Check if a ray has hit a corner

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I'm trying to find an algorithm to detect if a ray (line) is intersecting a corner can pass by it or is blocked.

On this paper, it states that the separating axis theorem can be applied to find it could, but after reading it I'm still very confused on how it can be done.

Example

The examples with orange lines show how a line could go past a corner, and the first picture illustrates how the ray wouldn't be able to.