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I have a weird problem in Blender where it seems that my faces and normals point in opposite directions. I have backface culling on in these shots.

Here's what a selection is supposed to look like. The normals and faces point in the correct direction, both facing outwards, with the selection on the outside: enter image description here

Here's the odd geometry: enter image description here

On the left, the faces point inwards, and the normals face outwards. But the selection is on the outside. (I flipped the normals in this case)

On the right, the faces point outwards, and the normals face inwards, as they should, but the selection is on the inside. (The normals are unflipped in this case)

It seems as if the normals and faces are pointing in opposite directions, because the selection is incorrect. What's happening here?

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I think you're misinterpreting what you're seeing.

I don't see any normals displayed in any of the images you've uploaded. When normals are displayed, they look like this:

enter image description here

I might be misunderstanding you. If so, please clarify.

I suspect that the normals are pointing exactly the direction you expect them to point (away from the visible side of the face). If you just Recalculate Normals -> Outside, it should correct the problem.

If that doesn't work, you should check for non-manifold geometry.

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First:

In blender, you cannot select the inside or the ourside of a face, you can only select a face as a whole.

Second:

May it be that you think that the 3D manipulator shows the normal of the face, however it does not?

You can set the 3D manipulator to be aligned to the normal of the currently selected face. In that case, the blue axis will be the normal.

Set it up like in this image at the bottom of the 3D view:

Image

It is however mouch more convenient to turn on normals display as Matt showed.

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