[MUD-Dev] Re: Hex-grid mapping (fwd)

[Nathan F Yospe]

Nathan F. Yospe - Born in the year of the tiger, riding it forever after
University of Hawaii at Manoa, Dept of Physics, second year senior (joy)
(On Call) Associate Algorithm Developer, Textron Systems Corp, Maui Ops.
yospe#hawaii.edu http://www2.hawaii.edu/~yospe Non commercial email only

---------- Forwarded message ----------
Date: Wed, 2 Dec 1998 21:20:02 -1000
From: Sunny Gulati <sunnywiz at radiks.net>
To: yospe at hawaii.edu
Subject: Re: [MUD-Dev] Re: Hex-grid mapping

I don't have posting permissions, and I haven't had a chance to fuly read
the Hex-Grid mapping thread, but if if you think this is warranted as valid
information, then could you pass it on to the list? 

"Tesselation" of a sphere using UNIFORM shapes is a pretty hard task.
According to one source (Hipparchus GIS library introduction) its pretty
much impossible - end up with a bunch of hexagones and one pentagon.  If one
were to relax the rules, though, one could use non-uniform tesselations, and
the problem becomes much simpler.  The method that source goes into is using
Voronoi cells.  (wish I could give you a link.  Its supposed to be pretty
standard).  Gives you irregular tesselation with all kinds of really cool
properties that make things really fast for finding data/cell memberships,
intersections, neighbors, etc. 

Mudwise, it translates to having a sphere broken down into (roughly) square,
pentagonal, and (mostly) hexagonal shapes (which could easily be rooms, or
"visible areas").   The shapes are not symmetrical(? - all sides being equal
is what I mean), but to the eye, they look pretty good.  And in the case of
varying densities of information, the cells can be dynamically split down in
size.  And its VERY fast. 

http://www.cuug.ab.ca:8001/~russellj/hipparchus.html - excerpt from the
documentation for a library that uses Voronoi tesselation.  

At 11:48 AM 12/2/98 -1000, Nathan Yospe wrote:
>On Tue, 1 Dec 1998, Ling wrote:
>
>:As listed in the FAQ, there's a page called Amit's Games Programming Page.
>:It has a few pointers in that direction:
>
>:<URL:http://www-cs-students.stanford.edu/~amitp/gameprog.html>
>
>:On an unrelated note, has anyone got any bright ideas on representing a
>:sphere with roughly equal shaped tiles?  Whereby tiles can be a hex or
>:otherwise.  A requirement is that the solution can be scalable for
>:different sized spheres for representing something like a moon and then a
>:large planet.
>
>Well... somewhere around here there is a list of the theoretical shapes,
>including the perfectly symmetric permutations, for highmass fullerenes.
>The C30 is the smallest permutation that is symmetric, the C60 is nicer,
>for purposes of approximating a sphere, and there are many larger ones a
>person could make a quite detailed sphere out of. I don't even think the
>geometries would be hard to code...
>-- 
>
>Nathan F. Yospe - Born in the year of the tiger, riding it forever after
>University of Hawaii at Manoa, Dept of Physics, second year senior (joy)
>(On Call) Associate Algorithm Developer, Textron Systems Corp, Maui Ops.
>yospe#hawaii.edu http://www2.hawaii.edu/~yospe Non commercial email only
>
>
>-- 
>MUD-Dev: Advancing an unrealised future.
>
>
 // Sunny Gulati 
 // sunnywiz at radiks.net (Home)