Alex wrote: > In message , PM 2Ring > writes > >Alex 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! That was my plan, also, but I didn't even get as far as the coding stage. > >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. I've been programming in C for almost 25 years, but I wasn't suggesting that it would be a task for we lesser mortals. :) I was hoping that deBruijn's construction might be incorporated as a standard pattern into the official POV, some time in the future. > >> >>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. I've rendered the demo files & am in the process of transforming one of Jaime's indoor scenes, rearranging and modifying the furniture & adding little things like a door handle. See below for an example. > > > >> >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. > -- Ah! The old Amstrad. Such a pleasant machine to program.