Is there an easy way to approximate a minimal surface (soap film)
spanning a skew polygon?

Assume the edges are all straight.

I need to fit pentagons and hexagons, neither of which seem obvious
candidates for a seamless bicubic patch.

-- 
"How'd ya like to climb this high without no mountain?" --Porky Pine
Anton Sherwood   *\\*   +1 415 267 0685   *\\*   Ant### [at] jpsnet

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Anton Sherwood wrote:
> 
> Is there an easy way to approximate a minimal surface (soap film)
> spanning a skew polygon?
> 
> Assume the edges are all straight.
> 
> I need to fit pentagons and hexagons, neither of which seem obvious
> candidates for a seamless bicubic patch.

In general, minimal surfaces are a nasty problem mathematically.  If you
can approximate the particular surface with a polynomial, pov will do up
to seventh degree polynomial surfaces.  If you can come up with a
suitable equation, you may also be able to do it with the isosurface
patch.  In general, however, your best bet (if you do not require strict
mathematical accuracy) is probably to lay out the polygonal skeleton
with sPatch and pull and tweak the surface until it looks about right. 
As a little tip, use quadrilaterals instead of triangles in sPatch (add
points if needed) to get a better result.

Jerry Anning
cle### [at] dholcom

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I wrote:
> Is there an easy way to approximate a minimal surface (soap film)
> spanning a skew polygon?

Afterthought: Failing that, if I slice it into flat triangles,
is there a trick with "normal" to hide the facets?

-- 
"How'd ya like to climb this high without no mountain?" --Porky Pine
Anton Sherwood   *\\*   +1 415 267 0685   *\\*   Ant### [at] jpsnet

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Anton Sherwood wrote:
> 
> I wrote:
> > Is there an easy way to approximate a minimal surface (soap film)
> > spanning a skew polygon?
> 
> Afterthought: Failing that, if I slice it into flat triangles,
> is there a trick with "normal" to hide the facets?

If that is good enough, just use smooth_triangles.  Calculate the
normals at each junction by averaging the normals of the triangles that
meet there.  (Get those normals by vcrossing any two sides of each
triangle).  This will be visually smooth, but it is just a normal fiddle
and the surface will not "dip" between corners as a real minimal surface
would.  If you need that "dip" the sPatch suggestion is still probably
the easiest and most flexible way to go.

Jerry Anning
cle### [at] dholcom

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Anton Sherwood wrote in message <358### [at] jpsnet>...
>I wrote:
>> Is there an easy way to approximate a minimal surface (soap film)
>> spanning a skew polygon?
>
>Afterthought: Failing that, if I slice it into flat triangles,
>is there a trick with "normal" to hide the facets?


Sure.
Use the "smooth_triangle" instead of the "triangle". With it you specify a
normal vector for each vertex of the triangle and POV-Ray uses the
information to interpolate the shading of the triangle so that it looks
smooth. Of course it doesn't work very good if the angle between the edges
is too large (like "smoothing" a cube to look like a sphere will not work),
but for the most triangle meshes it works ok.

See this URL (the whole thing including the "td=6" at the end is the URL) on
a discussion how those normals can be calculated. Also there is a tool
around that smoothes POV-Ray meshes. Sorry, don't have the URL...

http://heron.cc.ukans.edu/ebt-bin/nph-dweb/dynaweb/SGI_Developer/OpenGL_PG/@
Generic__BookTextView/27318;cd=7;td=6


Hope it helps,
Johannes.

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> Anton Sherwood wrote:
> > > Is there an easy way to approximate a minimal surface (soap film)
> > > spanning a skew polygon?
> >
> > Afterthought: Failing that, if I slice it into flat triangles,
> > is there a trick with "normal" to hide the facets?

Jerry Anning wrote:
> If that is good enough, just use smooth_triangles.  Calculate the
> normals at each junction by averaging the normals of the triangles
> that meet there.  (Get those normals by vcrossing any two sides of
> each triangle). 

Or, for my purpose: use the cross product of two adjacent sides of the
skeleton polygon.  (I may want an extra point in the center, whose
normal is the average of the corner normals.)

Thanks everybody, this is exactly what I need - I just didn't rtfm
far enough.  (smooth_triangles are not covered in the tutorial.)

Does the magnitude of the normal vector have any effect?
What if its sign (relative to the surface) changes?

-- 
"How'd ya like to climb this high without no mountain?" --Porky Pine
Anton Sherwood   *\\*   +1 415 267 0685   *\\*   Ant### [at] jpsnet

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I wrote:
> Thanks everybody, this is exactly what I need - I just didn't rtfm
> far enough.  (smooth_triangles are not covered in the tutorial.)
> 
> Does the magnitude of the normal vector have any effect?
> What if its sign (relative to the surface) changes?

A bit of experiment suggests that magnitude is irrelevant
but sign can have weird effects.

-- 
"How'd ya like to climb this high without no mountain?" --Porky Pine
Anton Sherwood   *\\*   +1 415 267 0685   *\\*   Ant### [at] jpsnet

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Try the Iridescence finish, it's detailed in section 7.6.3.6 of the 3.0
Manual

Josh English
eng### [at] spiritonecom
www.spiritone.com/~english


Anton Sherwood wrote:

> Is there an easy way to approximate a minimal surface (soap film)
> spanning a skew polygon?
>
> Assume the edges are all straight.
>
> I need to fit pentagons and hexagons, neither of which seem obvious
> candidates for a seamless bicubic patch.
>
> --
> "How'd ya like to climb this high without no mountain?" --Porky Pine
> Anton Sherwood   *\\*   +1 415 267 0685   *\\*   Ant### [at] jpsnet

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