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Can Cycles be coaxed to cast more rays in pixels containing a large gradient/discontinuity in depth (or high contrast in brightness)?

My scene is fairly simple (effectively an image mapped to a sphere as an emisive material). Rendering with a small number of samples (eg 5) produces good results for the surface, however the edge of the sphere is jagged/noisy. Increasing the the sample count to 30 cleans up the edge but greatly increases the render time.

Cycles is a requirement since I need equirectangular rendered images.

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What you are referring to is a strategy called Adaptive Sampling, which, unfortunately, cycles doesn't support yet.

To clean up the noise for this, I would recommend using the Branched Path Tracing integrator. This allows you to use different sample counts for different ray types!

It is likely that the noise is caused by only one or two of the ray types, or "passes" in Cycles. To find out which one(s) are causing the most noise, enable all the pass options in the Scene Properties tab and within the compositor, view the passes of the render output node individually.

Then, you can increase the samples for that specific pass using the corresponding "ray type" in the Branched Path Traceing sampling settings. This allows to increase the samples for a problematic element of the render while keep the samples the same for the rest.

Hope this helps! If you have further questions or need clarification, feel free to ask

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