SAT Collision detection - Corners fix

Question

I'm building a game and I'm currently working on the physics.

I'm using the SAT algorithm to detect collisions. The collisions are between the character (AxisAlignedBoundingBox) and some rectangles (with rotation).

Everything works fine, except the collision near to a corner in specific situations. (This is a pretty known problem but I didn't find any good solutions).

On Example 1, in the second scene the character should move upwards (stay on the obstacle).
It happens to move left.
On Example 2, in the second scene the character should not get up. Sometimes it gets.

I know why this is happening, because of dx and dy, the Minimum Translation Vector isn't always the wanted one.

There are several solutions to this problem, but not a really good one (in terms of solving the problem and not creating others!). I'm willing to even use a totally different algorithm from the beginning.

Please give me a hint about an algorithm better than the SAT, or some workaround.
THANK YOU!

Answer 1

A picture is worth many words.

The image has two boxes to test the red and the black..

Note how the center of the black box is always on the darker red box when it is just touching.

You can simplify any AABB test by increasing the size of one box by the size of the other. As long as you referance the boxes position by their centers all works well.

// x,y are box centers
var bBox = { w : 100 , h : 50, x : ?, y ? };  // black
var rBox = { w : 200 , h : 200, x : ?, y ? };  // red

to test if bBox is inside rBox

if(bBox.x > rBox.x - (rBox.w + bBox.w)/2 &&
     bBox.x < rBox.x + (rBox.w + bBox.w)/2 &&
     bBox.y > rBox.y - (rBox.h + bBox.h)/2 &&
     bBox.y < rBox.y + (rBox.h + bBox.h)/2)
    // boxes are touching.
}

Also works if boxes are moving. You just test if the vector of bBox movement intersects any of rBox's 4 sides.