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In the Freestyle render settings under the Freestyle Line Style rollout there are a group of settings having to do with chaining.

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I have played around with these settings in a number of ways and haven't really found any noticeable impact on the render. So what is chaining and what does it do?

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Consider the lines as "a whole" or "individually"

As reported in the manual, "chaining" is a parameter that controls the way in which lines are rendered.

If enabled, Blender will draw each line as if it was connected with the previous; on the other way, if disables, it will render each line separately.

You can see the effect by increasing line thickness and zoom in till you can see where one line ends and another starts:

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While the same object with chaining enabled is:

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It is useful to make custom line styles. Notice in the examples below how the same thickness modifier brings to different results:

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