How to convert an isosurface to a parametric isosurface?  I'm looking for a
formula.

Thanks,
Hugo

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On Thu, 15 May 2003 16:30:41 +0200, "Hugo Asm" <hua### [at] post3teledk> wrote:
> How to convert an isosurface to a parametric isosurface?  I'm looking for a
> formula.

There probably are some methods for some specific and very limited cases but I
doubt there is any universal method. Are you refering something you have
readed/seen ?

ABX

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> Are you refering something you have readed/seen ?

A vague memory about a formula that I could wrap around any function, and
have a parametric output. But I can't find information about it now. Maybe
it's not possible. There was a post in 2001 where Christoph Hormann replies
nearly the same as you.

http://news.povray.org/povray.general/19103/

This is all another attempt to meshify my isosurface (it could work with
Ingo Jannson's param.inc file.) The triscan macro you pointed me to
yesterday works, but makes too many errors. I'm running out of ideas. But my
isosurface mostly does surface displacement on a rounded box, so maybe I
should try another approch: To import a dense mesh of a box, and apply my
functions to it, then save the result.


Regards,
Hugo

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In article <3ec3a490@news.povray.org>, "Hugo Asm" <hua### [at] post3teledk> 
wrote:

> How to convert an isosurface to a parametric isosurface?  I'm looking for a
> formula.

You can't just convert any implicit isosurface to a parametric one. You 
can only do it for certain special cases.
What are you trying to do? This is most likely the wrong way to solve 
whatever problem you have. If you say what you are really trying to do, 
someone might be able to suggest a better option.

-- 
Christopher James Huff <cja### [at] earthlinknet>
http://home.earthlink.net/~cjameshuff/
POV-Ray TAG: chr### [at] tagpovrayorg
http://tag.povray.org/

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On Thu, 15 May 2003 17:13:37 +0200, "Hugo Asm" <hua### [at] post3teledk> wrote:
> But my
> isosurface mostly does surface displacement on a rounded box, so maybe I
> should try another approch: To import a dense mesh of a box, and apply my
> functions to it, then save the result.

(considering that rounded box macro has "linear" behaviour like in rounded
version of isocsg library)

You have notice that it will not be the same. When you have function of rounded
box and then you apply function of deformation then you receive new surface made
from points <x,y,z> where:

f_rbox(x,y,z) - f_def(x,y,z) = threshold

But if you would first create mesh for box and then displace about value of
f_def at box surface then result may be at different place.

I would do it going along normal of rounded box direction until it could reach
condition listed above. You can use optimization similiar to intersecting
isosurface surface but it would need knowledge written in isosurf.cpp :-)

ABX

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> I would do it going along normal of rounded box direction until
> it could reach condition listed above.

Arrgh, *pulling my hair*  :o)  This isn't going to be too easy.
But thanks!

Regards,
Hugo

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fvb7cvgmplund9qmi3ofjrj3ircr3gil1e@4ax.com...
> You have notice that it will not be the same. When you have function of
rounded
> box and then you apply function of deformation then you receive new
surface made
> from points <x,y,z> where:
> f_rbox(x,y,z) - f_def(x,y,z) = threshold

Just wondering: is it possible to "warp" a rounded box (bending, shearing,
twisting...) or another shape? Simple surface displacement can be done using
the formula above, but I've not been able to create more drastic
deformations.

G.

--

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- POV-Ray and Poser computer images
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On Thu, 15 May 2003 19:11:41 +0200, "Gilles Tran" <tra### [at] inapginrafr> wrote:
> Just wondering: is it possible to "warp" a rounded box (bending, shearing,
> twisting...) or another shape? Simple surface displacement can be done using
> the formula above, but I've not been able to create more drastic
> deformations.

I do not understand. Are you asking if it is possible to apply more complicated
"warping" deformations to functions and create isosurface (like I did in
http://news.povray.org/povray.binaries.animations/23891/167475/wip.mpg ) or are
you asking if it is possible to apply "warping" deformations to mesh builded
with method described in this thread? Both seems possible when considered in
concrete examples but probably again hard to be defined in universal way.

ABX

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On Thu, 15 May 2003 19:17:00 +0200, ABX <abx### [at] abxartpl> wrote:
> http://news.povray.org/povray.binaries.animations/23891/167475/wip.mpg

In case you can wonder what "warp" I mean then I was refering to waving of R. Of
course other modifications like
http://news.povray.org/povray.binaries.animations/15156/100730/DEFORM.MPG
are also possible (thought this animation is result of my other old patch)

ABX

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Gilles Tran wrote:
> 
> > f_rbox(x,y,z) - f_def(x,y,z) = threshold
> 
> Just wondering: is it possible to "warp" a rounded box (bending, shearing,
> twisting...) or another shape? Simple surface displacement can be done using
> the formula above, but I've not been able to create more drastic
> deformations.

'bending' is somewhat unprecise mathematically.  Shrearing is even a
linear transformation (can be done with a matrix transform, of course
possible with functions as well).  Twisting is probably meant as 'rotating
with varying rotation angle' - rotation is

#declare fn_rotated=
  function { 
    fn_original(
      x*cos(Angle)+y*sin(Angle), 
      -x*sin(Angle)+y*cos(Angle), z
    ) 
  }

therefore twisting would be something like:

#declare fn_twisted=
  function { 
    fn_original(
      x*cos(AngleFactor*z)+y*sin(AngleFactor*z), 
      -x*sin(AngleFactor*z)+y*cos(AngleFactor*z), z
    ) 
  }

Christoph

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