How to check if line segment intersects a rectangle?

Question

If you have 2 points, (x1, y1) and (x2, y2), which represent two opposite corners of a rectangle, and 2 other points, (x3,y3) and (x4,y4), which represent 2 endpoints of a

Answer 1

Get the dot product of all 4 vertices (the corners of the rectangle) with the direction vector of the line segment. If all 4 have values of the same sign, then all the vertices lie on the same side of the line (not the line segment, but the infinite line) and thus the line does not intersect the rectangle. This approach is only viable for 2D intersection detection. This can be used to filter through most of them quickly (using only multiplications and additions). You'll have to do further checks for line segments instead of lines.