How to determine the intersection of a segment and a polygon?

Question

Bots

Please advise a fast algorithm for finding the fact of intersection of a segment defined by 2 points and a polygon (rotated rectangle). Intersection coordinates are not needed.
clarification:
In fact, the task is to filter out segments that do not fall on the monitor screen. The layer on which the segments lie can be rotated. The segments' coordinates are given in the coordinate system of the rotated layer.

Answer 1

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Answer 4

It seems to me that you need to switch to the coordinate system of the rectangle, and then just study the special cases of finding a segment outside and in the rectangle

Answer 5

First, it is better to switch to a coordinate system in which the sides of the rectangle are parallel to the coordinate axes, and the center is at the point (0,0): let the transformation (x,y) -> (p*x+q*y+r,-q* x+p*y+s) the rectangle goes to abs(X) <= A, abs(Y) <= B.
Let (X1,Y1) and (X2,Y2) be the coordinates of the segment vertices after the transformation.
If max(X1,X2) < -A || min(X1,X2) > A || max(Y1,Y2) < -B || min(Y1,Y2) > B, then it does not intersect: the segment is behind one of the sides of the rectangle.
Otherwise, the intersection condition, as far as I understand, will be
abs(X1*Y2-Y1*X2) <= abs(A*(Y2-Y1)) + abs(B*(X2-X1))
Didn't check carefully, but chances are that the formula is correct, good.