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Inspecting pixels used on a facet

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This is more of a math question than a scripting question (unless there is a builtin method to do this) but I don't seem to know enough about the topic to create a useful search query...

I would like to inspect a facet to determine if the relevant portion of an image map applied to it is all black (0, 0, 0).

I can find the corner pixels on the image, but I'm not sure how to generate a list of all pixels contained within the polygon from that.

Is it necessary to go the other direction, and check each pixel between (min x, min y) and (max x, max y) to see if it is within the polygon?

 

Can anyone point me in the right direction?


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