile is at ((0,0),(1000,1000))?  Tiles don't overlap on a
given plane. If you are talking about different planes, then the
problem already exists in the current manhattan geometry.

> certainly the design rules would be a problem, as they are specifed as
> "edge" rules (but would have to be interpreted as "paint" rules with
> appropriate (complicated) changes to how they check layout.
> 
> /jeff

I don't think that edge-based design rules need to be altered.
However, I'm not so sure about the "corner" portion of the basic magic
design rule.

Also, Timothy Edwards wrote:
>
> Naturally, I have not thoroughly worked this out, so anyone
> who sees insurmountable logical fallacies with my idea is
> welcome to point them out.
>

One problem the I don't like is that if you start with a diagonal, and
partially paint a rectangle over it, the corners of the new rectangle
are not necessarily on the lambda grid anymore.  I would hate to see
my diagonals move around because of this.  Here is a simple example:
If you start with a 1x2 triangle, and paint a rectangle over half of
it, then the remaining triangle is 0.5x1.

Now I had originally thought: no problem, lets store the coordinates
as integer fractions.  But if you are dealing with large triangles, in
which the lengths of the sides are prime numbers (in lambda), things
can get horribly complicated real fast.

Fortunately, if we just stick to 45 degree angles, the problem doesn't
occur.

Philippe Pouliquen

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