> Anton Sherwood wrote:
>> I need it [portal pigment or "camera_view"] to complete a series
>> for http://en.wikipedia.org/wiki/Andreini_tessellation -- I made
>> most of the images there, with mirrors, and that's not possible
>> for some of the lattices on the list.

Karl Anders wrote:
> Nice images ! I just love everything that has even remotely to do
> with polyhedra ... though I fail to see why you would need mirrors
> or "camera_view" for those.

By definition these lattices are infinitely deep, and I prefer to 
"cheat" on that fact as little as possible.

Each of those scenes consists of four mirrors (forming 1/48 or 1/24 of 
the basic cube) and four or fewer cylinders.  The appearance of depth 
comes from the decay caused by repeated reflections in imperfect mirrors 
("finish {reflection 0.98}").

I'm more confident in my ability to do it that way than by building a 
finite number of copies of the basic cell; and I'm a big fan of concise 
code!

If anyone's interested in the technicalities --
The mirrors are the boundaries of the space 0 <= x <= y <= z <= 1,
except that in the "alternated" forms the mirror at x=0 is replaced by 
one at x+y=0.  The mirrors form an irregular tetrahedron, and a vertex 
of the lattice is placed somewhere within it (or on its boundaries).  A 
lattice-edge (cylinder) goes from the vertex to its image in each of the 
mirrors, and the vertex is so placed that each nontrivial edge has the 
same length.

-- 
Anton Sherwood, http://www.ogre.nu/
"How'd ya like to climb this high *without* no mountain?" --Porky Pine

Post a reply to this message