[RESOLVED] Sphere from triangles question.

[ThomasJohnsen]

I am working on making a sphere located at (0,0,0) from triangles in such a way that all triangles have identical size, cover the sphere entirely and are uniformly distributed. This has turned out to be a bit more complex than I initially imagined.
My current solution will take an icosahedron and use recursive subdivision on edges to turn each triangle into 4 smaller ones (currently 6 steps og subdivision yielding a total of 81920 triangles). This solution, although acceptable, has some annoying inconsistancies - the original points in the icosahedron will have 5 outgoing edges while all other points have 6 causing the triangles near these original points to look somewhat skewed. I can't think of another solution though, which is why I posted this. I don't need a detailed solution; an idea or some thoughts will suffice, since I'm a bit stuck atm. Due to the nature of spheres and triangles, a better solution may not exist, but since this forum has helped me alot in the past, I thought I'd give it a shot.

Regards Tom

[Shaggy Hiker]

You might try the game forum, as well, since the problem you describe is one encountered fairly often in 3D rendering. There may even be a common solution, though, considering the shape of heads in some 3D games, it may not be a good solution.

[stanav]

I don't know how to go about doing it, but if you look at a picture of the Missouri Botanical Garden's Climatron structure, it uses hexagons shapes. Since each hexagon can be divided into 6 equilibrium triangles, this may be an approach for you.
http://commons.wikimedia.org/wiki/Fi...al_Gardens.jpg

[Jenner]

Spherical tessellation. When I did it, I used an octohedron. You want to look here and when you are trying to texture map it, here.

[ThomasJohnsen]

You might try the game forum, as well, since the problem you describe is one encountered fairly often in 3D rendering. There may even be a common solution, though, considering the shape of heads in some 3D games, it may not be a good solution.

I will try that .

And thank you
Tom


Elaboration:
I am fairly familiar with 3D modeling (have written ray-tracers with physically based illumination models), so a solution involving Hermite or Bezier surfaces or any sort of patch or spline should be manageable. Problem is though, that in 3D modeling the need for evenly distributed equally-sized triangles in an object to be rendered isn't a concern in cases I have come across. As far as I am aware most applications use some sort of basic surface (be it a triangle, a Bezier surface or a spline of sorts) to approximate other general surfaces and objects, and never bother about the distribution or size of the individual sub-surfaces. Or maybe I have just been looking in the wrong places

#EDIT: Oh my - 2 answers while I wrote this
The link from Stanav gave me a few ideas that may produce better results.
The solution from Jenner was great - using a subdivided Octohedron apparently yields a significantly better result than subdividing an Icosahedron. I will try to implement that first.

Thank you very much guys - knew this forum could help; such brilliant members here!
Tom

[ThomasJohnsen]

Results produced from a octahedron yield similar abnormalities as those produced by an icosahedron (ie. some points have 4 edges whereas others have 6) although they are less obvious to the eye. An approximation of a sphere with hexagons (as Stanav suggested) or a dodecahedron seems like the only viable choices - pity both are difficult to model; will have to wait until tomorrow

Thanks for the help guys.
Tom