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Different internal formats in the mipmap levels of one texture?

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I'm just creating some kind of HDRL-Engine. For that, I'm rendering the image to a texture. I need the mipmap levels up to level 3 colored to create a blurr effect to make bright parts of the image glowing. All the levels up to the maximum level are just needed to determine the average luminance of an image, so it would be great if I'd just have the luminance information to save bandwidth. Can I store mipmap levels with different internal formats in one texture or am I forced to use 2 textures? Thx in advance, -mainframe-

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Zedzeek is correct. Section 3.8.10 in the 2.0 specification lists a few points about texture completeness, and this is the first point.
Quote:

The set of mipmap arrays [...] were each specified with the same internal format.

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