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From: Jeff W. Sondeen (sondeen AT rcf-fs DOT usc.edu)
Date: Fri Oct 27 2000 - 19:17:22 EDT

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    Philippe O. Pouliquen writes:
     > 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.
    
    yes, i was thinking about 2 planes, say a metal2 tile at 750,750
    checking something about metal1 (and what i said about the tile at
    753,753 was bogus), but you're right, that tile (at 750,750) has
    (almos) the same work to do in normal manhattan cases (that there
    might be a 1000x1000 metal1 tile at 0,0) (almost because with a normal
    tile it can just check the 'x' size of the tile (to see if it comes
    close to 750 but with a diagonal it has to consider angle).  also
    whatever i said about 'negative slope' is totally bogus.  sorry for
    the confusion.
    
     > 
     > > 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.
    
    by the way, what would help a rule-writer (for the current manhattan
    version) is, referring to figure 9.1 on page 29 of the magic
    maintainer's manual #2, more control over exactly which corner type(s)
    the 'cornerTypes' refers to; my recollection is that better rules can
    be written if you can distinguish between the corner type just ouside
    B (of that figure) and the one just inside B (ie. the type of B).
    
    this may get to the heart of the DRC rule issue: even with Timothy's
    policy of treating the diagonal type as a normal type, (ie. if it's a
    poly/space diagonal tile, treat it as a poly tile), it's not clear to
    me what will fall out of the edge rules.
    
    
     > 
     > 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.
     > 
    
    a good point. i think Tomothy's policy though would turn the diagonal
    into a normal tile, so your diagonal will disappear.  but i would
    prefer to keep all coords as integers, just because of my dwindling
    brain cells.
    
    /jeff
    
     > Fortunately, if we just stick to 45 degree angles, the problem doesn't
     > occur.
     > 
     > Philippe Pouliquen
    


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