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I'm curious on how Blender generates textures in 3D space for Volumetrics compared to 2D textures for a surface.

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    $\begingroup$ if you mean the procedural textures (e.g. musgrave noise) then it just so happens that many procedural noise generation algorithms can be generalized to be n-dimensional. the procedure for generating 2d musgrave noise is not much different from the one used to generate 3d Musgrave noise, which is not much different from one used to hypothetically generate 4d musgrave noise, or 5d, and so on.... also, generating a 3d texture on a single plane is the same as generating a 2d one, thats probably how blender does it. $\endgroup$ – Sebastián Mestre Jan 2 '18 at 8:49
  • $\begingroup$ That's very interesting that procedural textures can be scaled up like that. $\endgroup$ – Bradley Neon Jan 3 '18 at 2:04
  • $\begingroup$ @SebastiánMestre you should post that as an answer $\endgroup$ – Duarte Farrajota Ramos Jan 4 '18 at 23:52
  • $\begingroup$ @DuarteFarrajotaRamos sure thing, I just did $\endgroup$ – Sebastián Mestre Jan 5 '18 at 0:47
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Many procedural texture generation algorithms can be generalized to be n-dimensional. And even if a given algorithm cannot be generalized, the concept that the texture is based on most likely can be, so a new algorithm can be devised for higher dimensions.

Usually, the procedure for generating, let's say, 2d musgrave noise is not much different from the one used to generate 3d Musgrave noise, which is not much different from one used to hypothetically generate 4d musgrave noise, or 5d, and so on...

Also, almost always a high-dimensional texture generation algorithm can be generalized for lower dimensions by discarding high dimensional information. For instance : if you generate perlin noise in a volume (as in 3d noise) and take only a slice out of it, discarding the rest, then you've effectively generated perlin noise on a plane (as in 2d noise), this is most likely what blender does. (in reality most procedural textures are generated per-sample-point so this procedure doesn't really play out as described, you just don't generate samples in the whole volume, just ones that lay on the plane that you are interested in)

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