In message <web.42dd997f811cc7c3ad93754b0@news.povray.org>, PM 2Ring 
<nomail@nomail.?.invalid> writes
>Alex <pov### [at] lazysodorguk> wrote:
>
>
>> Projecting a specific subset of a 5 dimensional integer lattice onto a 2
>> dimensional plane to give the vertices of the rhombs. The principle is
>> very simple, and it's easy to do with a 3 dimensional lattice, but for
>> the life of me I can't work out the nitty gritty of the higher
>> dimensional cases. All the resources I can find just explain the
>> principle.
>>
>> Method discovered by deBruijn.
>
>Of course, how could I forget. I thought of using deBruijn's method, but I
>couldn't figure out a way to do it in POV. Also, it's been a while since
>I've played with higher-dimensional geometry, but I think that simple
>orthographic projections are used to project from n dimensions to n-1
>dimensions.
>
Yes. Projecting from n to n-3 dimensions is more tricky. I thought I 
sussed out how to do it (for the umpteenth time), but once I coded it it 
didn't work and I couldn't be bothered to look at it any more. I had 
originally hoped to be able to create a procedural texture!

>If I understand this stuff correctly, the deBruijn construction is a regular
>5D Voronoi diagram, so it should be easy to implement in POV by modifying
>the code for the crackle pattern.
>
I'm not messing with source code. I never did suss out c.

<snip>

>
>> >>I thought it might help the appearance
>> >> of the blurred reflections of distant tiles.
>> >
>> >That makes sense. Still, the floor is a little too dark for my tastes.
>>
>> Maybe. But make everything bright and the highlights don't show up as
>> much. It's a difficult one to judge.
>
>I suppose that this is where Jaime's Lightsys comes in very useful, although
>I've just started exploring Lightsys myself.
>
Just had a quick look at it, looks interesting. Lighting can be very 
tricky.

>
>> >Here's a Penrose tiling, using rounded pentagonal prisms, in standard stone
>> >textures. The tiles were placed by simple #while loops, not recursive
>> >macros.
>> >
>> Similar to a "pentaflake" fractal, but with some pentagons filling the
>> larger gaps.
>
>Yes. I few years back, I wrote a little C program for my Amiga to play with
>pentagonal tilings by hand. I spent many, many hours exploring these
>tilings.
>
I never knew about these tilings until relatively recently, although I 
have programmed similar L-system fractal algorithms on my old CPC464.
-- 
Alex

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