Sampling on the texel centers doesn't give proper results, OpenGL, C++

Question

Not so long ago I had a problem with displaying a texture as I was using edges of texels as texture coordinates instead of centers of texels. This, in combination with linear blending gave a smooth result of colors instead of pure colors given by a texture.

Thanks to advices given me here, I thought my problem is solved as I started to use centers of texels as coordinates, but it only worked in one case and I have no idea why only in that one case.

Again I'll show some pictures.

This is a texture I'm using (32x32 pixels) with border of 2 pixels:

My whole object that is being drawn consists of 9 quads, but they use only one texture (the one I showed). One of them will serve as an explanation to my problem:

I think it is well visible that colors of that quad aren't properly set according to the texture.

It looks like a problem with blending, but for setting texture coordinates I have used texels' centers, like this:

glBegin(GL_QUADS);
    // Bottom left
    glTexCoord2f(0.0 + texelCentersOffset, maxTexCoordBorderY + texelCentersOffset);
    glVertex2i(pos.x, pos.y + height - m_borderWidth);

    // Top left
    glTexCoord2f(0.0 + texelCentersOffset, (GLfloat)1.0 - maxTexCoordBorderY - texelCentersOffset);
    glVertex2i(pos.x, pos.y + m_borderWidth);

    // Top right
    glTexCoord2f(maxTexCoordBorderX - texelCentersOffset, (GLfloat)1.0 - maxTexCoordBorderY - texelCentersOffset);  
    glVertex2i(pos.x + m_borderWidth, pos.y + m_borderWidth);

    // Bottom right
    glTexCoord2f(maxTexCoordBorderX - texelCentersOffset, maxTexCoordBorderY + texelCentersOffset);
    glVertex2i(pos.x + m_borderWidth, pos.y + height - m_borderWidth);
glEnd();

For clarification:

m_borderWidth = 2

maxTexCoordBorderX = maxTexCoordBorderY = 2/32 = 0.0625

texelCentersOffset = 1/64 = 0.015625

Could anyone tell me what is wrong in what I've wrote?

EDIT1:

Here are settings for my texture:

glTexParameterf( GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER,
                 GL_LINEAR_MIPMAP_NEAREST );
glTexParameterf( GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR );

glTexParameterf( GL_TEXTURE_2D, GL_TEXTURE_WRAP_S,
                    GL_REPEAT );
glTexParameterf( GL_TEXTURE_2D, GL_TEXTURE_WRAP_T,
                    GL_REPEAT );
gluBuild2DMipmaps( GL_TEXTURE_2D, 4, m_width, m_height,
                   GL_RGBA, GL_UNSIGNED_BYTE, pixmap );

When I change from GL_LINEAR to GL_NEAREST, it works properly so it's obviously a problem with blending, but still can't figure out why it is wrong.

EDIT2:

When I increase height of quad to be the same as or larger than texture's height, it works correctly without changing any texture coordinates.

Answer 1

It seems to me, that when you set the quad size less than the texture's size. It must sample the texture using a mipmap.

Mipmaps are made by averaging 4 texel blocks. So, when you sample the mipmap you get information from more than one texel. So, by having your quad be smaller than the texture it has to sample a mipmap and you're getting texture bleed. Turn off the mipmapping and my guess is it will go away.