shading in meta[post/play] & PDF

shading in meta[post/play] & PDF

[Mojca Miklavec]

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There's a wonderful tutorial on drawing 3D graphics in PostScript on 
http://www.math.ubc.ca/~cass/graphics/manual/, specifically
http://www.math.ubc.ca/~cass/graphics/manual/code/doughnut.eps as an 
example.

And there's a detailed description on shading in PostScript in
http://partners.adobe.com/public/developer/en/ps/PLRM.pdf, page 259
(I attached an example and have some more on computer if anyone is 
interested; I downloaded them from Adobe, but don't know the URL any 
more) or on shading in PDF in
http://partners.adobe.com/public/developer/en/pdf/PDFReference16.pdf, 
page 272. (They're basically the same.)

In metapost, "perfect" spheres can be drawn, like on 
http://www.gnu.org/software/3dldf/cdsmpls.html. But how can I add colour?

Even if it would be too tricky to add colour and proper shading on the 
sphere - Is there any possibility to use advanced shading techiques 
described in PLRM inside metapost/metaplay for the most simple cases, 
say, like in the attached example? Metaplay allows circular and gradient 
shading and no others. I don't mind if I had to hard-code the shading.

PSTricks allows some more advanced shading techniques and even direct 
PostScript code integration (with \special I think). Is anything similar 
possible in metapost/play?

The spheres drawn directly in PostScript as in the examples above still 
have straight lines (well, I agree that with some mathematics it would 
be possible to draw them with proper splines as well).

Thanks for all the suggestions,
	Mojca

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Re: [metapost] shading in meta[post/play] & PDF

[Laurence Finston]

Mojca Miklavec wrote:

> There's a wonderful tutorial on drawing 3D graphics in PostScript on 
> http://www.math.ubc.ca/~cass/graphics/manual/, specifically
> http://www.math.ubc.ca/~cass/graphics/manual/code/doughnut.eps as an 
> example.

Thanks for the reference, it looks very interesting.

> 
> In metapost, "perfect" spheres can be drawn, like on 
> http://www.gnu.org/software/3dldf/cdsmpls.html. But how can I add > colour?

The spheres in that example are really just circles.  The "globe font" was
done using Metafont, which doesn't support color at all.  The sphere graphic
at the beginning of that file was done using MetaPost, so the circles could be
drawn in color, but I know this isn't what you mean.   
The glyphs from the globe font (which I plan to improve) could be colored,
e.g., by using the macros defined in the `colordvi.tex' file supplied with
`dvips'.  Of course, a given glyph could only be printed or displayed in a
single color.

GNU 3DLDF does not yet possess a `sphere' type, but I plan to add one in the
not-too-distant future.  I also plan to add shading, but that is in the more
distant future.  The shading methods I'm (vaguely) familiar with operate on
raster data and I haven't quite decided how to handle rasterization.  I'm
leaning toward using the PNG format rather than PostScript for this.  I
believe PostScript can be used for both vector and raster data, but my memory
of the details is hazy.

> 
> The spheres drawn directly in PostScript as in the examples above still 
> have straight lines (well, I agree that with some mathematics it would 
> be possible to draw them with proper splines as well).
> 

If you mean my spheres, that's an artefact of the PNG graphics.  The
PostScript versions look nicer.  I believe that on commonly available devices,
 curves are ultimately drawn as short straight-line segments, though.  In the
code in that file, the circles have 64 points, and I thought the results were
good enough.  Raising it to some value x such that x % 4 == 0 and x > 64 might
improve them, I haven't tried it.  32 wasn't enough.

Laurence Finston
http://www.gnu.org/software/3dldf/LDF.html

Re: [metapost] shading in meta[post/play] & PDF

[Mojca Miklavec]

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The answer to the mail follows, but to reformulate my question slightly:

How can I make shading inside metapost(play) to produce exactly what's 
in the attached picture (smooth shades). Or more generally: how can I 
"hardcode" some PS/PDF code in .mp, not (yet) supported by metapost(play)?

(PDF supports even 3D shapes (already shaded properly) since version 1.5 
or 1.6, but I suppose that's another story anyway.)

Here's the corresponding PostScript code:

%!PS-Adobe-3.0 Resource-ProcSet
%%Title: Hsbwheel.ps
%%Creator: Henry McGilton, Adobe Systems Incorporated (modified!)
%%EndComments

200 dup scale

/X3  1.0 3 div def
/X6  2.0 3 div def
/Y3  1.0 3 div def
/Y6  2.0 3 div def

/middlecolor  [ 1    1   1 ] def
/topcolor     [ 1    0   0 ] def
/rightcolor   [ 0.5  0   1 ] def

newpath
<<
     /ShadingType 6
     /ColorSpace /DeviceRGB
     /DataSource [
         0
           0.0 0.0    X3 0.0     X6  0.0   1.0 0.0
           1.0 .552   .552 1.0   0.0 1.0
           0.0 Y6     0.0 Y3     0.0 0.0   0.0 0.0    0.0 0.0
           middlecolor aload pop    rightcolor  aload pop
           topcolor   aload pop     middlecolor aload pop
     ]
 >> shfill

showpage

************************************************************************

Laurence Finston wrote:

> Mojca Miklavec wrote:
> 
> 
>>There's a wonderful tutorial on drawing 3D graphics in PostScript on 
>>http://www.math.ubc.ca/~cass/graphics/manual/, specifically
>>http://www.math.ubc.ca/~cass/graphics/manual/code/doughnut.eps as an 
>>example.
> 
> 
> Thanks for the reference, it looks very interesting.
> 
> 
>>In metapost, "perfect" spheres can be drawn, like on 
>>http://www.gnu.org/software/3dldf/cdsmpls.html. But how can I add > colour?
> 
> 
> The spheres in that example are really just circles.  The "globe font" was
> done using Metafont, which doesn't support color at all.  The sphere graphic
> at the beginning of that file was done using MetaPost, so the circles could be
> drawn in color, but I know this isn't what you mean.

Well - the main question is how to add the proper (smooth shading) color 
once I calculate the grid points in one way or another.

> The glyphs from the globe font (which I plan to improve) could be colored,
> e.g., by using the macros defined in the `colordvi.tex' file supplied with
> `dvips'.  Of course, a given glyph could only be printed or displayed in a
> single color.
> 
> GNU 3DLDF does not yet possess a `sphere' type, but I plan to add one in the
> not-too-distant future.  I also plan to add shading, but that is in the more
> distant future.  The shading methods I'm (vaguely) familiar with operate on
> raster data and I haven't quite decided how to handle rasterization.  I'm
> leaning toward using the PNG format rather than PostScript for this.  I
> believe PostScript can be used for both vector and raster data, but my memory
> of the details is hazy.

Well, PostScript can be used for raster images, but that doesn't bring 
anything. The examples on Cass' page are actually done using *vector* 
graphics (colors are really calculated only in grid points, but then the 
color is interpolated by postscript interpreter): the perfect sphere 
coloring is thus really limited to "floating point accuracy" and printer 
capabilities.

>>The spheres drawn directly in PostScript as in the examples above still 
>>have straight lines (well, I agree that with some mathematics it would 
>>be possible to draw them with proper splines as well).
>>
> 
> 
> If you mean my spheres, that's an artefact of the PNG graphics.  The
> PostScript versions look nicer.  I believe that on commonly available devices,
>  curves are ultimately drawn as short straight-line segments, though.  In the
> code in that file, the circles have 64 points, and I thought the results were
> good enough.  Raising it to some value x such that x % 4 == 0 and x > 64 might
> improve them, I haven't tried it.  32 wasn't enough.

No, I wasn't talking about the PNGs. I was talking about the PostScript 
pictures. http://www.math.ubc.ca/~cass/graphics/manual/code/doughnut.eps 
has a really *perfect* shading, but its edges are drawn using straight 
segments instead of drawing them with splines which damages slightly the 
whole impression of its perfectness. Some additional calculation for 
spline drawing would help, but I still find it easier to calculate the 
curves in metapost than in PostScript.

Those "straight-line segments" on printers are just as straight as they 
are on any laser print-out of texts if I'm not wrong - i.e. not worth 
considering.

Thank you,
	Mojca


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Re: [metapost] shading in meta[post/play] & PDF

[Laurence Finston]

On Wed, 19 Jan 2005, Mojca Miklavec wrote:

>
> How can I make shading inside metapost(play) to produce exactly what's
> in the attached picture (smooth shades). Or more generally: how can I
> "hardcode" some PS/PDF code in .mp, not (yet) supported by metapost(play)?
>

This is a very difficult question.  For an excellent introduction
to shading and other subjects I recommend:

Jones, Huw.
_Computer Graphics through Key Mathematics_.
Springer-Verlag London Limited 2001.
ISBN 1-85233-422-3.

>
> Here's the corresponding PostScript code:
>

Sorry, I don't know PostScript.

>
> >>The spheres drawn directly in PostScript as in the examples above still
> >>have straight lines (well, I agree that with some mathematics it would
> >>be possible to draw them with proper splines as well).
> >>

To the best of my knowledge, spline curves are drawn by means of
calculating short line segments.  You can make the "time" parameter
as small as you like, but you can't make it 0.

I believe plotters can draw genuine curves---and it's a lot more
fun to watch them work (it's like magic).
They're not so great at filling in regions,
though.  Much to my regret, the computer center here got rid of
the plotter.  They're probably as obsolete as the ENIAC now, except
perhaps for very high-quality work.

> Thank you,

My pleasure.

Laurence

Re: [metapost] shading in meta[post/play] & PDF

[Hans Hagen]

Mojca Miklavec wrote:

> How can I make shading inside metapost(play) to produce exactly what's 
> in the attached picture (smooth shades). Or more generally: how can I 
> "hardcode" some PS/PDF code in .mp, not (yet) supported by metapost(play)?

certain kind of native level 2 shaded can be done with the metafun macros 
(circular and linear vector based)

a couple of years ago mathew baker and i played with more advanced features 
using functions and such but i need to locate that code;

if you're willing to figure out what (in pdf) functionality is needed i can 
extend the current metapost shading handler with a few more alternatives [the 
function based ones, since that's what you're looking for])

[more a context mailing list issue than a metapost list issue]

Hans


-----------------------------------------------------------------
                                           Hans Hagen | PRAGMA ADE
               Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
      tel: 038 477 53 69 | fax: 038 477 53 74 | www.pragma-ade.com
                                              | www.pragma-pod.nl
-----------------------------------------------------------------

Re: shading in meta[post/play] & PDF

[Mojca Miklavec]

Hans Hagen wrote:

> Mojca Miklavec wrote:
> 
>> How can I make shading inside metapost(play) to produce exactly what's 
>> in the attached picture (smooth shades). Or more generally: how can I 
>> "hardcode" some PS/PDF code in .mp, not (yet) supported by 
>> metapost(play)?
> 
> 
> certain kind of native level 2 shaded can be done with the metafun 
> macros (circular and linear vector based)
> 
> a couple of years ago mathew baker and i played with more advanced 
> features using functions and such but i need to locate that code;
> 
> if you're willing to figure out what (in pdf) functionality is needed i 
> can extend the current metapost shading handler with a few more 
> alternatives [the function based ones, since that's what you're looking 
> for])

I'm not sure if I understood the question correctly (about what should I 
figure out).

I would like to draw a sphere (possibly with different colors on 
different points of the sphere; which would then be interpolated across 
the whole surface).

Problem description:
I have a computer program, which carries the data about the grid points 
on a sphere (possibly with different colors defined in these points) and 
how the points are connected with each other to form a grid. I would 
take these triangles (or quadrilaterals), draw them transformed on the 
plane (with curves, not with straight lines) and fill them with the 
appropriate shading pattern (colors defined in corners of the triangles 
(darker according to normal vector) simply interpolated between the 
three points). Yet another possibility would probably be to use 
function-based shading and define a function which knows how the points 
have to be shaded on the sphere, but the latter seems more complicated 
and less universal.

Problem reduction:
Fill a mp closed path with any more complex shading.

So I would probably need Type 6 or 7 shading (Type 4 would be OK as the 
picture can be clipped within metapost, so that the resulting sphere 
borders are not composed of straight lines; the articles on 
http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/ which 
inspired me to do something so crazy actually use Type 4 shading). Type 
one is probably the most general one, so it should be OK too, just 
complicated to do.

However: I'm not sure if, say, a (sampled) function to be passed to PDF 
can be specified in metapost elegantly.

Page 746 of PDF Reference, version 1.6 also defines an interesting new 
feature: 3D objects (3D Artwork as they call it), but I haven't found 
anything else about that.

In dvipdfm there's an example of using:
\special{pdf: bt rotate 90 xscale 2.0 }

These lines are to be used in TeX. MetaPost also knows a "special" 
command, I just don't know how to use it. (This is probably the 
"communication channel" to PDF when trying to implement some more exotic 
shadings.)

I glimpsed the mp-spec.mp file, but I didn't yet understand how the 
parameters are passed to PDF.

> [more a context mailing list issue than a metapost list issue]

So I left the metapost group out. Actually, 90% on the people here 
probably think I posted that to the wrong group anyway (in the sense of 
"Are you sure you didn't want to post that question to the 3D studio max 
mailing list?" :) The example above is probably not the most descriptive 
one, but having the possibility to add some more advanced shading 
patterns would be great.

Thank you,
	Mojca

Re: shading in meta[post/play] & PDF

[h h extern]

Mojca Miklavec wrote:

> Problem description:
> I have a computer program, which carries the data about the grid points 
> on a sphere (possibly with different colors defined in these points) and 
> how the points are connected with each other to form a grid. I would 
> take these triangles (or quadrilaterals), draw them transformed on the 
> plane (with curves, not with straight lines) and fill them with the 
> appropriate shading pattern (colors defined in corners of the triangles 
> (darker according to normal vector) simply interpolated between the 
> three points). Yet another possibility would probably be to use 
> function-based shading and define a function which knows how the points 
> have to be shaded on the sphere, but the latter seems more complicated 
> and less universal.
> 
> Problem reduction:
> Fill a mp closed path with any more complex shading.
> 
> So I would probably need Type 6 or 7 shading (Type 4 would be OK as the 
> picture can be clipped within metapost, so that the resulting sphere 
> borders are not composed of straight lines; the articles on 
> http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/ which 
> inspired me to do something so crazy actually use Type 4 shading). Type 
> one is probably the most general one, so it should be OK too, just 
> complicated to do.
> 
> However: I'm not sure if, say, a (sampled) function to be passed to PDF 
> can be specified in metapost elegantly.

i searched my machine extensively but it seems that i lost some code that could 
be used as starting point for that;

> Page 746 of PDF Reference, version 1.6 also defines an interesting new 
> feature: 3D objects (3D Artwork as they call it), but I haven't found 
> anything else about that.

there is a section about shading, the function numbers differ;

> In dvipdfm there's an example of using:
> \special{pdf: bt rotate 90 xscale 2.0 }
> 
> These lines are to be used in TeX. MetaPost also knows a "special" 
> command, I just don't know how to use it. (This is probably the 
> "communication channel" to PDF when trying to implement some more exotic 
> shadings.)

take a look at supp-mpe.tex, all we need is some variant on

\defineMPspecial{31}
   {\startMPshading{16}% type 3
    \setMPshadingcolors{4}{5}{6}{10}{11}{12}%
    \immediate\pdfobj
      {<</FunctionType 2
         /Domain [\gMPs1 \gMPs2]
         /C0 [\MPshadeA]
         /C1 [\MPshadeB]
         /N \gMPs3>>}%
    \immediate\pdfobj
      {<</ShadingType 3
         /ColorSpace /\MPshadeC\space
         /Function \the\pdflastobj\space 0 R
         /Coords [\gMPs7 \gMPs8 \gMPs9 \gMPs{13} \gMPs{14} \gMPs{15}]
         /Extend [true true]>>}%
    \stopMPshading}

(plus some more depending on what parameters need to be passed)

> I glimpsed the mp-spec.mp file, but I didn't yet understand how the 
> parameters are passed to PDF.
> 
>> [more a context mailing list issue than a metapost list issue] 
> 
> So I left the metapost group out. Actually, 90% on the people here 
> probably think I posted that to the wrong group anyway (in the sense of 
> "Are you sure you didn't want to post that question to the 3D studio max 
> mailing list?" :) The example above is probably not the most descriptive 
> one, but having the possibility to add some more advanced shading 
> patterns would be great.

if you can locate the right stuff in the pdf ref manual we can see what can be 
done (off list); i can add more 'special' handlers to the mp to pdf converted

Hans


-----------------------------------------------------------------
                                           Hans Hagen | PRAGMA ADE
               Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
      tel: 038 477 53 69 | fax: 038 477 53 74 | www.pragma-ade.com
                                              | www.pragma-pod.nl
-----------------------------------------------------------------

Re: shading in meta[post/play] & PDF

[Mojca Miklavec]

>> Page 746 of PDF Reference, version 1.6 also defines an interesting new 
>> feature: 3D objects (3D Artwork as they call it), but I haven't found 
>> anything else about that.
> 
> 
> there is a section about shading, the function numbers differ;

?
How? (I was talking only about shading types, not about function types 
at all anyway, but the number *should* be the same.)

> take a look at supp-mpe.tex, all we need is some variant on
> 
> \defineMPspecial{31}
>   {\startMPshading{16}% type 3
>    \setMPshadingcolors{4}{5}{6}{10}{11}{12}%
>    \immediate\pdfobj
>      {<</FunctionType 2
>         /Domain [\gMPs1 \gMPs2]
>         /C0 [\MPshadeA]
>         /C1 [\MPshadeB]
>         /N \gMPs3>>}%
>    \immediate\pdfobj
>      {<</ShadingType 3
>         /ColorSpace /\MPshadeC\space
>         /Function \the\pdflastobj\space 0 R
>         /Coords [\gMPs7 \gMPs8 \gMPs9 \gMPs{13} \gMPs{14} \gMPs{15}]
>         /Extend [true true]>>}%
>    \stopMPshading}
> 
> (plus some more depending on what parameters need to be passed)

Thanks for pointing it out.

This piece of code is very nice (however the whole bunch of code that 
resides in the file ... I wonder how you managed to put all that stuff 
together :)

  > if you can locate the right stuff in the pdf ref manual we can see what
> can be done (off list); i can add more 'special' handlers to the mp to 
> pdf converted

Here are some more examples:

http://partners.adobe.com/public/developer/ps/sdk/index_archive.html
http://partners.adobe.com/public/developer/en/ps/sdk/TN5600.SmoothShading.pdf
http://partners.adobe.com/public/developer/en/ps/sdk/sample/smooth.zip

(I didn't want to send the material to the list and I didn't find the 
links until now.)

I'll try to make the drawings I need (in PostScript for the beginning) 
and collect the ideas of how the things have to be implemented (which 
features supported and how). I'm in no way such a 'superwoman' to be 
able to do dozens of things efficiently in one day as you do, but I'll 
do my best; exams are approaching, so it may take me slightly longer - 
please apologize me.

Thanks again for being prepared to help. I'll write back as soon as I 
have something to report.

Mojca

Re: [metapost] shading in meta[post/play] & PDF

[Laurence Finston]

> 
> In metapost, "perfect" spheres can be drawn, like on 
> http://www.gnu.org/software/3dldf/cdsmpls.html. But how can I add colour?

You could use the intersection points of the circles as the corners of
rectangles and fill the latter.  The more circles you use, the better the
results will be.  The very primitive surface hiding I've implemented will
almost certainly fail, so you'll have to do this by hand or implement it
yourself.  You may be able to implement surface hiding and/or shading by
operating on the MetaPost file generated by GNU 3DLDF, or by the PostScript
file generated by MetaPost.

Laurence