Is it just me or is separating-axis-theorem-based polygon intersection way more straightforward if, for each edge, you just use the edge equation to check whether all points of the other polygon are on the same side of that edge?
It was a lot easier for me to understand starting with S-H as opposed to the other way around. I wish tutorials taught S-H first.
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*puts on maths hat* The whole "Separating Axis Theorem" thing is a super-unfortunate Computer Graphics idiosyncracy (like the infestation with row vectors that originated in Utah in the 70s). The axis is the wrong thing to look at; it's the dual of the thing that makes sense.
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The actual theorem in convex geometry is the Separating *Hyperplane* Theorem (and its generalizations such as the Hahn-Banach theorem). In 2D, it states (slightly simplified) that two convex objects are non-overlapping if and only if you can draw a line between them.
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