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Looking at the result of point and line under a magnifying glass, I realized that my assumption that there was a 1 to 1 correspondence between processing pixels and my monitor's pixels was naive.
I was surprised by a few things:
When I try to draw a line using a series of point calls, it looks very different than when I use line and neither one always does what I expected. (For example, drawing a simple line segment will look one way in isolation and then the entire line will look different if its drawn so that one of it's ends is adjacent to a different line.)
Can anyone point me to a source where I can learn what's happening on the pixel level with these functions.