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4 May 2024 01:12:47 EDT (-0400)
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From: Jon Buller
Subject: Re: Penrose Tile Macros
Date: 27 Jun 2006 12:05:00
Message: <web.44a156c36376349e48362b170@news.povray.org>
In a sort of follow-up to that last message, here is the exact same image,
but hooked up to a triangle drawing macro instead of a rhomb drawing macro.
 (And zoomed in a bit so the edges are more clearly visible.)  This image
will probably show what I was trying to say about triangle edge lining up
better than the description.  Red edges are generated with

"cylinder { pos, pos + vrotate (x, (ang + typ) *y) / 3, 1/20 }"

Green edges are the same but at ang-typ, and the blue edges are from ang+typ
to one third of the way toward ang-typ.  Notice how every edge has only a
single color.  The fact that any blue edge for one triangle is also blue
for the other triangle sharing that edge is why the rhomb drawing works as
described in the last message.

In case you are curious, the yellow curve is a set of torus sections
centered at pos, radius 1/2, connecting the red and green edges.  torus
sections connecting the green and blue edges also make large curves, but
ones connecting the red and blue edges just make circles around a single
vertex.

Jon


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