related to:

http://news.povray.org/povray.binaries.scene-files/thread/%3Cweb.57b4b6c879df8923b488d9aa0%40news.povray.org%3E/

octahedron and icosahedron models fully worked out.

Showing original polygon, and 1, 2, and 3 iterations of triangle subdivision (1
triangle --->  4 triangles)

Still trying to puzzle out the surface normal problem.

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Attachments:
Download 'subdivided_mesh_sphere[cropped].png' (49 KB)

Preview of image 'subdivided_mesh_sphere[cropped].png'

Dodecahedron done, while I was in the zone.

12 pentagonal faces redefined to (5 * 12) = 60 triangular faces

Cube and 3 rectangles with vector components based on Phi shown as per wikipedia
diagram

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Attachments:
Download 'dodecahedron.png' (60 KB)

Preview of image 'dodecahedron.png'

"Bald Eagle" <cre### [at] netscapenet> wrote:
> related to:
>
>
http://news.povray.org/povray.binaries.scene-files/thread/%3Cweb.57b4b6c879df8923b488d9aa0%40news.povray.org%3E/
>
> octahedron and icosahedron models fully worked out.
>
> Showing original polygon, and 1, 2, and 3 iterations of triangle subdivision (1
> triangle --->  4 triangles)
>
> Still trying to puzzle out the surface normal problem.

Thats interesting. I am sure that it will be of use, but it is also a neat thing
in itself. :)

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Le 18/08/2016 à 01:28, Bald Eagle a écrit :
> 
> related to:
> 
>
http://news.povray.org/povray.binaries.scene-files/thread/%3Cweb.57b4b6c879df8923b488d9aa0%40news.povray.org%3E/
> 
> octahedron and icosahedron models fully worked out.
> 
> Showing original polygon, and 1, 2, and 3 iterations of triangle subdivision (1
> triangle --->  4 triangles)
> 
> Still trying to puzzle out the surface normal problem.
> 

I want to thank you for stressing now the problem of ordering the points of triangle
in mesh.

Using my new toy in hgpovray (uv_vertex() and friends) I had misordered half of the
triangles.

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Attachments:
Download 'cut.png' (83 KB) Download 'sp.png' (73 KB) Download 'nurbsmesh.inc.txt' (2 KB) Download 'cut.pov.txt' (2 KB)

Preview of image 'cut.png'

Preview of image 'sp.png'

The thing that bothers me about most sphere approximations by
subdivision is that they are typically geared towards keeping the
triangles as close to equilateral as possible, while for some
applications it may be more important to aim for triangles of uniform
size (or, more precisely, for triangles corresponding to uniform solid
angles).

To that end, I suspect a pentakis dodecahedron (aka kisdodecahedron; a
dodecahedron with each face split up into five triangles, for a total of
60 triangles) might be a better starting point.

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clipka <ano### [at] anonymousorg> wrote:
> The thing that bothers me about most sphere approximations by
> subdivision is that they are typically geared towards keeping the
> triangles as close to equilateral as possible, while for some
> applications it may be more important to aim for triangles of uniform
> size (or, more precisely, for triangles corresponding to uniform solid
> angles).

I found a nice discussion about that a while back, here:
https://wattsupwiththat.com/2013/10/02/ipcc-climate-a-product-of-lies-damn-lies-and-statistics-built-on-inadequate-data
/#comment-1435364

> To that end, I suspect a pentakis dodecahedron (aka kisdodecahedron; a
> dodecahedron with each face split up into five triangles, for a total of
> 60 triangles) might be a better starting point.

That's indeed what I did with the code I posted for the "dodecahedron" in pbsf.
Though as you pointed out, it needs some edits.

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Am 18.08.2016 um 21:05 schrieb Bald Eagle:

>> To that end, I suspect a pentakis dodecahedron (aka kisdodecahedron; a
>> dodecahedron with each face split up into five triangles, for a total of
>> 60 triangles) might be a better starting point.
> 
> That's indeed what I did with the code I posted for the "dodecahedron" in pbsf.
> Though as you pointed out, it needs some edits.

Ah -- I didn't notice that one. I only concentrated on your
icosahedron/octahedron scene.

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