Question

What is the most efficient way to find out if one axis aligned rectangle is colliding with one rotated rectangle? Each class has a position vector and a size vector and the rotated class has an angle value.

Answer 1

You want to use the Separating Axis Theorem (SAT). Normally it’s used in 3d, but it collapses to 2d quite well. Since you’ve got a special case, the only axis you need to consider are 4 main axis of your rectangles:

[ 1,0 ]
[ 0,1 ]
[ sin(theta), cos(theta) ]
[ -cos(theta), sin(theta) ]

To check an axis, compute the dot product of every vertex with that axis. Then check the min and max of the 2 sets of values to see if they overlap. If any of the 4 axis gives ranges that don’t overlap then the rectangles do not overlap (you’ve found a separating axis). If all 4 axis show overlap then the rectangles intersect.

Here is a recent SO question on the same problem:
Separating Axis Theorem and Python

And here is the wikipedia article

http://en.wikipedia.org/wiki/Separating_axis_theorem