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Here's the thread I was trying to find and link to:
http://news.povray.org/povray.binaries.scene-files/thread/%3Cweb.56e1ce6a2f1b67735e7df57c0%40news.povray.org%3E/
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BGimeno <bru### [at] gmail com> wrote:
> Can someone think of a better way for cover the gaps left by these
> sphere_sweep (cubic_spline) curves with bicubic_patch?.
> ...
> ...
> If it is mathematically impossible to make a perfect circle based on
> patches, I suppose that the task of adjusting them smoothly to this form
> can not be carried out either.
>
> Any help or idea to the respective one is welcome, thank you very much
> in advance.
If you add more patches, your cross sections can get very close to circles.
In the two 'Bezier_Patches_Stitched' images here:
http://dataduppedings.no/subcube/POV-Ray_Images/
- I have tried to show how one can construct the control grid so that the
patches are joined smoothly. All the 8 control points surrounding each corner of
the patches are placed in the same plane.
The 'Bezier_Patches_Torus' image shows a torus that is made with individually
colored bicubic Bezier patches. I made some macros that stitches together the
patches automatically. (The macro takes an array with the positions of the white
spheres as an argument.)
I finally found the source code for these images (that I made back in 2003), so
I've now made some more images where I've tried to illustrate this better.
I'll post them here.
--
Tor Olav
http://subcube.com
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Attachments:
Download 'bicubicbezierpatches.png' (397 KB)
Preview of image 'bicubicbezierpatches.png'
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"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> BGimeno <bru### [at] gmailcom> wrote:
> > Can someone think of a better way for cover the gaps left by these
> > sphere_sweep (cubic_spline) curves with bicubic_patch?.
> > ...
> > ...
> I've now made some more images where I've tried to illustrate this better.
>
> I'll post them here.
--
Tor Olav
http://subcube.com
Post a reply to this message
Attachments:
Download 'bicubicbezierpatches_manualgrid.png' (512 KB)
Preview of image 'bicubicbezierpatches_manualgrid.png'
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"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> > BGimeno <bru### [at] gmailcom> wrote:
> > > Can someone think of a better way for cover the gaps left by these
> > > sphere_sweep (cubic_spline) curves with bicubic_patch?.
> > > ...
> > > ...
> > I've now made some more images where I've tried to illustrate this better.
> >
> > I'll post them here.
--
Tor Olav
http://subcube.com
Post a reply to this message
Attachments:
Download 'bicubicbezierpatches_controlgrids.png' (730 KB)
Preview of image 'bicubicbezierpatches_controlgrids.png'
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"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> > BGimeno <bru### [at] gmailcom> wrote:
> > > Can someone think of a better way for cover the gaps left by these
> > > sphere_sweep (cubic_spline) curves with bicubic_patch?.
> > > ...
> > > ...
> > I've now made some more images where I've tried to illustrate this better.
> >
> > I'll post them here.
The points in the blue sphere sweeps in this image follows cubic Bezier splines
made with the control points that lies along the edges of the bicubic Bezier
patches.
--
Tor Olav
http://subcube.com
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Attachments:
Download 'bicubicbezierpatches_spheresweeps.png' (480 KB)
Preview of image 'bicubicbezierpatches_spheresweeps.png'
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"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> > BGimeno <bru### [at] gmailcom> wrote:
> > > Can someone think of a better way for cover the gaps left by these
> > > sphere_sweep (cubic_spline) curves with bicubic_patch?.
> > > ...
> > > ...
> > I've now made some more images where I've tried to illustrate this better.
> >
> > I'll post them here.
--
Tor Olav
http://subcube.com
Post a reply to this message
Attachments:
Download 'bicubicbezierpatches_controlgridsandspheresweeps.png' (757 KB)
Preview of image 'bicubicbezierpatches_controlgridsandspheresweeps.png'
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"- I have tried to show how one can construct the control grid so that the
patches are joined smoothly. All the 8 control points surrounding each corner of
the patches are placed in the same plane."
Thanks - this may help me re-think things.
Can you elaborate a little bit on the implied relationship between the small
vectors between the corner and control points, and the larger vector between
corners is? And why?
I understand the necessity of having the same slope which I believe is what the
small patch shows, and can understand that in isolation, but I haven't yet made
the connection to understand the relation between that and the large vectors.
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"Bald Eagle" <cre### [at] netscapenet> wrote:
> "- I have tried to show how one can construct the control grid so that the
> patches are joined smoothly. All the 8 control points surrounding each corner of
> the patches are placed in the same plane."
>
> Thanks - this may help me re-think things.
>
> Can you elaborate a little bit on the implied relationship between the small
> vectors between the corner and control points, and the larger vector between
> corners is? And why?
>
> I understand the necessity of having the same slope which I believe is what the
> small patch shows, and can understand that in isolation, but I haven't yet made
> the connection to understand the relation between that and the large vectors.
I assume that you are looking at my 'Bezier_Patches_Stitched' files.
IIRC I added the large vectors as a suggestion for how one can create the
smaller vectors between the points in the control grid around the white corner
points. (The positions for these white corner points were specified "manually".)
The white corner points, together with their corresponding two small vectors,
defines the planes for the 8 control points surrounding each corner point. The
small vectors are also used to control the distances between these control
points.
AFAIK it is common to let the small vectors have the same direction as the large
vectors and to let their lengths be 1/6 of the length of the large vectors.
But I think that one can choose other orientations and lengths for the small
vectors (but I have not had time to experiment with this yet).
In the attached image I have given each Bezier patch a random color and placed
the camera at a different position.
--
Tor Olav
http://subcube.com
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Attachments:
Download 'colored_bezier_patches_stitched.png' (275 KB)
Preview of image 'colored_bezier_patches_stitched.png'
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"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> "Bald Eagle" <cre### [at] netscapenet> wrote:
> ...
> ...
> In the attached image I have given each Bezier patch a random color and placed
> the camera at a different position.
And here's an image where the camera is placed above the colored Bezier patches.
--
Tor Olav
http://subcube.com
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Attachments:
Download 'colored_bezier_patches_stitched_above.png' (252 KB)
Preview of image 'colored_bezier_patches_stitched_above.png'
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"Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> "Tor Olav Kristensen" <tor### [at] TOBEREMOVEDgmailcom> wrote:
> > BGimeno <bru### [at] gmailcom> wrote:
> > > Can someone think of a better way for cover the gaps left by these
> > > sphere_sweep (cubic_spline) curves with bicubic_patch?.
> > > ...
> > > ...
> > I've now made some more images where I've tried to illustrate this better.
> >
> > I'll post them here.
Here's an image where the planes for the control grid points around the Bezier
patch corners are shown as dark squares. I've also added spheres at the control
grid points.
Perhaps I've now posted too many images about stitching of bicubic Bezier
patches...
--
Tor Olav
http://subcube.com
Post a reply to this message
Attachments:
Download 'bicubicbezierpatches_controlgridplanes.png' (799 KB)
Preview of image 'bicubicbezierpatches_controlgridplanes.png'
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