3D in PS

[luser- -droog]

The only source I have for doing 3D drawing
in Postscript is Bill Casselman's Mathematical
Illustrations. Are there any other resources out there?

[tlvp]

Excellent question, which I promptly asked Google: [PostScript 3D drawing]?
And Google answered, in part:

> Three dimensional graphics, illustrations and animations with ...
> www.fauskes.net/nb/threedill/
> Nov 8, 2005 – When drawing 3D scenes it's necessary to have access to mathematical tools like rotation matrices, ... PSTricks is based on TeX and Postscript.

> MetaPost - TeX Users Group
> www.tug.org/metapost.html
> Mar 6, 2012 – ... MetaPost, a powerful tool for creating graphics in scalable PostScript. ... an independent implementation for 3d drawing with MetaPost syntax.

> PyX - Python graphics package
> pyx.sourceforge.net/
> It combines an abstraction of the PostScript drawing model with a TeX/LaTeX interface. Complex tasks like 2d and 3d plots in publication-ready quality are built ...

> gnuplot / plotpm3d (E)
> t16web.lanl.gov/Kawano/gnuplot/plotpm3d-e.html
> Dec 17, 2004 – How do I draw a colored 3D figure ? ... The figure is shown on your screen as well as PostScript or some image formats like PNG/JPG. gnuplot> ...

(This last is sorta cute, actually :-) .) HTH. Cheers, -- tlvp
--
Avant de repondre, jeter la poubelle, SVP.

[gernot....@hs-emden-leer.de]

Am Donnerstag, 19. Juli 2012 08:28:10 UTC+2 schrieb luser- -droog:
> The only source I have for doing 3D drawing

> in Postscript is Bill Casselman's Mathematical

> Illustrations. Are there any other resources out there?

Some applications:

http://www.fho-emden.de/~hoffmann/pstutor22112002.pdf

http://www.fho-emden.de/~hoffmann/cielab03022003.pdf
p.44 - p.48

http://www.fho-emden.de/~hoffmann/project18032004.pdf

http://www.fho-emden.de/~hoffmann/gamshow15052009.pdf

http://www.fho-emden.de/~hoffmann/track1cam15062012.pdf

Best regards -- Gernot Hoffmann

[luser- -droog]

On Thursday, July 19, 2012 2:47:20 AM UTC-5, tlvp wrote:
> On Wed, 18 Jul 2012 23:28:10 -0700 (PDT), luser- -droog wrote:
>

> > The only source I have for doing 3D drawing
> > in Postscript is Bill Casselman's Mathematical
> > Illustrations. Are there any other resources out there?

>
> Excellent question, which I promptly asked Google: [PostScript 3D drawing]?
> And Google answered, in part:
>

> > Three dimensional graphics, illustrations and animations with ...
> > www.fauskes.net/nb/threedill/
> > Nov 8, 2005 – When drawing 3D scenes it's necessary to have access to mathematical tools like rotation matrices, ... PSTricks is based on TeX and Postscript.
>
> > MetaPost - TeX Users Group
> > www.tug.org/metapost.html
> > Mar 6, 2012 – ... MetaPost, a powerful tool for creating graphics in scalable PostScript. ... an independent implementation for 3d drawing with MetaPost syntax.
>
> > PyX - Python graphics package
> > pyx.sourceforge.net/
> > It combines an abstraction of the PostScript drawing model with a TeX/LaTeX interface. Complex tasks like 2d and 3d plots in publication-ready quality are built ...
>
> > gnuplot / plotpm3d (E)
> > t16web.lanl.gov/Kawano/gnuplot/plotpm3d-e.html
> > Dec 17, 2004 – How do I draw a colored 3D figure ? ... The figure is shown on your screen as well as PostScript or some image formats like PNG/JPG. gnuplot> ...

>
> (This last is sorta cute, actually :-) .) HTH. Cheers, -- tlvp
> --
> Avant de repondre, jeter la poubelle, SVP.

I peeked at these, and did my own search (belatedly),
but I fear most of these tools use postscript as
a raster format. The one enticing link I found
was to a one-page pdf from Eurographics 90 describing
3D extensions to postscript. But no copies available
on Amazon. :(

So I'm thinking Casselman's still my best bet.
I'll probably need it to understand Gernot's code.

I suspect there's good stuff buried in the archives
of this group (and maybe comp.windows.news too)
but it may be a pain to search through.

One bonus from my search: I think my new L-system
code is slicker than anyone else's. :)

--
<</F{F - G + F + G - F}/G{G G}>>begin
{F - G - G}7{[exch{dup where{exch get aload pop}if}forall]}repeat
cvx<</F{3 0 rlineto}/G 1 index/-{120 rotate}/+{-120 rotate}>>begin
100 100 moveto exec fill showpage

[tlvp]

On Fri, 20 Jul 2012 20:43:48 -0700 (PDT), luser- -droog wrote:

> One bonus from my search: I think my new L-system
> code is slicker than anyone else's. :)
>

> <</F{F - G + F + G - F}/G{G G}>>begin
> {F - G - G}7{[exch{dup where{exch get aload pop}if}forall]}repeat
> cvx<</F{3 0 rlineto}/G 1 index/-{120 rotate}/+{-120 rotate}>>begin
> 100 100 moveto exec fill showpage

Sure is compact. And terse. As I totally fail to follow the geometric
motivation of even the tiniest morsel in it, I'd even go so far as to call
it obscure. And oh! would I appreciate a good commenting on it :-) .

Including also why "L" for what I see as a "Kuratowski gasket"?

Cheers (and thanks for the code), -- tlvp

[luser- -droog]

On Saturday, July 21, 2012 12:27:51 AM UTC-5, tlvp wrote:
> On Fri, 20 Jul 2012 20:43:48 -0700 (PDT), luser- -droog wrote:
>

> &gt; One bonus from my search: I think my new L-system
> &gt; code is slicker than anyone else&#39;s. :)
> &gt;
> &gt; &lt;&lt;/F{F - G + F + G - F}/G{G G}&gt;&gt;begin
> &gt; {F - G - G}7{[exch{dup where{exch get aload pop}if}forall]}repeat
> &gt; cvx&lt;&lt;/F{3 0 rlineto}/G 1 index/-{120 rotate}/+{-120 rotate}&gt;&gt;begin
> &gt; 100 100 moveto exec fill showpage

>
> Sure is compact. And terse. As I totally fail to follow the geometric

> motivation of even the tiniest morsel in it, I&#39;d even go so far as to call

> it obscure. And oh! would I appreciate a good commenting on it :-) .
>

> Including also why &quot;L&quot; for what I see as a &quot;Kuratowski gasket&quot;?

>
> Cheers (and thanks for the code), -- tlvp
> --
> Avant de repondre, jeter la poubelle, SVP.

Well, here's a slightly different one with comments.
Wikipedia should do the rest.

%!
%Reference:
%http://en.wikipedia.org/wiki/L-system#Example_7:_Fractal_plant
%
<< %start constructing a dictionary

%Deterministic Context-Free L-System
%simulated by repeated macro-expansion
%of elements in the array with definitions
%in the currentdict
% proc(ie. array) repeat-count DOL expanded-proc
/DOL { % arr M
{ % arr
[ exch % [ arr
{ % [ ... arr_N perform substitutions on each element
currentdict exch 2 copy known % [ ... dict arr_N bool
{get aload pop}{exch pop}ifelse % [ ... arr_N'
} forall % [ arr_0 arr_1 ... arr_N-1
] % arr' zip up array
dup length = %report size of proc
dup 0 exch { /X eq { 1 add } if } forall = %how many 'X's
dup 0 exch { /F eq { 1 add } if } forall = %how many 'F's
()= %blank line
} repeat % arr'^M array transformed M times
cvx % convert array to proc
}
%transformations (Productions)
/X {F -[[X]+ X]+ F[+ F X]- X}
/F {F F}
>>begin %define DOL and transformations

{X} % seed-proc
6 DOL % expanded-proc

<< % graphical interpretation of expanded proc
([){gsave}
(]){currentpoint 1 0 180 arc stroke grestore}
/X{}
/F{0 3 rlineto currentpoint stroke moveto}
/a 25
/-{a rotate}
/+{a neg rotate}
>>begin %define interpretation

200 200 moveto %establish currentpoint
exec %execute the proc
showpage

[tlvp]

Wow! I'm out of breath!

Ages ago, as a college frosh, it would take me an hour to digest a page in
my calculus textbook. Today, it seems to me, it'd take me an hour to grok
each *line* of that PS routine. With lotsa luck, I might even get to grasp
it all by the end of the month, if I put in enough time each day.

Without the comments, even 1 line per day would be super-optimistic :-) .
So: many thanks! And cheers, -- tlvp

[luser- -droog]

On Saturday, July 21, 2012 9:16:07 PM UTC-5, tlvp wrote:
> On Sat, 21 Jul 2012 13:23:34 -0700 (PDT), luser- -droog wrote:
>

[some google-butchered code]
> Wow! I&#39;m out of breath!

>
> Ages ago, as a college frosh, it would take me an hour to digest a page in

> my calculus textbook. Today, it seems to me, it&#39;d take me an hour to grok

> each *line* of that PS routine. With lotsa luck, I might even get to grasp
> it all by the end of the month, if I put in enough time each day.
>
> Without the comments, even 1 line per day would be super-optimistic :-) .
> So: many thanks! And cheers, -- tlvp
> --
> Avant de repondre, jeter la poubelle, SVP.

Well, there are at least two levels going on.
First is the the program. How it cracks and
reconstructs an array, performing substitutions
on each element, and how the result is then
used as graphics commands.

Second is how the transformations of the strings
guide the evolution of the image. For this I
have to use paper. Sketching out the first few
stages to see how it grows.

The wikipedia page is essentially a book review
for this amazing free book:
http://algorithmicbotany.org/papers/#abop

Here's the first one I've actually devised
the strings for.

%Pythagoras Tree
<</F{G - - G - - H - - G - - G} % replace line with CCW square
/H{G + + + [ F + + F ] + + + G} % replace line with CW rt tri
>>begin
{F} % start with a line
19 % after about 15 it starts to "bloom"
{[exch{currentdict exch 2 copy known{get aload pop}{exch pop}ifelse}forall] %expand
cvx
%dup == % watch the strings grow
% (if you dare! (try a smaller repeat number, like 4))
}repeat
<</r 90/a 45
/F{r 0 rlineto}/G 1 index/H 1 index/-{a rotate}/+{a neg rotate}
([){/r r 2 copy 2 sqrt div def} %save length, reduce
(]){def} %restore length
>>begin
250 150 moveto exec stroke showpage

[Steve]

tlvp <mPiOsUcB...@att.net> writes:
>On Sat, 21 Jul 2012 13:23:34 -0700 (PDT), luser- -droog wrote:

<Snip>

>> showpage
>
>Wow! I'm out of breath!
>
>Ages ago, as a college frosh, it would take me an hour to digest a page in
>my calculus textbook. Today, it seems to me, it'd take me an hour to grok
>each *line* of that PS routine. With lotsa luck, I might even get to grasp
>it all by the end of the month, if I put in enough time each day.
>
>Without the comments, even 1 line per day would be super-optimistic :-) .
>So: many thanks! And cheers, -- tlvp
>--
>Avant de repondre, jeter la poubelle, SVP.

Hi,

Yes. A bit to digest. Thanks for the exercise.

Regards,

Steve N.

[tlvp]

On Sun, 22 Jul 2012 02:40:37 -0700 (PDT), luser- -droog wrote:

>
> Well, there are at least two levels going on.
> First is the the program. How it cracks and
> reconstructs an array, performing substitutions
> on each element, and how the result is then
> used as graphics commands.
>
> Second is how the transformations of the strings
> guide the evolution of the image. For this I
> have to use paper. Sketching out the first few
> stages to see how it grows.
>
> The wikipedia page is essentially a book review
> for this amazing free book:
> http://algorithmicbotany.org/papers/#abop

Ah ... that sheds much needed light on the role your F G H + - symbology
plays ... thanks *very* much. (A neat book on its own merits as well :-) .)

> Here's the first one I've actually devised
> the strings for.
>
> %Pythagoras Tree
> <</F{G - - G - - H - - G - - G} % replace line with CCW square
> /H{G + + + [ F + + F ] + + + G} % replace line with CW rt tri
>>>begin
> {F} % start with a line
> 19 % after about 15 it starts to "bloom"
> {[exch{currentdict exch 2 copy known{get aload pop}{exch pop}ifelse}forall] %expand
> cvx
> %dup == % watch the strings grow
> % (if you dare! (try a smaller repeat number, like 4))
> }repeat
> <</r 90/a 45
> /F{r 0 rlineto}/G 1 index/H 1 index/-{a rotate}/+{a neg rotate}
> ([){/r r 2 copy 2 sqrt div def} %save length, reduce
> (]){def} %restore length
>>>begin
> 250 150 moveto exec stroke showpage

Cute :-) . Thanks. Now to see whether I can use any of the ideas I can
harvest from that book to help display visually evocative 2D projections of
that 3D object, the eight-eared sphere :-) (aka convex puffed-up cube with
inflexible wire-frame edge-lines).

Cheers, and thanks for the follow-ups, -- tlvp

[luser- -droog]

I've been thinking about this. I think the easiest way
to start would be to make a wireframe by intersecting
the shape with the planes x=0,y=0,z=0,x=1,y=1,z=1,x=-1,y=-1, etc.
Then we'd at least have a path to work with--in 3D
coordinates, of course, but still a path.
Then we project each 3D coordinate to the z=1 plane
and drop the z 'ordinate.

At least, that's my "pseudocode" at the moment.
I don't actually know how to do step 1, yet, though.

Adding a rotation shouldn't be difficult once the
above is done.

[tlvp]

A little geometric insight triggered by your term "wireframe".

Background: I'm thinking of spheres and/or circles of radius 2, diameter 4.

Start with a wireframe square of *diagonal* 4.
Clearly that can be inscribed in a circle of diameter 4 (*).
Such a square's edges all have length: 2 sqrt(2) mul .

Now visualize a wireframe cubical frame with each face a square, as above,
of diagonal 4, edges of length 2sqrt(2). The distance from its epicenter
(centroid, center of gravity, center of mass) to each point on any of its
linear edges is at least 2, and usually greater than 2, so a sphere of
radius 2 could be "imprisoned" within that cubical frame (as "jail").

At the same time, an open ("hollow") cylinder of radius 2 can just
pass snugly over that cube if approaching it face on in any of the three
principal "face-on" directions (that's just re-interpreting (*) above).

It'd be nice to see an SVG -- or even an animated GIF sequence -- showing:

: a sphere of radius 2
: the cubical wireframe "jail" with side-faces of diagonal 4 "imprisoning" that sphere
: the three open (hollow) cylinders passing just over that "jailed sphere" complex
: the (somewhat larger) full intersection of the three cores those cylinders carve out (imagine it all submerged in a tray of jello, and literally carving out those cores).

Or a single PS capturing all the essential graphic features just described.

Wishful thinking? I hope not :-) . TIA! Cheers, -- tlvp

[Herbert Voss]

http://melusine.eu.org/syracuse/pstricks/pst-solides3d/
uses always PS for the the 3d stuff

Herbert

[Peter Billam]

On 2012-08-08, Herbert Voss <Herber...@alumni.tu-berlin.de> wrote:
> http://melusine.eu.org/syracuse/pstricks/pst-solides3d/
> uses always PS for the the 3d stuff
> Herbert

That's very impressive; I might have to explore that one.
It helps that I speak French :-)
But I still can't spot the link to the debian package, for example,
and the .tex file comes to me wrapped in html; I can extract text
with lynx -dump and vi but there should be a neater way...
Impressive, though.

Peter

--
Peter Billam www.pjb.com.au www.pjb.com.au/comp/contact.html

[JohnF]

More precisely, as suggested by the link, he seems to always use
the LaTeX pstricks package, along with the package pst-solides3d.
See, for example,
http://melusine.eu.org/lab/bpst/pst-solides3d/objfusion/joao.pst
and click the [LaTeX] button to get his joao.tex file.
That's not a bad thing, per se, but not the same thing as
Casselman's approach.
--
John Forkosh ( mailto: j...@f.com where j=john and f=forkosh )

[tlvp]

On Wed, 08 Aug 2012 15:48:23 +0200, Herbert Voss wrote:

> Am 19.07.2012 08:28, schrieb luser- -droog:

>> ... doing 3D drawing
>> in Postscript ... any other resources ... ?

>>
> http://melusine.eu.org/syracuse/pstricks/pst-solides3d/
> uses always PS for the the 3d stuff
>
> Herbert

Lovely link, Herbert :-) ! Thank you. Cheers, -- tlvp

[Herbert Voss]

it _is_ based on Casselman's ideas!

More examples are here:
http://tug.org/PSTricks/main.cgi?file=Examples/Gallery3D/Gallery3D

Herbert

[JohnF]

My bad. I guess I was focusing more on the postscript language
itself rather than on the algorithms being implemented.
But the thread subject clearly states it the other way around.
Thanks for the additional link.

[luser- -droog]

Found something in the archive of this group.

https://groups.google.com/d/topic/comp.lang.postscript/7GRTbd4K4Sg/discussion

[Mark Carroll]

Alas, when I've wanted to do 3D, I've calculated the z-stacked 2D
projection in code in a different programming language, then made it use
a custom drawing library that just printed out postscript code under the
hood for drawing the scene from "bottom" to "top".

Mark

[luser- -droog]

Any more juicy details you'd care to spill about this
"custom drawing library"? We're all drooling fangs out here!

:-D

lusor basiliensis (droug)

[luser- -droog]

Why in the hell is it upside-down??