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copied!<p>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:</p> <ul> <li>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).</li> <li>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.</li> <li>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 <a href="http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline2d/" rel="nofollow noreferrer">here</a>, for example.</li> <li>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.</li> <li>Repeat the above steps for each update.</li> </ul> <p><strong>EDIT:</strong> A rough pseudocode (incorporating what was discussed in the comments) would look as follows:</p> <pre><code>...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... } } </code></pre>

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