How to use OpenGL LOD in Texturing?

How do GL_TEXTURE_MIN_LOD, GL_TEXTURE_MAX_LOD and LOD_BIAS work?

To check it visually, i have created 6*6 texture with mipmapping and for values > 0.5 for MIN_LOD I get a 3*3 texture irrespective of values for MAX_LOD. If I change LOD_BIAS it does not affect my o/p. I am not able to figure out how it works exactly.

Can anyone explain it by stating an example?

Edit: I am creating mipmap levels manually so that I can observe which level it is picking up. Here is my code:

glTexImage2D(target, 0, GL_RGBA,9 ,9, 0, GL_RGBA, GL_BYTE,subpix);
glTexImage2D(target, 1, GL_RGBA,4 ,4, 0, GL_RGBA, GL_BYTE,&subpix[4]);
glTexImage2D(target, 2, GL_RGBA,2 ,2, 0, GL_RGBA, GL_BYTE,&subpix[10]);
glTexImage2D(target, 3, GL_RGBA,1 ,1, 0, GL_RGBA, GL_BYTE,&subpix[18]);
glSamplerParameterf(sampler,GL_TEXTURE_MIN_LOD,0.862);
glSamplerParameterf(sampler,GL_TEXTURE_MAX_LOD,0.99);
glSamplerParameterf(sampler,GL_TEXTURE_LOD_BIAS,0.0);

In this case I am expecting it would take 2nd mipmap level which is of 2*2 but It chooses 1st mipmap level of 4*4. When I set min lod < 0.5, It takes 0th level of 9*9. And it this happens irrespective of the value set to max lod.

Solution

First some references:

TEXTURE_MIN_LOD Sets the minimum level-of-detail parameter. This floating-point value limits the selection of highest resolution mipmap (lowest mipmap level). The initial value is -1000.

TEXTURE_LOD_BIAS specifies a fixed bias value that is to be added to the level-of-detail parameter for the texture before texture sampling. The specified value is added to the shader-supplied bias value (if any) and subsequently clamped into the implementation-defined range - bias max bias max , where bias max is the value of the implementation defined constant GL_MAX_TEXTURE_LOD_BIAS. The initial value is 0.0

So if you are surprised by the mipmap selection, I suggest following steps (not necessarily in order):

Create mipmaps by hand so that they are visually distinctive from each other
Verify your mipmaps are supplied correctly.
Verify that your LOD_BIAS setting doesn't just put all of the values outside the range, making the sampler effectively always use the maximum or minimum LOD.

Searching around this, I've found textureQueryLod. It might also be of some interest to you to aid debugging.