On Thu, 17 May 2001 09:25:32 -0700, Anton Sherwood wrote:
>You know about the 17 "wallpaper" symmetry groups?
>

>> . . . I wonder if any of the other archimedians have duals, and
>> what they would look like... Thanks :-> I already had so little
>> time, now I have a new branch to explore !
>
>Every tiling has a dual.
>The dual of a semiregular tiling is a Voronoi map, and thus can be
>implemented as a variant of crackle, with the nuclei on a lattice.
>
>Yet another crackle extension that I want to try.  (see also
>http://ogre.nu/tumble/)  Is there a faq somewhere for patchers-wannabe?

No, but if you have any specific questions or want to know where to start
with crackle, the folk in povray.programming would be more than happy to
help out.

I'm probably the local expert on the current crackle implementation, since
I wrote the MegaPOV mods.  Nathan's done some work on them, too, so I'm sure
he could help as well.  All ya gotta do is modify that, the parser, and
the list of tokens, and one of your parents has a brother named Robert.  If
you need any help with any of those three things, feel free to ask in an
appropriate forum and I'll answer to the best of my ability..

I'm investigating the possibility of adding the two things you already 
mentioned, or at the very least the metric infinite thing, myself, although
probably not to MegaPOV.  Stay tuned.

Adding an option for duals of archimedean tilings would somewhat stretch
the existing crackle code, though (not to mention that it'd be only 2d.)
It'd be better as a separate pattern.  Some of the duals are boring, too:
6.6.6 is the dual of 3.3.3.3.3.3, and 4.4.4.4 is its own dual.  The rest
are tilings of irregular (but symmetric) triangles (the duals of 8.8.4,
12.4.6, and 12.12.3) quadrilaterals (the dual of 6.4.3.4) and pentagons 
(the duals of 4.4.3.3.3, 4.3.4.3.3, and the two 6.3.3.3.3's.) 

To see the dual of a specific tiling, use my tiling macros in p.t.s-f and
replace the definition of G with

#local G=pigment {gradient z color_map {[.1 rgb 0][.1 rgb 1]}}

-- 
#macro R(L P)sphere{L F}cylinder{L P F}#end#macro P(V)merge{R(z+a z)R(-z a-z)R(a
-z-z-z a+z)torus{1F clipped_by{plane{a 0}}}translate V}#end#macro Z(a F T)merge{
P(z+a)P(z-a)R(-z-z-x a)pigment{rgbf 1}hollow interior{media{emission 3-T}}}#end 
Z(-x-x.2x)camera{location z*-10rotate x*90normal{bumps.02scale.05}}

Post a reply to this message