Herman Serras wrote:
> 
> Hello,
> 
> > It struck me as the easiest and most uniform way to do it.  It could
> > have been easier if I had used box{} for the cube, but then it would not
> > have been constructed similar to the other polyhedra.
> 
> I think it's a good idea to try to obtain a uniform way to describe the
> platonic solids. So I don't mean you should use "box" for the cube. 

Sorry.  I was unclear.  I was just explaining my methods and reasoning. 
I didn't mean to say that I thought you had suggested it.

> But
> the nice thing I learned from your include file is to avoid "polygon" by
> using your macros. 

I am an almost-decent Forth programmer.  I find the overlap between
factoring code in Forth nicely similar to building POV scenes out of
primitives.  I try to use Forth's "simplify as much as possible, and
remove everything that can be removed" strategy as often as I can.

> As I wrote, there can be difficulties if the 3D
> polygon is not a planar one, and this can be a matter of rounding off.
> The only polygon we're sure that it is a planar one is the triangle!

This is why I did something relatively simple, instead of, say, all the
rest of the polyhedra.  :)

> > Interesting that Mr. Towle seems (I have not been able to examine the
> > include files yet; I still need something to unpack .SIT and .HQX files)
> > to have provided the "pipes-and-balls" structures, too.  There is
> > nothing new under the sun.
> 
> The .hqx files can be expanded using "stuffit". You can find this
> program on the web.

Yes, I used to be a Mac person.  I recognize the file type.  I once had
a toolkit for such files that worked on unix, but I am having a hard
time finding it again.

> I also examined some of the files from Mr. Towle. But being a
> mathematician I want to construct the polyhedra (or obtain their data)
> myself.  I think Mr. Towle obtained his data using an other programme:
> all his data are written in decimal form (not using square roots
> etc...).

I am not a mathematician, just someone who wants to better his SDL
skills.

[I've actually got a problem relating to that, but I'm not sure if
povray.programming is the right place, or if it should go in
povray.newusers.  It involves translating something from C to a macro. 
It's rather nasty.]

> > It also occurs to me that I should have used a unit cube.  I would not
> > have found the bug in the icosa- and dodecahedra.  Heh.
> 
> One of the advantages starting from the cube and deriving the other four
> platonic polyhedra form it is that one doesn't need to use spherical
> geometry (or spherical trigonometry). 

To be honest, I took a look at your site last night and I haven't the
faintest idea how I would, for example, construct a dodecahedron out of
a cube in POV-Ray, the way you describe it on your page.

> I think most young people don't
> study those things at school and the whole thing can be done starting
> from the cube and using some analytical geometry. 

Or, in my case, have studied it far too long ago to remember any of it. 
:/

Deaken

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