What are the reasons why automatic normal recalculation might fail

Question

I see this question pop up repeatedly, and people trying to remedy it without discussing and understanding why it happens in the first place. If ctrl+N doesn't work as hoped, what are the possible causes? Are there quick ways to highlight problem areas?

(This question is intended to provoke a canonical set of answers - or community wiki)

On the fence as far as opinion based for some people probably, but I think this could be helpful. — J Sargent, May 29 '15 at 11:16
i don't think the answers to this are opinion based, they will all be testable. — zeffii, May 29 '15 at 11:24
As long as people do not post theoretical answers, then yes. — J Sargent, May 29 '15 at 14:18
internal faces will usually make it seem as if the calculation has failed. — MarcClintDion, May 29 '15 at 19:03
I hope to give a comprehensive answer in a couple of days if no-one else takes a bite. @MarcClintDion you rightly add 'seems to' fail.. — zeffii, May 29 '15 at 19:13
the calculation can fail for models that loop around through themselves like some of the Klein bottles on the following page. http://blender.stackexchange.com/questions/18955/modelling-a-klein-bottle — MarcClintDion, May 30 '15 at 20:55
AFAIK Any mesh which doesn't have a defined inside or outside. So non-manifolds and manifolds with intersecting geometry. — gandalf3, Jul 23 '15 at 06:37

score 1 · Accepted Answer · answered Jul 23 '15 at 06:07

I had a series of models in a Blender file where the Mesh Normals were pointed both inward and outward. Pressing Recalculate Normals fixed a few of the 15000 faces but not all. Trying to select inward faces failed, nothing lit up after trying to select them. I found that the recalc would fail if the model had doubles or had Non Manifold mesh. Deleting the doubles and removing the non manifold meshes was the answer. Once gone, the Recalculate repaired all the inward facing faces.

What are the reasons why automatic normal recalculation might fail

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