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On what criteria will this function adapt its number of samples?... Is there a particular situation where you could take advantage of this option ? I usualy set up the min and max sampling value without knowing their coherence.

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With adaptive sampling Cycles automatically reduces the number of samples in areas that have little noise, for faster rendering and more even noise distribution.

More info here: https://docs.blender.org/manual/en/latest/render/cycles/render_settings/sampling.html

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When you render you can see the pixels being updated with new sample information according to the integration method used by the renderer.

With adaptive sampling on, every other sample is integrated just like that into a separate image buffer. Every pixel is compared to the corresponding pixel for the final image. When the difference between these pixels is less than your designated threshold that pixel is considered "done" and is skipped for any subsequent samples.

Unless of course you haven't hit the minimum number of samples, which you can also set.

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