What's the most efficient way to detect triangle-triangle intersections?

Question

How can I tell whether two triangles intersect in 2D Euclidean space? (i.e. classic 2D geometry) given the (X,Y) coordinates of each vertex in each triangle.

Answer 1

One way is to check if two sides of triangle A intersect with any side of triangle B, and then check all six possibilities of a point of A inside B or a point of B inside A.

For a point inside a triangle see for example: Point in triangle test.

When we test collisions on polygons we also have a surrounding rectangle for our polygons. So we first test for rectangle collisions and if there is a hit we proceed with polygon collision detection.