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I made the camera position 10 units from an object, but not behind it. I dont want the camera position behind the object right away when it rotates, I want that when I will rotate the object, the camera position will move slowly until it will be behind the object.
Check out the Camera Sample in XNA App Hub: http://create.msdn.com/en-US/education/catalog/sample/chasecamera
It basically does what you describe: it’s a chase camera that lags behind the object and follows it using a “spring like” behavior.
From the overview: “The motion of both the ship and the camera are governed by simple physics. When the ship speeds away, the camera pulls back. When the ship turns, the camera lags behind in the turn to show a partial profile view of the ship. When the ship stops moving, the camera gradually slides back into place”