A new method called PCS (parameterized cuboid structure) is presented for augmented reality. In particular, our method can insert animated virtual objects into a static scene, with geometric consistency, and also allow the user to interactively position and rotate the virtual objects with respect to a world coordinate system in a physically (or intuitively) meaningful way. Such capability cannot be achieved by using the existing calibration-free methods. To achieve this goal, we develop a new method for estimating camera parameters, which uses a cuboid structure (or more generally, a parallelepiped structure) as the reference object. The reference cuboid structure can be either explicit or implicit-implicit in the sense that the cuboid structure can be inferred by human perception even though it does not appear explicitly in the image. This method can determine the sizes of the cuboid (or parallelepiped) as well as the intrinsic and extrinsic parameters of the camera. To insert a virtual object into a single uncalibrated image, some human interaction is unavoidable. We have implemented an AR authoring system based on the proposed PCS method which provides an auxiliary line and a refinement criterion to assist human interaction. Experimental results have demonstrated that our method can successfully insert virtual objects into both static and dynamic scenes with highly convincing geometric consistency.