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OpenGL Cubemap filtering via GLSL

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I am trying to wrap my head around IBL and I am currently looking at the UE4 approach . I think I understood the concept behind, but I am still a bit dubious on a simple implementation detail due to my inexperience with OpenGL or similar. 


I need to filter a cubemap on various mip levels and I wanted to try it in shader, but is at this point that my doubts come in. How can I approach this? 


My googling led me to a way to create a cubemap FBO, but the only thing I can think of is  process each face singularly using quads as geometry and outputting to the right cubemap face. Is there any way to make this more clever, directly outputting to the final cubemap in one go?  I don't have a scene to render in it, just "copy" and filter an existing cubemap.



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