I had previously asked this for 3D but now I changed my strategy and would like to do the intersection in 2D.

The Rectangle is axis aligned and will always be in a fixed position, and has a constant shape and size, basically I want to clip the red areas of the triangles that extend outside the bounds of the rectangle The triangles could be in any position, shape or size, I my code I have a loop where I check the triangles one by one however I am still clueless about the math.

I have identified 5 cases of triangle rectangle intersection as shown here.

How do I find the intersection points of the triangle and the rectangle?