I have 3 perpendicular 3D unit vectors. Imagining them rotate around a Point in space, I can see how they could represent an object's orientation. However, I have no idea how to convert those vectors into Euler angles (or a rotation matrix, quaternion, etc.). Thinking about it, I don't think you need 3 vectors to describe every possible orientation. As long as there is a forward and an upward directional vector, there should be no confusion about how the object would be oriented.

Anyone have an idea on how to calculate an orientation from two (or three) perpendicular vectors?