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The nature of hair or fur is that it is made up of a lot of very fine/thin strands. Typically the smaller something is in screen space, the more Anti-Aliasing Camera (AA) samples is are required to render it smooth and without flickering in animation, which makes rendering hair challenginga challenge. To make fur rendering easier on the sampling Arnold has introduced something called "Min Pixel Width" (MPW).

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Min Pixel Width is also applied to the points primitive. But a motion-blurred radius will disable its effect.

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Optimization

Making the hairs hair transparent has a big impact on render times. For optimal rendering speed, it is very important to use sensible values. How smooth/slow hair renders depends on three things:

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