[help-3dldf] Fwd: Re: Your FEATPOST website

[Laurence Finston]

------ Forwarded message -------


From: "Laurence Finston" <address@hidden>
To: L. Nobre G.  <address@hidden>
Date: Fri, 10 Dec 2004 23:16:32 +0100

Hello Nobre,

L. Nobre G. wrote:

> 
> No. Get it from
>
http://www.ctan.org/tex-archive/graphics/metapost/macros/featpost/doc/tug2004.
pdf

Thanks.

> and remember that Karl Berry had a tremendous work editing that 
article.

Karl has also been very helpful to me.  As you may know, he is an 
important person at the Free Software Foundation.

May I have your permission to post your questions and my answers to the
address@hidden' mailing list?  Some of the subscribers (there are half a
dozen or so) might be interested, and I'd like to have them in 
the archive.

> 
> Yes. I´ll shoot some questions about 3DLDF right now.
> Removes hidden lines?
> How?

No, it doesn't remove them, it just draws or fills over them.  There are four
ways of sorting the objects on a `picture', including the "null" 
sort, i.e., not sorting them.  This method only works for the simplest cases. 
 As you probably know, most surface hiding algorithms, at least the ones I
know about, work on pixel data, which is one of the reasons I plan to
implement output in the PNG format.  However, I always want 3DLDF to be able
to output MetaPost, so I also plan to implement better surface hiding for the
MetaPost output.  Roughly, I plan to do this by dividing objects until there
are none that intersect, removing the ones that are completely covered by
other objects, and drawing the rest in order.  This is one reason I'm so
interested in intersections.

> The input routine that you are working on accepts plain MetaPost code?

Unfortunately not.  It might be possible to set things up so that 3DLDF can
process code written in a subset of the Metafont and MetaPost languages.
I originally wanted any valid MF or MP input to be valid in 3DLDF, and with
the same interpretation, but I don't believe it will be possible to implement
this.  These are the reasons:

1.  I think it may genuinely be impossible to write a parser using Bison that
simulates the behavior of Knuth's hand-written parser.  I'm pretty sure it
wouldn't be possible with a reasonable amount of effort.

2.  I've made some decisions that make it impossible to simulate certain
aspects of MF's behavior.  For example, in MF, the following works:

transform t;
xpart t = 3;
show t;
(3, ypart t, xxpart t ...)

(MF isn't installed on the Windows PC I'm using now, so I can't double-check
this, but I have tried it, or something similar.)   So in MF, `xpart
<transform primary>' is an lvalue.  In 3DLDF, it's not.  `xpart <transform
primary>' causes a temporary object of type `real' (i.e., either `float' or
`double') to be created, and the fact that it's value was copied from a
particular `Transform' is not stored anywhere.  

3.  I haven't implemented features corresponding to all of the features of
MF/MP.  Doing this is a very big job.  For example, the only connectors that
currently make sense in 3DLDF are `..', `...', 
`--', and `---'.  I'm not sure how to define `tension' and `curl' in three
dimensions.  I think there may be more than one possible interpretation.  In
order to do this I will have to implement NURBS, which is the next item on the
agenda after the coming release.

> 
> And another question. This is because I have never met anybody close
> enough to this subject. Once, I found a special polyhedric torus that 
can
> be plaited or planified on a single piece of paper. Is this original?
> 

I don't know about tori, but there's a chapter about constructing polyhedra by
plaiting in Cundy, H. Martyn and A.P. Rollet, 
_Mathematical Models_, Oxford University Press, London 1961, chapter 3,
section 14, p. 152.  They state that the method was discovered by Dr. John
Gorham "[...] who published a book on the subject---_Plaited Crystal
Models_---in 1888".  Cundy and Rollet also mention an article by A.R. Pargeter
in _Math. Gazette_, 43 (1959), 88.  

I believe these constructions became popular later under the name
"hexaflexagons", and that Martin Gardner wrote some articles about them, which
have been republished in book form.  If you don't have access to them where
you are, and you're interested, I could check the books out of the library
here and give you exact references.

Laurence