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What is causing this strange shading when adding bump/normal maps? This happens in the viewport and the final render.

See image below were the sun transitions into shadow. It should be more smooth.

Blender v2.79
Cycles
HDRI lighting

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Bump map close-up: enter image description here

Also, it seems that adding subdivions increases quality but at a great cost of performance.

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Given the image, and the fact that subdivisions help, I'm inclined to say that it's a terminator problem. Sadly, it's a common problem on most ray/pathtracers, so your solutions are:

  • Increase subdivisions.
  • Increase light sizes. This will make shadows softer, and will mask the problem a bit.
  • Use a non-tracer renderer (like Blender Internal or, maybe Eevee), that doesn't have this problem.
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