How do I test for collision of two moving 2d oriented bounding boxes?

Question

The OBBs have a position(x,y), a velocity(x,y) and an orientation(Matrix). Given periodic updates, the OBBs must collide with each other, returning the fraction of the move tha

Answer 1

If you have two bounding boxes (i.e. rectangles) with some arbitrary orientation (which I assume means some "rotation"), then I would do the following:

• Starting at an initial position (where I assume the bounding boxes are not intersecting), translate each box forward based on its velocity (however you're applying movements over time).
• Find the coordinates of the corners of each translated bounding box. These 4 coordinates define the endpoints of the 4 line segments that make up the edges of the bounding box.
• For bounding box #1, test for an intersection between each of its line segments and the 4 line segments of bounding box #2. You can do this using standard equations for computing the intersection point of two lines, as discussed here, for example.
• If there was an intersection, figure out the fraction of a move that was successful using the coordinates of the intersection points and the known translation you applied.
• Repeat the above steps for each update.

EDIT: A rough pseudocode (incorporating what was discussed in the comments) would look as follows:

...test for intersections between the OBB edges...
if any intersections are found{
    ...run code for when OBBs are partially overlapping...
}else{
    P = line segment whose endpoints are the OBB centers;
    ...test for intersections between P and OBB edges...
    if P intersects edges of both OBBs{
        ...run code for when OBBs are not touching...
    }else{
        ...run code for when one OBB is completely inside the other...
    }
}