andrel wrote:
> Rune wrote:
>> There is no way to create smooth n-sided
>> bicubic patches from 4-sided bicubic patches.
>
> I take that as a challenge.

Sounds good to me. I'm skeptical, but if you do succeed, I'd be
interested in the result.

Rune
--
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rune|vision:  http://runevision.com **updated Dec 30**
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Christoph Hormann <chr### [at] gmxde> wrote in
news:2bd### [at] tritonimagicode: 

> 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. 

Yes I think that would work.

I don't know if this would easier to implement, but here's
what I thought of:

Divide space into cubes and only then allow each box to
occupy exactly one cube. Then let macros find out which
sides, edges and cornes need to be rendered. (If a box has
a neighboring box at one of their sides, then their common
side, edges and corners should not be rendered. It would
be more difficult to make rules for boxes that are neigh-
bours only at edges or corners.)


> 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 :-)).


Hehe...

Yes, but I love solving geometric problems in POV-SDL =)

I have tried to force myself to not look into tesselation
algorithms and surface subdivision before I'm have studied
surface modelling with splines in greater detail.
(And that may take a while.)

Btw.: I suspect there to be strong relations between the
math used for tesselation and the math used when modelling
with splines.


Tor Olav

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"Gilles Tran" <tra### [at] inapginrafr> wrote in
news:3ffaacd7@news.povray.org: 


> message 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.

Thank you for the link Gilles.

I'll have a look into his code.


Tor Olav

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andrel <a_l### [at] hotmailcom> wrote in news:3FF### [at] hotmailcom:

> 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.

Thank you for your input.

Maybe I too will have delve into the polynomials used
for these patches, so that I can convince myself that
your conclusion is correct.

I have a (diminishing) hope that you are wrong  :(


Tor Olav

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"Daniel Nilsson" <dan### [at] daniel-nilssoncom> wrote in
news:3ffb270d@news.povray.org: 

> "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.

I too had some thoughts about doing it that way. But I
thought that it would probably not work. So I wouldn't
spend any time modifying my macros in order to try it.

But now that you suggest this too, I will give it a try.

(I was afraid that I had to change the locations of the
corner points so that the shapes became less rectangular.
Now I hope that it is only necessary to move the two
control points in the middle of each edge.)

Thank you for your suggestion.


Tor Olav

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"Rune" <run### [at] runevisioncom> wrote in news:3ffc172f$1@news.povray.org:

> 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.

I recall a faint memory of such a discussion in p.a.u.
But I didn't follow that thread very closely.

Maybe now would be a good time to read through it.

For you others, I found it here:
http://news.povray.org/povray.advanced-users/26671/


> The promising result can be seen here:
> http://news.povray.org/povray.binaries.animations/26690/

Yes, it looks good.


> 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.


Can you please point me to thoses papers ?


Tor Olav

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Tor Olav Kristensen wrote:
> "Rune" <run### [at] runevisioncom> wrote:
>> 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.
>
> I recall a faint memory of such a discussion
> in p.a.u. But I didn't follow that thread
> very closely.
>
> Maybe now would be a good time to read through it.
>
> For you others, I found it here:
> http://news.povray.org/povray.advanced-users/26671/

> Can you please point me to thoses papers ?

The link to them is in the first post in the thread you just linked to.
http://zhengjj.freeyellow.com/html/publications.html
The publication "Control point surfaces over non-four-sided surfaces"
explain exactly how to implement 3, 5 and 6-sided bezier patches.

The direct link to that article is:
http://zhengjj.freeyellow.com/archive/ZhengBall97.zip

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" <run### [at] runevisioncom> wrote in news:3ffca979@news.povray.org:

> Tor Olav Kristensen wrote:
>> "Rune" <run### [at] runevisioncom> wrote:
>>> 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.
>>
>> I recall a faint memory of such a discussion
>> in p.a.u. But I didn't follow that thread
>> very closely.
>>
>> Maybe now would be a good time to read through it.
>>
>> For you others, I found it here:
>> http://news.povray.org/povray.advanced-users/26671/
> 
>> Can you please point me to thoses papers ?
> 
> The link to them is in the first post in the thread you just linked to.
> http://zhengjj.freeyellow.com/html/publications.html
> The publication "Control point surfaces over non-four-sided surfaces"
> explain exactly how to implement 3, 5 and 6-sided bezier patches.


Ooops.
- I should have glanced at your post before asking...


> The direct link to that article is:
> http://zhengjj.freeyellow.com/archive/ZhengBall97.zip

Thank you.


Toor Olav

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This is not yet an answer to the n-sided polygon question,
but something more fundametal on bicubic patches.
I studied the math involved again over the last few days
and reached some conclusions.
1) you can stich bicubic patches seemlessly together.
  you can follow the rule of thumb on having controlpoints
  in one plane (though it is somewhat more subtle than
  that). I can even explain it, but that would
  make a very long post, with some math in it.
  If anybody is interested, he/she must point out what is
  the right way (e.g. newsgroup) to publish that.
  I withdraw hereby my former claim that you can not have
  continues normals along the entire length of the edge.
  I apologize for causing confusion. I mixed up control
  points and actual surface points when I was thinking about
  it before. The math for bicubic patches is relatively simple
  but sometimes tricky (especially when you expect the wrong
  answer :( ).
2) I (and probably others) have been fooled by the way
  POV-Ray renders these patches. For the moment I think
  that there is something wrong with the normals.

Attached are two images. Both of four patches stitched together.
The wide angle picture suggests that there are kinks (cracks, bends?)
in the surface on the left going upwards crossing the middle and
on top going from left to right. I also included a lot of markers
where the surface should be, and it is precisely there.
In the closeup view of the green line you can clearly see that
the shadows have sometimes little to do with the curvature of
the surface.

Can anybody with access to the source explain the shape of the
shadows, or point out where I am wrong?

	Andrel

Rune wrote:
> andrel wrote:
> 
>>Rune wrote:
>>
>>>There is no way to create smooth n-sided
>>>bicubic patches from 4-sided bicubic patches.
>>
>>I take that as a challenge.
> 
> 
> Sounds good to me. I'm skeptical, but if you do succeed, I'd be
> interested in the result.
> 
> 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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Attachments:
Download 'testpatch.jpg' (40 KB) Download 'testpatch_close.jpg' (27 KB)

Preview of image 'testpatch.jpg'

Preview of image 'testpatch_close.jpg'

In article <400### [at] hotmailcom>,
 andrel <a_l### [at] hotmailcom> wrote:

> Attached are two images. Both of four patches stitched together.
> The wide angle picture suggests that there are kinks (cracks, bends?)
> in the surface on the left going upwards crossing the middle and
> on top going from left to right. I also included a lot of markers
> where the surface should be, and it is precisely there.
> In the closeup view of the green line you can clearly see that
> the shadows have sometimes little to do with the curvature of
> the surface.
> 
> Can anybody with access to the source explain the shape of the
> shadows, or point out where I am wrong?

I'm not entirely sure what you're talking about...I see some things that 
could be rendering or JPEG artifacts, but they aren't in the closeup. 
There are rather strong vertical and horizontal lines in the shading, 
one of them vertically splitting the closeup, but it looks like you used 
a noise function to displace the surface, and the Perlin noise used in 
POV produces such artifacts.

-- 
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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