Tor Olav Kristensen wrote:
> 
>>These all look very interesting, i wonder if this could be extended to a 
>>system to design shapes with smooth transits, with a few elements like 
>>this you could build a rounded version of any CSG made of axis-aligned 
>>boxes.
> 
> 
> Good idea.
> 
> It should certainly be possible, but I'll have to think
> about it for a while to find out how to do it.

Thinking a bit more about it: There are possible special cases where 
things might get quite complicated - But it should not be too difficult 
to do for a difference between two boxes for example: check every corner 
  of the second box if it is inside the first box and trace along all 
edges.  This information should be enough to build the resulting shape.

The whole thing might be easier though if you start with a analytical 
tesselation algorithm (approach would be similar as drafted above with 
insideness tests and traces) and then apply a subdivision algorithm and 
forget about bicubic patches (and if you are even lazier you forget 
about POV-SDL and model your shape in Wings3D :-)).

Christoph

-- 
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"Rune" <run### [at] runevisioncom> wrote in news:3ff973fd@news.povray.org:

> I have never been able to figure out how to completely smoothly have
> another number than four bicubic patches meet at a point. What rules did
> you use to accomplish it?
> 
> It would be nice if you gave all the patches the same color, and maybe a
> little phong or specular, so the smoothness can be better examined. From
> the posted images, it's impossible to tell if the surface really is
> completely smooth.


I have rendered some images with specular highlights.

They show that the surface might not be completely
smooth around the "seems" between the patches.

My idea was to have all the 8 control points that
surrounds each "corner point" to lie in the same
plane.

It seems that the results are better if the star
around each of the corner points is regular.

But I now have a growing suspicion that it may not
be possible use bicubic Bezier patches to make such
a surface (that is completely smooth).


Does anyone know if I'm right about this ?

Or have anyone seen images that shows the contrary ?


Tor Olav

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Attachments:
Download 'SixPatches08.jpg' (52 KB) Download 'SixPatches07.jpg' (43 KB)

Preview of image 'SixPatches08.jpg'

Preview of image 'SixPatches07.jpg'

Tor Olav Kristensen <tor_olav_kCURLYAhotmail.com> wrote in 
news:3ffa3519@news.povray.org:

...
> I have rendered some images with specular highlights.
> 
> They show that the surface might not be completely
> smooth around the "seems" between the patches.
...


More "evidence" attached.


Tor Olav

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Attachments:
Download 'SixPatches04.jpg' (20 KB) Download 'SixPatches05.jpg' (19 KB) Download 'SixPatches06.jpg' (20 KB) Download 'SixPatches09.jpg' (49 KB)

Preview of image 'SixPatches04.jpg'

Preview of image 'SixPatches05.jpg'

Preview of image 'SixPatches06.jpg'

Preview of image 'SixPatches09.jpg'

de news:3ffa3519@news.povray.org...
> Or have anyone seen images that shows the contrary ?

Look for Ron Parker's image "Borrow.jpg" and the corresponding zip file.
http://www.irtc.org/stills/1999-02-28/view.html
It contains code for stitching bezier patches but I can't say if it's ***
perfectly *** smooth.

G.

-- 

**********************
http://www.oyonale.com
**********************
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- POV-Ray and Poser computer images
- Posters

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A couple of months ago I did some thinking and computations
on bicubic patches. If I remember correctly, you can get
bicubic patches 2nd order continuous in the vertices (or
any two points along the edge), but only zeroth order
along the edges. So, sorry, completely smooth surfaces
can not be made with bicubic pathes in general in this way.

     Andrel


Tor Olav Kristensen wrote:

> "Rune" <run### [at] runevisioncom> wrote in news:3ff973fd@news.povray.org:
> 
> 
>>I have never been able to figure out how to completely smoothly have
>>another number than four bicubic patches meet at a point. What rules did
>>you use to accomplish it?
>>
>>It would be nice if you gave all the patches the same color, and maybe a
>>little phong or specular, so the smoothness can be better examined. From
>>the posted images, it's impossible to tell if the surface really is
>>completely smooth.
> 
> 
> 
> I have rendered some images with specular highlights.
> 
> They show that the surface might not be completely
> smooth around the "seems" between the patches.
> 
> My idea was to have all the 8 control points that
> surrounds each "corner point" to lie in the same
> plane.
> 
> It seems that the results are better if the star
> around each of the corner points is regular.
> 
> But I now have a growing suspicion that it may not
> be possible use bicubic Bezier patches to make such
> a surface (that is completely smooth).
> 
> 
> Does anyone know if I'm right about this ?
> 
> Or have anyone seen images that shows the contrary ?
> 
> 
> Tor Olav
> 
>

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"Tor Olav Kristensen" <tor_olav_kCURLYAhotmail.com> wrote in message
news:3ffa3519@news.povray.org...
>
> They show that the surface might not be completely
> smooth around the "seems" between the patches.
>
> My idea was to have all the 8 control points that
> surrounds each "corner point" to lie in the same
> plane.
>
> It seems that the results are better if the star
> around each of the corner points is regular.
>
> But I now have a growing suspicion that it may not
> be possible use bicubic Bezier patches to make such
> a surface (that is completely smooth).
>
> Does anyone know if I'm right about this ?

I did some work with bicubic patches once and iirc I could get at least
tangent continuity between patches if the control points on both sides of
the edge is in a straight line. I found this mostly by my own
experimentation and have no mathematical proof.
To fix you patches try to make the points A, B and C in the attached image
be in one line (and similar for the other edges). That way your star will
actually become a pentagon.

-- 
Daniel Nilsson

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Attachments:
Download 'SixPatches.jpg' (6 KB)

Preview of image 'SixPatches.jpg'

Tor Olav Kristensen wrote:
> But I now have a growing suspicion that it may not
> be possible use bicubic Bezier patches to make such
> a surface (that is completely smooth).

I strongly suspect that too.

This thread supports the suspicion:
http://news.povray.org/povray.general/3084/

That's why I was at one point so interested in bicubic patches with 3, 5
and 6 edges, which is another approach to solving the topology problem.
The promising result can be seen here:
http://news.povray.org/povray.binaries.animations/26690/

My ultimate goal was quite similar to yours: To be able to define a list
of points and a list of patches with corners in those points. Only
difference was that exactly four patches had to meet in a point, but
then the patches could have 3, 4, 5 or 6 edges. I abandoned it though -
the triangular bicubic patch was coded by Micha Riser and improved by
me. However, Micha Riser never coded similar patches for 5 and 6 edges,
and I didn't understand the scientific papers on which the special
bicubic patches were based, so I couldn't do it myself.

Rune
--
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rune|vision:  http://runevision.com **updated Dec 30**
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Rune wrote:


> My ultimate goal was quite similar to yours: To be able to define a list
> of points and a list of patches with corners in those points. Only
> difference was that exactly four patches had to meet in a point, but
> then the patches could have 3, 4, 5 or 6 edges. I abandoned it though -
> the triangular bicubic patch was coded by Micha Riser and improved by
> me. However, Micha Riser never coded similar patches for 5 and 6 edges,
> and I didn't understand the scientific papers on which the special
> bicubic patches were based, so I couldn't do it myself.

If you stich three 4-sided patched together you have a new patch with
6 edges all of which are cubic. (Actually you could do that with 2
but you lose some symmetry then).
If you need 5, you migth consider aligning 2 of these edges from 
neighbouring patches in such a way that they both are described
by the same cubic function. Then you can use that to connect a
single edge of another patch.
I did not have time to test that idea myself, but I suspect that
although the edges are seemless in mathematical space, there could
be cracks in POVRAY becouse of different approximations in the
neighbouring edges.

> Rune
> --
> 3D images and anims, include files, tutorials and more:
> rune|vision:  http://runevision.com **updated Dec 30**
> POV-Ray Ring: http://webring.povray.co.uk
> 
>

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andrel wrote:
> If you stich three 4-sided patched
> together you have a new patch with
> 6 edges all of which are cubic.

The way you propose to make a 6-sided bicubic patch requires stitching
together 3 bicubic patches so their corners meet in a point. As you can
read in other posts in this thread, you can't do that and still have a
smooth surface.

There is no way to create smooth n-sided bicubic patches from 4-sided
bicubic patches.

Rune
--
3D images and anims, include files, tutorials and more:
rune|vision:  http://runevision.com **updated Dec 30**
POV-Ray Ring: http://webring.povray.co.uk

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Rune wrote:
> andrel wrote:
> 
>>If you stich three 4-sided patched
>>together you have a new patch with
>>6 edges all of which are cubic.
> 
> 
> The way you propose to make a 6-sided bicubic patch requires stitching
> together 3 bicubic patches so their corners meet in a point. As you can
> read in other posts in this thread, you can't do that and still have a
> smooth surface.

I know, I was one of the people to make that claim.

> There is no way to create smooth n-sided bicubic patches from 4-sided
> bicubic patches.
I take that as a challenge. The major problem with stitching together
of the patches is that the derivative for a point on the edge depend
on all 16 parameters of the patch. In your and Tor's scheme you have no
control over many of the other points because they have there own
constraints. But in this case you are completely free to choose any of
the constants, so perhaps in this case it is possible. Most of my week
is scheduled for triangles and general meshing around, so it has to wait
untill the weekend before I can do something on patches again :)
In the mean time I will post some patch-work ball I created earlier.

> Rune
> --
> 3D images and anims, include files, tutorials and more:
> rune|vision:  http://runevision.com **updated Dec 30**
> POV-Ray Ring: http://webring.povray.co.uk
> 
>

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