I have some difficulties to understand how to be sure if there is a collision between a space ship (black) and an asteroid (in blue). A space ship is placed on a case and an asteroid comes from the right, like on the image.
Also Y1 != Y2, there are not exactly on the same line. What is the best way, in that case, to detect if there is a collision ? Is AABB collision the correct algorith I need ?
I think either AABB collision test or circle-circle is sufficient for your needs. Usually it is not necessary to have perfect pixel level precision in determining whether 2 objects hit.
For circle-circle, have all your objects have a center x,y and a radius r; to determine whether 2 circles overlap: test (obj1.x-obj2.x)^2 + (obj1.y-obj2.y)^2 > (obj1.r + obj2.r)^2
For box, have all your objects have x,y, width and height, and check whether the box overlap in x axis and y axis.
Edit: In case that you really really want to use triangle - polygon level of precision, you need to first implement/find a intersection test for lineSegment vs lineSegment. Then for the intersection test between 2 polygons, test whether any combination of their edges intersects OR whether one object fully contains the other (point in shape test).
To complete @user55564 I give some more information about line segments intersection.
In general you can check if any Intersection exist between your two polygon (even non-convex) as what I've described Here.
