POV-Ray : Newsgroups : povray.binaries.images : New tetrahedron splitting in tesselation patch Server Time
19 Aug 2024 04:24:09 EDT (-0400)
  New tetrahedron splitting in tesselation patch (Message 1 to 8 of 8)  
From: Warp
Subject: New tetrahedron splitting in tesselation patch
Date: 22 Jan 2001 10:40:51
Message: <3a6c547d@news.povray.org>
Jerome threw the idea of splitting each sampling cube into 5
tetrahedrons
instead of 6 and I liked the idea so much that I tried it.
  Here is the result. The first image is made with the old version and the
second image is made with the new version (the pov-file is identical).
  I like the new version.


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Download 'testold.jpg' (77 KB) Download 'testnew.jpg' (72 KB)

Preview of image 'testold.jpg'
testold.jpg

Preview of image 'testnew.jpg'
testnew.jpg


 

From: Margus Ramst
Subject: Re: New tetrahedron splitting in tesselation patch
Date: 22 Jan 2001 11:13:14
Message: <3A6C5C81.BB055738@peak.edu.ee>
Warp wrote:
> 
>   Jerome threw the idea of splitting each sampling cube into 5
> tetrahedrons
> instead of 6 and I liked the idea so much that I tried it.

Hmmm....
When I tried something similar, the only way I could figure out how to split the
cube was into 5 tetrahedrons (4 with faces coinciding with cube faces, 1 "in the
middle"); how did you distribute the 6 ones?

-- 
Margus Ramst

Personal e-mail: mar### [at] peakeduee
TAG (Team Assistance Group) e-mail: mar### [at] tagpovrayorg
Home page http://www.hot.ee/margusrt


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From: Tony[B]
Subject: Re: New tetrahedron splitting in tesselation patch
Date: 22 Jan 2001 13:22:26
Message: <3a6c7a62@news.povray.org>
Has the bug dissappeared? Please say it is so... :)


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From: Anton Sherwood
Subject: Re: New tetrahedron splitting in tesselation patch
Date: 23 Jan 2001 01:34:42
Message: <3A6D2814.F1110DBB@pobox.com>
Margus Ramst wrote:
> When I tried something similar, the only way I could figure out how to
> split the cube was into 5 tetrahedrons (4 with faces coinciding with
> cube faces, 1 "in the middle"); how did you distribute the 6 ones?

One way is to start with a diagonal of the cube as an edge common to all
six.  Is there another?

-- 
Anton Sherwood  --  br0### [at] p0b0xcom  --  http://ogre.nu/


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From: Jérôme Grimbert
Subject: Re: New tetrahedron splitting in tesselation patch
Date: 23 Jan 2001 02:55:35
Message: <3A6D3904.50CEA78D@atosorigin.com>
"Tony[B]" wrote:
> 
> Has the bug dissappeared? Please say it is so... :)

Not Yet :-(


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From: Jérôme Grimbert
Subject: Re: New tetrahedron splitting in tesselation patch
Date: 23 Jan 2001 03:10:58
Message: <3A6D3C9F.DF9D7F40@atosorigin.com>
Anton Sherwood wrote:
> 
> Margus Ramst wrote:
> > When I tried something similar, the only way I could figure out how to
> > split the cube was into 5 tetrahedrons (4 with faces coinciding with
> > cube faces, 1 "in the middle"); how did you distribute the 6 ones?
> 
> One way is to start with a diagonal of the cube as an edge common to all
> six.  Is there another?
> 

Yes, the one used initially by Warp (it is in the code, you should have looked)

                TesselateTetrahedron(&info,0,4,2,1,Sm); /* 1 */
                TesselateTetrahedron(&info,6,4,2,1,Sm); /* 2 */
                TesselateTetrahedron(&info,6,3,2,1,Sm); /* 3 */
                TesselateTetrahedron(&info,4,5,6,1,Sm); /* 4 */
                TesselateTetrahedron(&info,5,6,3,1,Sm); /* 5 */
                TesselateTetrahedron(&info,6,3,7,5,Sm); /* 6 */

Assuming you're at -z, looking to +z, left is -x and up is y

1: bottom left corner of the cube in front of you
6: top right corner of the cube away 

union(2,3,4,5) is a slice of the cube  between two parallel planes.

one diagonal of the cube is used as a common segment (from
the left bottom corner away to the top right corner near you).

2: opposite segment is the diagonal of the front face (top left to bottom
right).
3: opposite segment is the top segment on the left face.
4: opposite segment is the bottom segment on the right face.
5: opposite segment is the diagonal of the back face (top left to bottom right)

Hope this help you see the split.


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From: Warp
Subject: Re: New tetrahedron splitting in tesselation patch
Date: 23 Jan 2001 09:09:54
Message: <3a6d90b2@news.povray.org>
I'll save you the trouble of thinking that out:


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pic2.png


 

From: Margus Ramst
Subject: Re: New tetrahedron splitting in tesselation patch
Date: 23 Jan 2001 21:28:52
Message: <3A6E3E52.77DD9D1B@peak.edu.ee>
Warp wrote:
> 
>   I'll save you the trouble of thinking that out:
> 

Thanks.
Funny, now it seems so obvious. But I spent hours scetching cubes and
tetrahedrons in a vain attempt to do a division into 6 parts (the place where I
read about this tessellation method specifically said 6). Finally gave up and
decided the author must've made a typo :)

-- 
Margus Ramst

Personal e-mail: mar### [at] peakeduee
TAG (Team Assistance Group) e-mail: mar### [at] tagpovrayorg
Home page http://www.hot.ee/margusrt


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