Mipmapping a single level

OpenGL OpenGL: Basic Coding
1

Quick question, is there a way you can mipmap a single level, for example instead of generating 5 mipmaps for a texture, that you would generate only one but at a certain level, ie. texture is 512x512, but you only generate on for 32x32, instead of generating all 256x256, 128x128…etc

Thanks

2

Is there a good reason why you’d want to do that?

3

I guess the only reason would be memory efficiency …

4

I have seen another reason, cheap pseudo depth of field effects.

5

maybe texture lod bias

6

If you generate the mipmaps yourself, you could generate the 32x32 and then scale it up to 64x64 and 128x128 with a simple 1texel --> 2x2 --> 4x4 area?

7

according to the opengl standard you either must generate no mipmaps or all down to 1x1.
everything else may cause ‘undefined beahvior’ (;